id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_arithmetic_matrix_svd_level_7_7_900
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[15, -17, -12, 21, -19, 18, 14, 19, -5, -7, -9, 7],\n [-4, 1, 14, -17, 25, 16, -4, -17, 24, -26, 2, 19],\n [14, -22, 17, 2, 25, 23, 22, -7, -19, -2, -26, 9],\n [17, -11, -22, 23, 23, 24, -14, -26, -19, -26, -7, 12],\n [24, -2, 2, -24, 26, 2, -9, 26, -9, -3, 26, -21],\n [1, 25, -13, -1, -20, -16, -6, -22, 4, 18, 18, 0],\n [6, 7, 23, 9, 19, -22, -1, 21, 25, 8, -7, -13],\n [-22, -15, -14, 21, 0, 0, -11, 24, -23, -14, -9, 18],\n [-15, -8, -10, 15, -20, -6, 19, 12, 26, -26, -13, -24],\n [5, -18, -16, -4, 3, 20, -22, 3, 24, -1, -23, 25],\n [0, 2, 18, 11, -20, -11, -19, -2, -3, 14, 14, 24],\n [24, -6, 16, -11, 14, 20, -16, -19, 8, 19, -21, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
582
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_901
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-16, 1, 15, 25, -16, -21, 13, 3, -13, -14, 8, -21],\n [22, 6, -16, -26, 0, 3, 19, -1, 1, 14, 5, -17],\n [-15, 26, 9, 23, 16, -5, -11, -9, -20, 25, 9, -25],\n [-18, 17, 3, 1, 2, -8, 1, 14, -2, 2, -4, -17],\n [14, -22, 26, 6, 21, 14, -22, -23, 10, -23, -2, 5],\n [-13, 0, -1, -19, 3, -14, 5, 26, 16, 26, 26, 2],\n [-4, 1, -13, -17, -20, 24, 22, -1, 9, 25, 0, 1],\n [19, 3, 17, 16, -3, -26, 14, 0, -26, -17, 16, -22],\n [-18, -24, 2, -25, -9, -13, 2, -22, 19, -22, -25, 12],\n [-4, 4, 23, -11, -5, 0, 2, -22, 25, -15, -14, -19],\n [19, -3, 1, 10, 0, 9, -18, -12, 19, -22, 1, -12],\n [9, -9, -5, -22, -5, -10, -5, -6, 19, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
99
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_902
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -8, -14, 18, 18, 7, 20, 6, 20, -11, 16, 3],\n [-24, 0, -7, 5, -6, 19, 26, -22, 22, -25, -5, -20],\n [15, -17, 25, 13, -26, -11, 14, 1, 21, -7, -1, -12],\n [14, 3, -15, -25, -17, 0, -6, -11, 10, 18, -5, 12],\n [14, -5, 22, -10, -10, -1, 10, 11, 11, 14, 15, 22],\n [-24, 25, -18, -26, -8, -13, 13, 23, 11, -25, -20, 11],\n [16, 1, -17, -2, -5, -16, 13, 18, 11, -17, -9, 20],\n [-22, -16, 0, 26, 0, 9, -14, 20, 1, -25, -20, 5],\n [-21, -8, -12, -4, -3, 19, 21, 25, 1, -3, 26, -5],\n [15, -21, 20, -23, 7, 24, 12, 0, 16, -5, 20, -11],\n [5, -22, 14, 6, 18, 8, -22, -4, 19, 10, 5, 25],\n [-13, 26, 6, 16, -22, 8, 15, 14, 20, 11, -5, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
557
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_903
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[13, 7, -23, -25, -18, 3, 10, -8, 24, -18, -22, -11],\n [-1, -20, -25, -13, 4, -5, 6, 13, 22, 4, -8, -21],\n [19, 13, 16, 19, -17, 22, -15, -1, -23, 24, 22, -22],\n [3, -3, 19, 12, 8, -22, -22, -19, 8, -26, -25, -20],\n [-12, -13, -14, 17, 2, 23, -25, -20, -17, -7, -2, -1],\n [15, -21, -23, -19, -14, 10, -19, 13, 2, 0, -18, -13],\n [-16, -2, -4, -17, -20, -14, -5, 14, 13, 22, 19, -9],\n [-18, -5, 26, 20, 21, 25, -18, 15, -13, -15, 13, -10],\n [-10, 24, -3, 23, -14, 22, 9, -9, 26, 3, 15, 15],\n [10, -26, -13, -17, -22, -5, 14, 2, 22, 24, 5, 4],\n [10, 6, 3, 12, 6, -17, 8, 22, 1, 15, -18, 14],\n [-16, 18, 0, 5, 14, -6, -15, -20, -5, 5, -24, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
105
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_904
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-14, -5, 15, 11, 26, 1, 25, -22, 3, 5, 18, -7],\n [-7, 14, -18, -20, -20, -1, 6, 23, 4, 17, -13, 20],\n [8, 3, 8, -8, -18, -9, -26, -10, -5, -15, -9, -25],\n [-3, 12, -23, -4, -23, -6, 0, -16, -3, 0, 9, 0],\n [1, 20, 7, -25, 14, -1, 18, -12, -3, -8, -20, -10],\n [21, -23, 9, 13, 3, 25, 16, 14, -13, 15, 21, 19],\n [26, -7, 2, 15, 26, -1, -8, -19, 11, -7, -26, -11],\n [-26, 8, -19, -19, -25, 1, 4, 17, -11, -16, 22, -13],\n [10, 6, -19, 14, 7, -14, 16, -11, 9, 12, -6, -10],\n [12, 26, 7, -9, 14, 14, 16, 9, 9, -22, 1, 22],\n [-22, -23, -24, 6, 25, -24, -19, -4, -21, 0, -5, 7],\n [-26, 25, 9, 0, -18, 17, 24, -2, -13, -9, 22, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
96
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_905
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[22, 0, -18, -15, 24, 20, -9, 22, -13, -17, -7, -5],\n [7, 21, 11, -22, 3, -26, -1, -20, -20, 18, -22, -7],\n [23, 1, -4, -19, 20, -11, 14, 21, -21, -16, -14, -25],\n [22, -25, -14, -8, 6, 10, -2, 21, 11, 19, 13, -9],\n [2, 10, -16, 18, 14, 20, 18, -4, -4, 8, -24, 20],\n [-9, 25, -18, 21, -7, -3, -10, 18, -15, 6, -21, 3],\n [-21, 21, -4, 19, -20, -1, -24, -2, -24, -12, 12, -23],\n [11, 18, -6, 3, -20, -14, 23, 16, -20, -4, 17, -20],\n [-17, -13, -22, -8, 10, 6, 26, -13, -24, -20, 3, 0],\n [9, 11, -16, 16, 9, -11, -10, -8, 8, 11, 21, 18],\n [-25, 12, 0, 24, -26, -25, 26, 22, 25, -12, -26, -21],\n [3, 17, 0, -10, 13, -3, 23, 24, -5, -12, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
94
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_906
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[0, -11, 20, -13, -23, 25, -3, -14, -22, 13, 6, 18],\n [10, -19, 12, -8, -17, 15, 12, -8, 4, -13, -2, -19],\n [-23, 20, -22, 9, 17, -21, 3, 13, 11, 10, 14, -8],\n [15, 16, -9, -6, 10, 16, -10, 4, -6, -16, -11, -18],\n [24, -4, 12, -4, 25, -24, 22, -21, -7, -12, 19, 3],\n [5, -21, 4, -11, 2, -5, 13, 1, -12, -6, -19, -26],\n [3, -25, -3, 22, -22, -15, -22, 7, -13, -15, 0, -25],\n [22, 9, 18, 11, -24, 9, -19, -25, 14, 15, 2, 18],\n [-2, 22, -23, -17, 17, -10, -26, -24, 11, 3, -22, 17],\n [-16, 26, -18, 20, -13, -8, -14, -6, 12, 16, -25, 3],\n [-4, 0, -26, -20, -25, -4, 4, 24, 2, -13, 16, -22],\n [-16, 19, 14, 6, 2, -21, -20, 18, -17, -7, -18, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
96
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_907
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, 19, -21, -26, -16, 16, -10, 12, -18, -11, 26, 0],\n [14, -22, 11, -19, -18, -14, -24, 0, 23, 10, -7, 6],\n [-14, 25, -3, 23, 15, -3, -7, 0, -9, 1, 9, 6],\n [5, -20, -12, -13, 8, 25, 24, 13, 4, 24, 23, 4],\n [-1, -2, 19, -21, 24, 0, 5, -15, 20, 3, -3, -3],\n [-5, -23, -8, -2, -22, -23, 2, -18, 24, 11, 13, 26],\n [7, -19, -16, 7, 19, 5, 5, 22, -22, 5, -22, 5],\n [-26, -21, 12, -2, 0, 19, -13, 21, -18, 1, 23, -3],\n [-18, 9, 12, 10, 22, 15, 7, -24, -6, 12, 10, 15],\n [9, -25, -10, 24, 14, 2, -2, -6, -8, 2, -24, 12],\n [-15, 17, 24, -1, 12, 4, -19, 8, -22, 0, -1, 0],\n [-14, -4, -26, 23, 1, -12, -14, 13, -22, 12, -1, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_908
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, 8, 22, -5, 26, -18, -26, -12, 26, 3, -24, -21],\n [4, -22, -23, -2, -16, 16, -13, -2, 22, 25, 0, 2],\n [25, 14, -26, 19, -22, -6, 13, 10, 7, -25, 18, 24],\n [-9, -12, 19, 6, 25, -16, 24, 2, 2, -19, -26, 3],\n [16, 26, -17, -21, 18, -26, -18, 23, 25, 16, -11, -24],\n [15, -25, -19, 3, -9, -24, -21, 18, 24, 19, -14, -12],\n [-5, -8, 23, 17, -19, -13, -4, -2, 6, -26, -26, -10],\n [26, -9, 25, -2, -12, 24, 0, 3, -18, -2, 7, 13],\n [13, 20, -16, -12, 24, 2, 3, -16, -26, -10, -16, 2],\n [19, -15, 3, 17, 0, 9, -12, -18, 4, -2, -12, 7],\n [-11, -4, 6, 2, 5, 5, -11, -12, -6, 1, -13, -6],\n [-3, 8, 11, 16, -20, 4, -5, -2, 19, 15, -23, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
549
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_909
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[9, -1, 2, 20, -21, -8, 23, -2, -17, 9, 21, 24],\n [16, -17, -11, -12, 22, 7, 19, 13, -12, -26, -21, 25],\n [-8, 16, -21, 24, -23, -17, 16, 13, -18, -26, 24, -10],\n [14, 1, 22, -15, 19, 14, 12, -11, -13, -21, 20, 3],\n [18, -1, -7, -22, -12, 4, -9, -14, 16, -16, 17, 24],\n [-15, 26, -8, -8, -26, -13, -10, -25, 12, 11, -6, -7],\n [25, -4, 3, -26, -21, -12, -10, 9, -1, -25, 21, 26],\n [18, -16, 16, 21, -17, -23, -8, -1, 12, -9, 17, -5],\n [15, 2, -12, 17, 6, 15, -16, -7, 0, 24, -12, -24],\n [-11, 1, 25, 26, 21, 15, -12, 13, -1, 7, 9, 0],\n [-13, 23, -24, -24, -4, -22, -25, 11, 9, -25, 24, -12],\n [-25, 9, 1, -13, -15, 3, 8, -19, 5, -7, 15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
97
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_910
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-12, -13, -1, -2, -8, -7, 24, -1, 5, -4, -13, -5],\n [3, 1, 11, 13, 3, 24, -24, 8, -23, 12, 7, 18],\n [-16, -14, -25, 9, 26, 3, -11, 5, -12, -4, 20, 8],\n [18, -10, -9, 5, -11, -26, -13, -25, -21, -1, 17, -19],\n [-3, 12, 23, 16, 4, -6, -7, -25, 16, 13, -7, 22],\n [-5, -14, -7, 17, 4, -4, -1, 16, 26, 3, 18, -18],\n [12, 15, 26, 5, 17, 13, -15, -15, 0, 19, -1, 16],\n [-13, -13, -16, 7, -19, 12, -12, -23, -26, 8, 26, -21],\n [24, -25, 20, -8, 4, 26, -8, -4, -18, -8, -14, -19],\n [1, 0, 26, 11, 15, -18, -12, 19, 7, -2, -26, -16],\n [-12, -1, 20, 11, 6, 22, 8, 19, 0, 25, -15, -7],\n [-15, 10, -21, -7, -4, -12, 1, 7, -19, -7, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
90
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_911
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[22, -9, -13, -7, 15, 18, 22, -26, -4, 13, -11, 18],\n [12, -8, -19, -3, 26, 17, -11, -14, 23, 3, -14, -6],\n [-8, 0, 11, 17, 11, 24, -4, -11, 19, -3, 17, 23],\n [-11, 22, -11, -16, -1, -11, 14, -12, -9, 13, -9, 8],\n [-22, -25, 3, 4, -2, 16, 4, -8, 7, -9, 12, 21],\n [6, 18, -24, -9, 9, 25, -1, 1, 5, 22, 10, -20],\n [1, 5, 14, 9, -5, -18, -10, -17, 0, -10, 5, 17],\n [15, -16, 18, -2, -10, 0, -12, -22, 16, -14, -21, 15],\n [-7, -24, 1, -24, 6, -25, 10, 2, -13, -20, 17, -23],\n [23, -6, -2, -18, -15, -15, -22, 2, 0, 12, 22, -7],\n [2, -8, 9, 6, -19, 3, 7, 4, -26, 8, -8, 19],\n [-9, 19, -10, 15, 4, -7, 2, 12, 16, -6, -18, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
80
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_912
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -9, 22, 26, 24, -17, -26, 1, 6, 12, -9, 16],\n [18, -18, 1, -4, -1, 22, 16, 6, -7, -11, -8, 5],\n [-16, 19, 17, 13, 20, -1, -26, 11, -15, -18, 23, -19],\n [4, -7, -8, 5, -22, 4, -5, -7, -15, -8, 10, -25],\n [-23, 3, -4, -6, -22, -20, -15, 14, -16, 19, -13, 12],\n [-24, -4, -24, 9, 12, -3, 14, 6, 5, 3, 9, -24],\n [-21, 5, -21, 16, -23, -23, -14, 22, 16, -24, 8, 17],\n [20, -11, -3, 13, -3, 19, -3, 11, -22, 25, -8, -20],\n [3, -2, -26, -25, -19, -23, 20, 5, 19, 11, 22, -21],\n [17, 22, 13, 6, 10, -17, -3, 9, -24, 20, 10, 0],\n [-3, -11, 20, 5, 26, -11, -18, -11, 23, -11, -23, 22],\n [-16, -3, 20, 4, 23, -3, -3, -3, 9, 5, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
537
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_913
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 12, -15, -10, 14, 15, -25, 12, 23, -21, 24, 4],\n [22, -2, 1, 18, -1, -23, 2, -12, 7, 6, -11, 13],\n [12, -22, 25, 7, -5, 10, -17, 4, -13, 7, 26, -8],\n [10, -6, 10, -3, 5, 3, 10, 11, -10, 19, 9, 4],\n [23, 23, 16, -10, -13, -21, 3, -8, 23, 0, 13, 10],\n [4, -11, -14, -12, -1, 2, -26, 6, 7, 24, 7, 21],\n [7, -6, -20, -26, -26, -9, 5, 4, -9, -11, -26, 17],\n [-16, 3, 14, 1, -1, -4, -17, -16, 18, 17, -21, 2],\n [-5, -13, -21, 17, 23, -7, -16, -25, 17, -2, -12, 11],\n [-22, -12, -1, -16, 20, 24, 6, 10, 9, 14, 11, -16],\n [8, -18, -16, 14, 6, 18, 6, 0, -9, -16, 20, 3],\n [-11, -3, -26, -16, -21, -15, -1, -8, -26, 26, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
511
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_914
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, -3, 5, 6, 12, -17, -5, 21, 20, 14, -13, -23],\n [2, -21, 20, 13, 15, 12, 22, -2, 18, -19, -16, -26],\n [-21, 11, 1, 5, -18, 7, 22, -25, -5, 12, -4, 24],\n [25, -24, 16, 18, -11, 14, 3, -8, 17, -1, -11, -5],\n [-21, 10, -22, 16, -13, -3, -13, -18, 13, -16, -17, 4],\n [24, -2, 26, -7, 4, -11, 10, -21, 16, -16, 21, 13],\n [-8, -26, 0, -6, 14, -13, -7, 8, 10, 4, -25, -9],\n [-6, -2, -14, 9, -10, 19, -15, 15, -5, -3, -12, -20],\n [-24, -7, 16, -1, 18, 1, 26, 8, 18, 13, -18, -20],\n [13, -13, -9, -17, 8, 21, -12, 18, -23, 21, 23, -8],\n [21, 1, 17, -4, -5, -5, 7, 13, -16, 17, 11, 21],\n [4, 0, -22, 15, 2, -22, -9, 2, -25, -13, -4, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
97
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_915
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 12, -19, -23, 10, 5, 22, 11, 2, 2, -26, -24],\n [15, 18, -8, -13, 5, -4, 16, -1, -9, 16, -12, -2],\n [9, 16, 11, -5, -9, -15, 0, 21, -7, -11, 23, 19],\n [22, -12, -17, 12, -22, 16, 26, 8, -10, 24, 14, 3],\n [-23, 20, 26, -5, 4, 2, 14, 26, -11, -2, -10, -9],\n [10, 10, 2, 14, 0, 4, -4, 15, -2, -5, -14, -10],\n [18, 12, 25, -24, -26, 15, 20, 18, -10, 2, -9, 15],\n [25, -18, -1, -3, 6, -15, 16, 16, -12, 25, -13, -18],\n [4, 7, -25, 21, 11, 18, 11, -26, 18, 7, -4, -26],\n [6, -16, 21, -18, -20, 19, 10, 24, -3, 22, -19, 9],\n [-25, 25, 18, 25, -21, 23, 10, -15, -8, 25, 2, -8],\n [4, 20, 12, 2, 24, -6, 8, 6, -6, -17, -23, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
94
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_916
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-15, -17, -24, -19, -22, 21, 9, 21, -5, 8, -4, -23],\n [-11, 10, -5, -6, 23, 0, 25, 13, -19, -20, 15, 7],\n [3, 25, -2, 11, -12, 19, 1, 13, -18, -22, 10, 14],\n [-5, 12, 13, -12, 8, 26, 0, -10, -8, -9, -17, -25],\n [-25, 22, 20, 0, -11, 5, 11, 25, -1, 5, 7, 20],\n [26, 23, -19, 9, 3, -22, 5, -19, -5, 22, 11, 20],\n [-26, -16, 11, -21, -7, -7, -9, -9, -20, 5, -1, -3],\n [21, 24, -15, -1, 3, -9, -23, 7, -4, 2, -18, 12],\n [-15, 10, -15, -11, -8, -15, -26, -26, -8, 25, 17, 10],\n [14, 17, -25, -14, -23, -8, 13, 18, 6, -10, -10, -23],\n [-19, 3, 25, 10, 21, 5, -25, -2, -1, 14, -14, -8],\n [-3, -18, 8, 5, -26, 4, -9, -12, -3, -26, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
553
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_917
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[23, 24, -7, 3, 24, 25, -14, -22, 10, -16, 15, -21],\n [11, -2, 18, 11, 12, 13, 15, 16, 2, 10, 13, 6],\n [-20, -9, 17, 24, 13, 8, -17, -4, -13, -8, 24, 3],\n [-18, -22, 12, 18, 23, 18, 5, 12, 13, 1, 9, 22],\n [-17, -23, 10, 1, 10, 23, -3, 7, 16, 0, -26, -6],\n [-20, 17, 13, 17, -12, -13, 3, 25, -26, 26, -24, 6],\n [-16, -4, 14, -2, -23, 13, 22, 5, 19, -7, -11, -7],\n [7, -3, -19, 20, -23, 3, 26, 20, 26, -26, 0, 4],\n [-14, -5, -20, -11, 0, 9, -24, 17, -9, -13, -26, 12],\n [-8, -24, -5, 20, 24, 14, 23, -26, -20, 2, 20, -20],\n [-18, 26, 21, 24, 5, 17, 23, 5, -11, -22, 7, 21],\n [5, 11, 13, -8, 6, 2, -6, 10, 24, -20, 15, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
85
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_918
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, 12, 10, -9, -17, -4, -4, 13, 9, 6, 18, 15],\n [-15, -7, 7, -21, -17, -17, -24, 11, 1, -12, 17, -18],\n [-23, 11, 23, 3, 11, 6, -15, 8, -15, 8, 15, 11],\n [26, -10, 6, 7, -8, -7, -1, 11, 15, 4, -17, 23],\n [-19, 25, -20, 15, 6, 20, 15, -5, 8, -18, 18, 11],\n [-8, 5, 7, 17, 16, -14, -5, 8, 22, 14, -12, -12],\n [9, 5, -13, 3, 19, -13, 1, 23, 8, 11, 13, 24],\n [7, -22, -3, -18, -16, 21, -7, 7, 12, -22, 6, 1],\n [26, 9, 14, 3, 20, 0, 23, 15, -16, -10, 23, 17],\n [5, -4, 18, -9, -5, 1, 22, 15, -12, -7, 5, -4],\n [-19, 26, 16, -9, 9, 24, -4, -5, 7, -7, 8, -11],\n [-26, 22, 17, 24, 15, 25, -14, 4, 19, 21, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
90
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_919
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[1, 6, -3, 23, -24, 19, 22, -3, 19, 26, -19, 17],\n [-13, -25, -21, -15, 9, -1, 2, -23, 3, 21, 25, -11],\n [-19, 5, 8, 13, -3, 4, 18, 12, 7, -22, -13, 10],\n [9, -10, -7, -26, -11, 16, -4, -16, 22, -23, 21, 17],\n [-4, 4, 4, -22, 0, 2, -14, 18, 8, -18, 23, -9],\n [-12, -3, 4, 26, 20, -20, -18, -11, 7, 5, -4, -7],\n [18, 9, 19, -18, -13, 16, -7, -14, -10, -5, -22, 9],\n [5, 2, 18, -15, 8, -23, -10, -6, -9, 20, 12, -18],\n [-13, 15, 15, 24, -3, -14, 8, -11, 16, -23, -24, 7],\n [-12, 4, -26, -26, 6, -1, 26, 15, -26, -11, 10, 25],\n [23, 8, -19, 20, 8, 24, -25, 17, 26, -9, -17, -17],\n [18, -15, 12, -3, 21, -5, 14, -22, -5, -23, 14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
96
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_920
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 19, 6, -5, -21, 11, 19, 21, 11, 25, -16, 19],\n [14, -20, -3, -19, -15, -17, -16, -7, 11, 17, -4, -5],\n [18, -5, 12, 14, -24, 8, -11, -9, -14, -5, -18, -21],\n [20, -18, -9, 25, 18, 6, 11, 24, -5, 6, 17, 2],\n [-11, -23, 9, -17, 5, 5, -13, -7, -9, -24, -21, -9],\n [5, -18, -1, 18, 24, 15, 21, -8, -21, -25, 1, 21],\n [-7, -13, 6, -23, 26, 1, 10, 15, 3, -9, -18, -20],\n [9, 26, -12, 0, 22, -22, 16, 11, -22, -5, -4, -14],\n [-21, 20, 18, 18, 15, 7, -25, -18, -5, -1, -7, -17],\n [-6, -16, 26, 13, -6, -9, -25, 26, 9, 2, 23, -5],\n [-11, -3, -25, 4, -1, -20, 9, 10, -9, 0, 3, -17],\n [14, 4, -11, -8, 22, 9, 6, -21, -11, 18, -23, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
548
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_921
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-18, -2, -4, -23, -22, -1, 0, -23, -6, -2, -16, 4],\n [-10, -20, 14, 0, 22, 24, -14, 4, -23, -18, 16, 18],\n [3, -3, 21, 15, -23, -24, 26, 12, 2, -6, -15, -9],\n [-22, -4, -10, 10, 25, 4, -15, 21, 21, -5, 12, 25],\n [18, -22, 24, -7, -11, -17, -15, -21, -4, -2, -6, -8],\n [26, 7, 13, -7, 14, -24, -20, -24, 16, 17, 18, -23],\n [7, -21, -6, 17, 15, 25, -23, 22, -15, 24, -6, 20],\n [7, -20, 24, 13, 23, 19, 13, -6, -2, -21, 0, 8],\n [17, -26, -10, -22, 17, 5, -9, 18, 14, 8, 9, 15],\n [-17, -25, -9, 8, 16, -5, -22, 20, -3, 5, 22, 7],\n [10, 22, -16, -17, -4, 24, 11, -17, 16, -20, 21, 26],\n [-14, -4, -16, 8, -19, -4, 9, -20, -17, -15, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
108
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_922
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -1, -22, 24, 20, -20, 9, -20, 12, 15, 9, 23],\n [-21, -6, -26, -25, -24, 12, 7, -13, -2, 10, 10, -11],\n [-12, 21, -3, 14, -19, -25, 15, -1, -9, -9, -8, 10],\n [6, 5, -2, 0, -6, -4, -16, -6, 16, 4, 8, 8],\n [-11, 25, 20, 4, -14, 15, -8, -17, 21, 11, -22, 20],\n [22, -23, 13, -15, 18, 14, -1, 20, 16, -12, 5, 2],\n [3, 2, 0, -12, 9, 1, -11, -17, 7, -15, -2, -19],\n [26, 22, 5, -3, -22, -8, -16, -10, 1, -3, 11, -15],\n [4, -20, 21, -24, -15, -1, 13, -24, 20, 26, 11, 2],\n [13, 17, 18, -6, 22, 22, 2, 2, 19, -1, -11, -16],\n [11, -1, 3, 15, 12, -4, -18, 1, -5, 15, 1, -15],\n [-8, 17, -8, 20, -7, 11, 20, -7, 21, -25, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
517
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_923
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -22, -19, 16, -12, 10, -13, 1, -17, -21, 19],\n [-7, -23, 19, -24, 4, 23, -7, 16, -2, -2, -15, 21],\n [-7, 14, 26, 16, 1, 4, -18, -18, 12, -18, 6, 9],\n [11, -5, 16, 22, -26, -13, -10, -3, 22, -18, -17, -9],\n [-18, -14, 16, 7, -23, 16, 4, 4, 0, 14, -2, -3],\n [-15, -6, -10, -25, 1, -13, 25, -18, -23, -22, 22, -14],\n [-6, -13, -9, -18, -1, 15, 17, 0, 14, -6, 3, 17],\n [-17, 5, -21, -1, -3, 14, 25, 19, -13, 18, -1, 9],\n [-20, 10, 9, 23, -25, 2, -7, 15, 13, 25, -18, 4],\n [-6, 8, 2, -9, 25, 3, -14, -16, -2, -1, -7, -2],\n [-17, 26, -14, 5, 8, -2, -3, 2, 8, 25, 25, 22],\n [-6, -15, 18, 21, 24, -20, -20, -6, 26, -10, 20, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
95
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_924
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 22, 6, -19, -9, -11, 4, 21, 14, -10, 2, 14],\n [-10, -1, -17, -12, 4, 13, 22, -19, 22, 18, 13, -25],\n [26, -12, -3, 1, -21, 13, -24, -11, -25, -17, -24, -16],\n [20, -2, -25, -18, -8, 22, 3, -26, -4, 13, -26, -16],\n [-11, 2, 12, 20, -20, 11, -23, 9, -17, -3, 3, 24],\n [-17, 17, 25, 14, -20, 6, -7, -21, -5, -11, -11, 7],\n [-4, -24, -5, 1, -8, 11, 15, 13, -6, 6, -24, 6],\n [-19, 12, -16, 15, 1, 1, 2, -7, 16, 4, 25, -10],\n [-13, 9, 6, -6, 10, 7, 15, -9, -18, -9, -22, -15],\n [21, -25, -25, -6, -11, 9, 8, -7, 7, 7, -7, -15],\n [18, 24, -4, 6, -20, 24, 18, -23, 21, 23, -12, -16],\n [-22, -13, 16, 23, 13, -18, 17, 5, -6, -2, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
103
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_925
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, 4, 4, 14, 13, -9, -5, -10, 18, -4, 11, 1],\n [-20, 7, -25, 17, -25, -5, -26, 7, 10, -16, 0, -13],\n [-19, -10, -14, 13, 20, -20, -12, 14, 19, -12, 16, 9],\n [-13, 3, 20, 9, -13, -23, -18, 6, -19, -12, 11, 2],\n [-26, 11, 25, 0, -13, -19, -20, -3, -11, -26, 15, -15],\n [14, -17, 15, 8, 7, -18, 22, -5, 10, -15, 9, 15],\n [5, -10, -25, 4, -7, 11, -22, -19, -11, 5, -24, -18],\n [9, 6, -21, 5, -9, -23, 17, 19, 1, 8, 24, 7],\n [7, 22, 10, 6, -11, 11, 10, 17, -10, -4, -16, 24],\n [7, -2, 21, -8, -19, -23, -21, -3, -7, -24, 14, -4],\n [-8, -26, -24, -4, -26, 20, -22, 1, 21, -22, -8, 17],\n [-14, 3, -19, -10, -2, -15, 19, 2, 16, -26, -25, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
87
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_926
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, 6, -26, -17, -9, -5, 26, 26, 4, -25, -4, -24],\n [19, 17, -3, -2, 14, -14, -17, -21, -22, 23, 12, -11],\n [16, -6, 15, 13, -22, 6, -24, -12, -17, -26, -17, -11],\n [4, 17, 1, 10, 0, -16, -6, 10, 11, 7, -5, -17],\n [-23, 17, -22, -4, -11, -8, -12, 24, -2, -15, 6, 15],\n [-19, 26, -24, 17, 12, 25, 11, -22, 19, 12, 20, 21],\n [5, -4, -8, 0, -6, 7, -25, 26, 26, -18, 4, 5],\n [-17, 9, -2, -26, -5, -22, 24, 6, 26, -10, -5, -8],\n [8, 8, 17, -8, 0, -16, 15, 1, -17, 8, -9, -22],\n [-21, -5, 3, -9, 18, -26, -23, 15, 21, 21, -3, -10],\n [16, -6, -19, 19, -9, 6, 3, -18, 25, -16, -23, -25],\n [0, -9, 10, 7, -16, -25, 4, 17, -2, 15, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_927
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, -20, -13, 18, -26, 25, 6, 7, -11, 4, -25, -15],\n [-8, -12, -11, -11, 1, -16, -21, 0, -10, 12, -16, -14],\n [21, -14, -19, -2, 14, 10, -13, -6, 16, 17, -7, -7],\n [15, 0, 6, 4, -11, -20, -11, 19, -23, -24, 3, -8],\n [0, 2, 22, 17, -10, -26, -6, 6, -2, -16, 8, 9],\n [12, 23, 1, -7, 12, 16, -2, 19, -19, 5, -7, 21],\n [23, 17, 14, -7, -18, 26, -14, 11, -5, 3, 10, 15],\n [-4, -16, -13, -11, 12, 1, 23, 13, 0, 19, -17, 19],\n [-7, 0, -5, 18, 5, 5, 22, 11, 20, 13, -22, 13],\n [-18, -20, -9, 19, 13, -26, 22, -21, -13, -3, -10, -10],\n [17, -6, 21, 8, 22, 7, -14, -13, -23, -3, -21, -7],\n [5, -4, 14, -13, -5, -10, 13, 24, 26, -25, 22, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_928
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[8, 9, 23, -13, -7, 1, -14, 22, 17, -20, -24, -22],\n [26, 25, 6, 19, -18, 26, 0, -12, 7, -9, -23, 7],\n [18, -6, -9, 25, 9, 8, -20, 7, 19, 10, -25, 14],\n [-11, 1, 3, 4, -19, 11, 8, -20, -9, 21, 9, -6],\n [-23, 5, -11, -9, 7, -5, 0, -15, 14, 5, -20, 13],\n [11, 17, 13, -17, 9, -17, -20, 24, -24, -15, 5, 24],\n [3, -17, -6, 11, -7, -12, -6, 4, -8, 16, -19, 15],\n [-5, 19, 25, 19, 20, -15, -10, 15, -15, 4, 24, -19],\n [21, -9, 25, 0, 15, 26, 16, -21, 1, 2, -9, 18],\n [16, 19, 19, -4, 9, -17, 25, 0, -9, 14, 26, -14],\n [-4, 24, 13, 16, -4, 13, 23, 22, 2, -17, 3, -5],\n [4, 15, -4, -23, 13, -25, -13, 13, -1, -5, 19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
548
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_929
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, -19, 15, 9, -16, 19, -11, 15, -12, 13, 20, -8],\n [-19, -10, -9, -25, 10, 21, -3, -10, -12, 24, -3, -4],\n [0, -5, 20, -14, 22, 25, -15, 8, 1, -17, -17, 18],\n [-3, 1, 12, 10, -18, 9, 8, 16, 22, -25, 26, 14],\n [11, -4, -15, 24, -6, 2, 9, 16, 10, 25, 0, -21],\n [-7, 21, 16, 14, -5, -4, 7, -23, 5, -11, -23, 1],\n [1, 14, -5, -19, -1, 12, 3, 23, 26, -18, -1, 15],\n [-16, -2, 7, 0, 24, -17, -12, 23, -22, -15, -19, -21],\n [-3, -26, -2, 18, 20, -16, -4, 9, 13, -20, 0, 18],\n [-6, -22, 6, -11, -16, 5, 23, -3, -18, 9, -20, 1],\n [-4, 12, -14, 24, -20, -6, 12, -14, 9, -15, -19, 21],\n [16, 9, 26, 20, 17, -4, 7, -4, 11, 2, 23, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
81
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_930
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -15, -11, -26, 24, 3, 9, 15, 15, -3, 12, 11],\n [5, 5, -15, -17, -15, -14, -12, 3, 26, -14, 24, 21],\n [16, -26, -9, 12, -15, 23, 17, -18, 22, -23, 0, 1],\n [-3, -23, 1, 25, -7, 2, 6, 3, -24, -8, -6, 13],\n [-6, -7, 6, 11, -18, 23, 4, 5, 14, -4, -4, 25],\n [15, -11, -6, -15, -21, -13, -5, 4, 13, 20, 15, 1],\n [-22, -1, 25, 0, 2, -11, -1, -19, -16, -24, -25, -26],\n [-26, -7, 15, 4, 23, -11, 24, 21, -24, 12, -21, 16],\n [10, 14, 9, -15, -17, 8, 12, -25, 4, 13, 18, -12],\n [6, -25, 0, 23, -3, 0, 24, 4, -20, -1, -5, -25],\n [-11, -2, -11, -4, 9, 22, -13, 13, -18, 13, 4, 23],\n [-20, 18, -26, -6, 2, -19, -18, -8, 20, 8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
101
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_931
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 16, -13, -15, -22, 7, -20, -22, 8, -2, 3, 15],\n [-16, -19, 11, 1, -15, 18, 7, 4, -6, -11, -3, -5],\n [-14, -18, 18, 20, -19, -4, 22, -17, 14, -10, 2, 22],\n [24, 24, -25, -16, -19, -6, 22, 6, 23, -20, 14, -2],\n [-18, 15, 21, 16, 11, 0, 17, 26, -17, 21, -1, 0],\n [-5, 19, 22, -7, -1, 10, 9, 2, -14, -20, -16, 16],\n [26, 17, -24, 17, 8, -26, 15, -26, 6, -1, 16, 21],\n [-24, -3, 8, 13, 18, -11, 20, 15, 22, 8, -13, 6],\n [-18, -8, 3, -17, 26, -16, -1, -1, -13, -11, 12, 3],\n [-18, -14, 12, -26, 12, -25, -4, 7, -26, 14, 15, 15],\n [-22, 12, 5, -17, -5, -3, 8, 4, 17, 25, 21, 23],\n [21, -6, -17, 0, 6, -11, -22, -3, 17, 21, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
98
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_932
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-17, -11, 2, -12, -5, 16, -21, 24, 20, 0, 2, 18],\n [1, -8, 6, -17, -16, 17, 3, -13, -11, -20, 26, -23],\n [-11, 24, 8, -18, 22, 9, -18, 5, 19, -1, 17, -8],\n [26, 16, -23, 4, -14, 19, -17, 21, -7, 25, -21, 17],\n [21, -19, 8, -12, 2, 23, -19, -18, 2, -4, 25, -15],\n [1, 20, 17, -12, 23, 8, 2, -9, 13, -9, -17, -20],\n [-25, -9, 15, 24, 8, 11, -17, -7, -17, -14, 26, -3],\n [15, 24, 19, -16, -7, -11, 8, -14, 19, -18, 4, 9],\n [-13, 16, -15, -4, 22, 5, 21, -26, -11, 23, -16, 2],\n [-25, -11, -11, 0, 9, 6, -1, -16, -20, 11, 11, -2],\n [25, 23, -19, 1, -21, 13, 2, -24, 9, -21, 22, -26],\n [-12, 2, -12, -15, -21, 25, 10, -20, 13, 15, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
91
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_933
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[19, -23, 26, -17, -14, -20, 8, -22, -9, -20, 11, -19],\n [12, 25, 26, 16, 15, -1, -21, -9, 11, -17, -18, 13],\n [-15, 2, -6, -6, 0, 15, -15, 2, -1, 23, -1, 24],\n [1, -13, 18, -2, 12, -19, -12, 0, 14, 8, -22, -23],\n [25, -6, 26, -7, -21, 2, 13, -24, 9, -10, 22, 10],\n [22, -2, 17, 8, -6, -25, -16, 11, -10, 4, -8, 2],\n [-14, -6, 10, -22, 24, 1, -12, 0, -23, 11, -24, 2],\n [-16, 24, 9, 0, 12, 8, -22, -11, -6, -2, 3, 24],\n [23, -24, 10, -20, 12, -24, 14, -19, -6, -9, -17, -7],\n [13, 13, 22, 2, 22, 3, 9, 5, -21, -8, 4, 6],\n [-23, -16, -21, -15, 10, 19, 4, -10, -23, -12, 11, 18],\n [-15, -17, -21, -5, 14, 4, -11, -19, 12, 19, 9, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
101
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_934
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[2, -24, 24, -17, 19, 5, -6, -21, 17, 5, 17, 1],\n [-23, 3, 15, 17, -10, 1, 12, -17, -26, 24, 4, 5],\n [-7, 2, 10, -2, 11, -26, -12, 7, -4, 2, 23, -14],\n [-25, 13, -22, -5, -12, -14, 3, -2, -6, -10, 9, 12],\n [7, 14, 7, 22, 26, 23, 11, 23, 11, -1, -25, 7],\n [11, 14, 9, 15, 25, 7, 18, -23, -16, 15, -14, 12],\n [9, -22, 12, -16, 0, -24, 18, 1, 8, 10, -13, 2],\n [25, 10, -10, -13, 4, 21, 25, 11, -22, -9, -9, -12],\n [24, -23, 11, 26, 26, 14, -18, -8, -2, 22, -7, -13],\n [-19, -18, -6, 7, 13, 14, -14, -1, 15, 18, 10, 3],\n [20, -7, -20, 17, -7, -11, -25, -17, 14, 25, 8, 16],\n [1, -17, -14, -5, 7, -11, -19, -7, -17, 2, 22, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
543
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_935
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[25, 26, 15, 3, -3, -25, 7, 15, -6, 7, 5, 3],\n [-13, -8, 3, 14, 0, -11, -2, -2, -3, -24, -3, -16],\n [5, -4, -15, 12, -6, 10, 25, 7, -6, -1, 9, 22],\n [23, 7, -18, -9, 17, 15, 12, 3, -24, 23, -25, -24],\n [-12, 14, -24, 11, 16, 7, -10, -24, -20, 4, -17, 24],\n [8, 1, -7, -26, 15, -14, -19, -3, -5, 0, 20, 6],\n [-1, 17, -24, 3, 11, -17, -21, -10, -20, -13, 7, 19],\n [-21, 6, -9, -21, -9, 3, -23, -2, 19, -24, 19, -22],\n [19, 24, 13, -22, -17, 18, 11, -7, 15, -14, 25, 15],\n [-26, 3, 9, 18, 11, -19, -18, 14, 19, 6, 10, 22],\n [-21, -10, -4, 10, -25, -9, 11, 1, -13, -5, -26, 16],\n [15, 20, 14, 12, 17, -19, 0, -17, 7, 19, 14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
85
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_936
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[21, 10, -19, 3, -7, -26, 22, -20, -16, 12, -20, 26],\n [9, -7, 6, 20, 7, -4, -3, -18, -4, 19, 21, -10],\n [12, 7, -21, -24, 26, 11, 11, -19, 13, -18, -12, 3],\n [22, -23, 2, 6, -21, 2, -8, 10, 0, -16, 15, -18],\n [-11, 24, -9, -14, -20, -10, -18, 5, -1, 15, 25, -5],\n [18, 1, -11, 9, -2, 1, 2, 15, -26, 4, 3, 13],\n [-2, 25, 26, -9, 10, 16, 24, -18, -12, 2, 10, -22],\n [17, -18, 10, -17, -2, 11, -17, 11, -7, 15, -18, -24],\n [16, -16, -23, 22, 1, 14, 11, -16, 24, 5, -9, 13],\n [19, -8, -11, -24, -14, 22, 24, 10, 26, 21, 3, -13],\n [24, 25, 9, -21, 5, 14, 13, 5, -15, 16, 12, -2],\n [-2, -19, 15, 8, -21, 16, -23, 17, 8, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
550
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_937
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[-3, -17, -20, -1, 1, -25, 17, -13, -20, -10, -12, -5],\n [5, -1, -4, -1, 23, -3, -5, 0, -6, 10, 16, -19],\n [-13, -25, 25, -20, 0, -19, -23, -17, 19, 20, -17, -11],\n [-24, -4, -25, -26, -16, 21, 17, 10, -7, -6, 3, -2],\n [20, -10, 13, 24, -4, -8, 17, -6, -20, -21, -25, -24],\n [14, -16, -5, 23, 21, 26, 15, 21, -18, -7, -25, 23],\n [-11, -1, 25, -4, -13, -6, -4, -15, -23, -10, 4, 1],\n [25, 26, 25, 12, 9, 20, -13, 25, 4, 6, -18, -5],\n [9, 3, 25, -18, -18, -15, 1, -11, 10, 22, -21, -18],\n [16, 7, 4, -20, 5, 22, 16, -3, 3, 15, -1, 6],\n [-1, -8, -26, 25, -7, 11, 21, -15, 16, -5, 23, -20],\n [-5, 0, -13, -14, -7, -19, 19, -9, -23, -4, -4, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
94
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_938
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[14, -25, 19, 17, -5, 24, 23, 17, -26, -17, 7, 4],\n [-13, 25, 21, -8, 19, 2, 19, 9, 3, -16, 3, -5],\n [26, -25, 12, -2, 18, -19, 5, 17, -20, -5, 2, -25],\n [11, 16, 22, -12, -7, -1, -16, -4, 14, 22, 25, 15],\n [-23, -23, 21, -26, -4, -3, 0, -20, 7, -23, -25, -4],\n [21, 9, -5, -17, 15, 8, 14, 0, -3, -20, 24, -6],\n [-19, 23, 9, -22, -11, -9, 11, -4, 17, 25, 10, 24],\n [-6, 18, -5, -14, 9, -16, -21, -18, -7, 12, -3, -15],\n [15, 8, 12, -2, 0, 15, -26, -15, -26, -14, 12, 23],\n [13, -21, 2, 20, 23, -23, -4, 17, -19, 10, -25, 23],\n [-23, 24, -4, -6, 26, -1, 13, 3, 6, -5, -15, -21],\n [-7, -20, 3, 16, 14, -19, -10, 16, 1, 5, 21, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
100
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_939
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, -23, -24, 17, 23, 9, 21, -20, -17, 6, -13, -9],\n [6, -1, 12, 23, -10, 16, 1, -25, 13, 10, 5, 0],\n [4, -23, 8, 5, -16, 26, -4, 20, -4, 12, 8, -10],\n [25, 22, -7, 16, 23, 5, 11, 19, -22, -12, 5, 7],\n [-1, 24, -12, -18, -22, 7, 6, -6, -24, 3, -22, -3],\n [25, -11, -21, 13, 8, -1, 17, -26, -7, 19, -16, -7],\n [12, -23, 11, 19, 15, 3, 9, 18, -5, 13, -9, -22],\n [17, 3, -22, 12, 24, -13, -16, 25, -6, -16, 5, 2],\n [-24, -14, -21, 21, 1, 4, -4, 11, 11, 26, -21, -5],\n [18, 13, 22, 7, 11, 11, -20, -26, 5, -5, 13, -24],\n [-23, -10, 8, -4, 2, -25, 19, -21, 23, -3, -25, -15],\n [-22, 15, -12, -14, -17, -5, 2, 22, 18, -20, -5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
549
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_940
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-25, -5, -3, -1, -5, -22, -17, -8, 14, -5, 0, -25],\n [-6, -2, -5, -18, 4, 18, -26, -12, 3, -14, -13, 16],\n [7, -2, 6, 16, -6, 5, -11, -22, 0, -1, -8, -5],\n [-17, 25, -12, 7, 3, 8, -13, -4, 22, -20, 19, -1],\n [2, -17, 21, 3, 19, 19, -4, -17, 20, -1, -9, -26],\n [-24, 14, -17, 2, -22, -22, -12, -1, -1, 9, -23, -1],\n [23, 2, 12, 25, -5, -26, 1, 19, 12, -8, 14, 26],\n [-15, 15, -21, 8, -16, -26, -26, -20, 16, 15, 2, 7],\n [-20, 4, -26, 10, -1, 23, 2, 8, 10, -17, -22, 3],\n [23, 19, -23, -20, 24, -7, 1, -20, -16, 22, -13, -19],\n [-3, 24, 4, -25, -19, 0, 16, -3, 24, -21, -16, 22],\n [-11, 25, 2, 14, 3, 18, -20, -11, 9, 4, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
548
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_941
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[-13, -12, -19, -15, 16, -3, 11, -14, -9, 8, 2, -7],\n [7, -24, 13, 8, 15, 4, -20, -18, 26, 23, 21, -10],\n [25, -20, 24, -22, -3, -12, -25, -12, -6, 10, -13, 24],\n [-25, -2, 0, 25, 26, 24, 11, 26, -8, 15, 21, 3],\n [22, -17, 4, -14, -14, 0, 19, -8, -8, 10, 14, -12],\n [1, 17, 9, 1, 23, 6, 17, -5, -18, 9, -21, -25],\n [16, 16, -1, -22, -4, -21, -26, 8, 26, 14, 6, -1],\n [-2, -14, -10, -11, 17, 3, -25, -23, -14, 11, -10, -4],\n [2, 21, -18, -12, -25, 2, 7, -10, -13, -12, -1, 7],\n [-24, -9, 10, 9, 12, -20, -4, 10, -1, 25, -12, -3],\n [-7, 10, -3, -13, 5, 8, -4, 6, -25, -14, 3, 7],\n [-16, 10, -15, -9, -7, 22, -14, -21, -17, 6, 23, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
532
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_942
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-23, 14, 10, 15, -15, 25, -22, -2, -2, 6, 25, -12],\n [-7, 12, -15, -13, -5, -3, -15, -7, 21, 1, -16, -5],\n [23, 6, -13, -14, -2, 13, -11, 3, -26, 1, 4, 9],\n [21, 18, 23, -25, 15, 10, 16, -25, 6, 22, 9, 3],\n [25, 7, -9, 9, -3, -26, 19, -3, -6, 2, -14, -17],\n [-14, -16, 11, -21, 24, -17, 23, -14, 21, 23, 8, 20],\n [-5, -10, -24, 3, 7, 0, 18, -23, 6, 16, 4, -8],\n [-16, 25, 10, -12, -7, 10, 22, -19, -25, 11, 23, 0],\n [23, -13, -3, 8, 1, 7, -10, 6, -4, -19, 6, -8],\n [-15, -23, 4, 17, -6, -15, -20, -9, 12, -16, 6, -5],\n [-19, 12, 4, 26, 0, 24, 1, -4, 14, 0, -17, -4],\n [6, -1, -14, 4, 0, -14, 21, 20, 7, 20, -20, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
89
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_943
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, -22, 11, -21, -1, -8, -12, -18, -14, 8, 20, 7],\n [7, 2, 12, 0, 19, 18, -15, 12, -25, 20, 9, 26],\n [-9, -21, 3, -6, -5, -16, 12, 13, 15, -20, -20, 4],\n [-21, -1, 9, -18, 9, -24, 17, 4, 26, 3, 4, 16],\n [16, 13, 3, -18, -21, -2, 3, -1, -24, -5, 15, 18],\n [-18, 23, 8, -20, 10, 21, -18, 0, 1, 18, 17, 6],\n [23, -21, -10, -4, -2, -8, 25, 2, 4, -21, 10, 7],\n [-3, -17, -16, -3, -25, 23, 2, -11, -4, 8, 16, -5],\n [8, -21, -4, -4, 3, 10, 15, -7, -16, -3, -9, 0],\n [26, -20, 21, -6, -12, -19, 1, -6, -19, 1, 7, 20],\n [-12, 17, 16, 10, 26, 0, 14, -1, -15, 7, 4, -24],\n [-1, -21, -7, 24, 13, -10, 14, -26, -14, -9, 25, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_944
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[25, -15, 17, -15, -1, 15, 13, 1, 17, -2, -6, 21],\n [23, 22, -16, -18, 26, 8, 9, 22, 2, 13, -10, 10],\n [21, 22, -19, 26, 17, 20, -22, -4, -17, 20, 14, 20],\n [-12, -11, 0, 5, 13, 24, 18, 19, 8, 10, -3, 4],\n [24, 8, -11, 13, 9, -15, -11, 22, -22, 20, -22, -7],\n [21, 11, 9, 5, 13, -16, -16, 16, 22, 1, -15, 19],\n [4, 13, 3, -7, 0, -2, 23, 7, 8, 16, 25, -22],\n [13, 12, -19, -8, 16, -9, -11, -8, -12, 2, -12, 2],\n [-10, -12, 13, -16, -24, -14, 11, -18, -7, 21, -1, -15],\n [22, 4, -25, 6, -11, -22, 26, -10, 22, 13, 5, -12],\n [-15, -10, -17, -1, 17, 1, 1, -4, -7, -10, 25, 17],\n [-19, 23, -12, 14, -4, 26, -13, 13, 19, 0, 16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
544
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_945
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[12, 16, -2, -1, 17, -16, 11, -18, 16, 6, 24, -11],\n [22, -7, -20, 6, -14, 20, 8, -23, 4, 3, -24, 14],\n [0, 5, 20, 11, -21, -19, -3, -12, -2, 0, 17, -14],\n [-7, -22, 11, -20, -22, 1, 10, 2, 15, 10, -20, 19],\n [-1, 20, -8, -17, 15, -7, 19, 4, 9, 19, -21, -12],\n [-3, 3, -18, -26, 23, 20, -12, -21, -12, -20, 19, 0],\n [-17, 5, -6, 17, 10, 11, 9, -13, 15, 12, 14, 21],\n [-13, -25, -3, -17, 15, -21, -24, 7, -1, -17, 11, -6],\n [25, -2, -25, 9, -26, 17, 15, 9, 17, -3, -17, 24],\n [8, -5, 19, 20, 7, 5, -11, 3, 9, 4, 3, -22],\n [-3, 19, 9, 0, -13, 10, -14, -7, 1, 24, -21, -18],\n [-5, -4, -19, -26, -20, -15, 12, -10, 23, -11, -23, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
95
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_946
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, -18, 0, -15, 7, -4, 8, 13, -18, 16, -14, 25],\n [23, 19, 16, -25, 20, -25, 2, 18, -5, 16, -6, 20],\n [-21, 20, 1, -11, -26, -4, -19, 25, -19, 15, -26, -16],\n [-19, 20, 24, 4, 19, 9, -19, -3, 0, 2, 17, -9],\n [-18, 9, 11, -13, -14, 13, 25, -3, 12, -13, -19, -15],\n [25, 4, 7, 9, -6, -23, -16, 15, 10, 14, -20, -15],\n [-22, -24, 5, 13, 25, 8, 9, -15, 3, 6, 13, 14],\n [-24, -1, 11, 25, 14, 7, -24, -13, 18, 19, -13, -10],\n [-12, -15, 12, 14, 17, 3, 22, 24, -20, 21, 8, 24],\n [24, 25, 4, 25, 13, 10, -13, 24, 1, 26, -15, 14],\n [-21, -23, 6, -22, -18, 12, -9, 5, 4, 7, 13, 0],\n [10, 10, 12, 17, -14, -23, -18, -19, 19, -21, 6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
555
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_947
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[21, -10, 10, -14, -5, 23, -8, 1, 26, 16, -2, 17],\n [-19, 18, 5, 20, -16, 11, -9, 21, 0, 11, 10, 19],\n [15, 9, 14, 7, -12, -14, 0, -8, 9, -14, -20, 18],\n [-26, 14, -6, -11, 22, 2, -3, -8, 0, 21, 20, -26],\n [0, -13, -16, -4, 20, -7, 26, -1, -9, 9, 3, 26],\n [-23, -8, -22, -25, -17, 22, 16, 16, -16, 24, -5, 16],\n [-19, -24, 14, 26, 13, -9, 23, -5, -16, -25, -5, 14],\n [24, -12, -19, -8, -18, -22, -19, 6, 22, -12, -12, 14],\n [-20, -6, 19, -1, -26, 24, -1, -1, 1, -18, -1, 24],\n [-14, -22, 19, -9, 26, -4, 1, 10, -22, 0, -7, 9],\n [10, 7, -13, 20, -21, 0, -25, -18, -16, -22, -16, -24],\n [-1, -13, -18, -8, -10, 22, 19, -3, -13, -17, -20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
93
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_948
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[8, 4, 11, 15, 10, 26, 2, -21, -19, -2, -22, -17],\n [-4, -26, -14, 10, -1, -8, -1, 21, 23, 24, 15, -25],\n [14, -8, -15, 17, 8, 5, 26, -14, 9, -26, 6, 26],\n [-23, -25, -19, -11, -5, -17, -18, -20, 13, -10, 3, -16],\n [16, -12, -20, -24, -4, 0, 3, 21, -11, -13, 25, -5],\n [23, -7, -17, 2, -23, 4, -13, -22, 11, -23, -16, -2],\n [-15, 25, 4, -16, 12, 5, -16, -20, -25, -26, -2, -18],\n [19, 25, 9, 2, -17, 0, -8, -8, 26, 26, -7, 2],\n [26, -24, -5, -5, 2, -4, 13, -1, 20, 26, -5, 11],\n [-18, -6, 9, 23, 21, 9, 5, 5, 7, -4, -1, -11],\n [11, 22, -24, 18, -25, 9, -18, 1, -3, 22, 18, 1],\n [-20, -1, 19, -26, 14, 18, 14, 8, -9, -5, -14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
93
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_949
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 24, 2, -6, 15, -18, 2, -15, -19, -17, 7, 20],\n [-7, -11, 15, 18, -16, 21, -13, 4, 13, 24, 7, -23],\n [23, 21, -20, 15, 11, -26, 23, 19, -3, 15, 1, -3],\n [-14, 11, -17, -1, -25, 6, 1, 0, -21, 24, -10, 6],\n [-12, 19, -24, -17, 2, -20, 23, 9, 25, 17, -5, 4],\n [12, -13, -25, 22, -21, -8, 0, -21, -25, -14, 20, -17],\n [13, -22, -13, 4, -2, -21, -15, -24, 20, 23, -4, -26],\n [-12, 22, 13, -14, 11, -13, -8, -18, 1, 6, 26, 6],\n [18, 12, 6, -23, -9, -1, -2, 8, 12, -9, 6, -9],\n [2, 14, -19, 22, -25, -23, -12, -19, 3, 20, 12, -3],\n [14, 25, -15, 9, -13, 16, 5, 24, -13, 1, 16, -7],\n [-14, 19, 18, -10, 3, 21, 13, -10, 5, 17, -8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
555
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_950
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[16, -1, -26, 22, -8, 18, -15, 17, 1, 18, 11, 4],\n [-14, 26, 16, 25, 26, 26, -16, -15, -4, 20, 2, -18],\n [-13, 5, -24, -20, -21, 8, 0, 1, -4, -17, -10, -12],\n [-13, -16, 2, -9, -1, 20, 24, -2, 13, 16, -26, -24],\n [-8, -16, 1, 24, -9, 26, 19, -13, -14, -8, 17, 24],\n [5, 16, 6, -21, 3, -17, 3, -18, -21, 18, -21, -7],\n [-10, -25, -25, -17, -26, 7, 20, 26, 9, 13, 24, -7],\n [5, -10, 12, -5, -22, -26, 4, -9, -22, -2, -20, -13],\n [-20, 3, -10, -14, -3, 9, -15, -9, -4, -5, -2, 17],\n [-2, 9, -6, 21, 19, 2, 26, -19, 22, -22, -25, 25],\n [-4, -25, -5, -6, 17, 22, -10, 13, 4, -2, -20, -2],\n [-9, 5, -19, 20, -13, 21, -21, -4, -12, -5, 9, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
84
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_951
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[18, 17, -18, -22, -15, 2, -26, 6, -6, -6, 0, -25],\n [-19, -15, -5, 22, -18, 17, 11, 2, -24, -5, -23, 2],\n [14, -14, -3, -25, -24, -12, -3, 23, -1, -19, 13, 26],\n [20, -22, -19, 19, 12, 19, 5, 4, -19, -10, -4, 12],\n [23, -14, 17, -12, 18, 1, 21, 3, -12, 11, -19, 19],\n [-12, 11, 12, 24, 7, 9, -7, 17, -14, 17, 18, 20],\n [-6, 20, -4, 19, -24, -5, 2, 13, 3, -3, -2, -15],\n [23, -7, 6, 12, -5, 19, -8, 5, 26, 24, -1, 17],\n [-20, -19, -16, 13, -11, -18, 14, -23, -16, -17, 26, 2],\n [14, -22, -24, -14, -11, 14, -19, 1, -3, 11, -25, -21],\n [-8, -9, 11, -3, 12, -7, -3, -25, 9, -11, 8, -20],\n [3, 8, 12, 16, -11, -11, -3, -13, -11, 5, 25, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
86
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_952
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -4, -25, -18, 10, 15, 5, 16, -5, -9, 15, 19],\n [-4, -18, 0, 7, -18, -6, -10, -22, -13, -9, -3, 24],\n [-18, 4, -6, 8, -1, -10, -23, -20, -24, 14, 4, -6],\n [-13, 17, 0, 11, -4, -17, 19, -6, 23, -24, 21, -16],\n [-14, -18, 19, -12, 24, -25, -3, -14, -3, -4, 23, 7],\n [-24, -13, -1, -26, 2, -15, -22, 24, 25, 14, -20, 8],\n [-20, 20, -2, 5, 1, 16, -1, -17, 6, -18, 8, -21],\n [-9, -23, -8, -21, 6, -23, 6, 22, -23, -6, 1, -20],\n [-19, 8, -15, -8, 15, 25, 11, -9, 1, 11, 5, 3],\n [5, -5, 23, -22, 16, -20, -18, -24, -8, 17, -9, 3],\n [20, 25, 10, -19, 2, 17, -10, -8, -13, -11, -12, 9],\n [-9, 13, 10, 4, 22, 13, -14, -18, 19, 22, 11, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
86
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_953
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 9, 0, 25, 16, -17, -14, 25, -5, 18, -21],\n [23, -6, 0, 17, 7, -21, -20, 8, 3, -16, 3, -6],\n [14, 19, -16, -21, -8, 20, -2, 5, 0, 19, -15, -14],\n [-22, -15, 22, -1, 24, 8, -9, -9, 14, -24, -1, 16],\n [25, 21, -12, 11, -1, 14, -26, -13, 24, 8, -18, 0],\n [14, 5, -22, 5, 4, -21, 26, 4, 4, 17, 12, -20],\n [25, -17, 21, 22, 4, 18, -22, 5, -13, 14, -13, -19],\n [-7, 15, 14, 12, -17, -17, -19, -10, 25, 11, 25, 24],\n [-14, 10, 9, -6, 17, 20, -25, 3, 20, -8, 13, -12],\n [-3, 15, -14, -3, 24, -26, 16, -9, 24, -9, 24, 12],\n [10, 19, -16, 1, -16, 26, 5, 7, 14, -26, -12, -3],\n [13, -25, -21, -25, -10, -20, -24, -3, 24, -15, -9, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_954
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[17, -1, -26, -26, 15, -24, 15, -23, -3, -15, -13, 13],\n [-3, 3, 12, 6, 22, -6, -12, 20, 5, 10, 26, 4],\n [-26, 24, 6, 7, 16, 17, -16, 13, 25, 9, 26, 7],\n [-18, 4, 2, -14, -17, -18, 18, -24, 22, -9, 0, 5],\n [-19, -14, -9, -1, -11, -6, 19, -2, 18, -23, 6, 3],\n [4, 6, -21, -12, -12, 12, 4, -18, 5, 18, 11, 15],\n [-6, 26, -15, 8, -12, 25, 16, 1, 5, 24, -1, -17],\n [14, -4, -26, -11, -6, 20, -10, -7, -1, -10, -2, -2],\n [-23, 1, -26, -13, -5, -13, -12, -22, -12, 25, 17, 20],\n [7, 2, -5, -11, -20, -26, 24, -20, 15, -5, 23, -19],\n [11, -26, -4, 5, -2, 18, -19, -3, 9, -22, 20, 10],\n [-3, 16, 15, 14, -19, -25, 5, -4, 5, 21, -24, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
95
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_955
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[-9, 15, 23, 8, 1, -7, -5, -26, 15, -19, -19, -7],\n [-10, -12, 16, 21, -5, -11, 6, -3, -7, 3, 6, -2],\n [19, 19, 9, -19, 3, -11, 13, -12, 0, 23, 18, -17],\n [-3, 4, 11, -8, -26, -25, 12, -15, 3, 13, -14, -2],\n [6, -2, -9, -19, 5, -15, -8, -6, 17, -25, 26, 20],\n [-16, 24, -2, -26, 8, 6, 14, 0, -6, -13, 21, -24],\n [14, 2, -10, 22, -23, 17, 19, -5, -13, -13, 21, -18],\n [-25, 10, -22, -9, 16, 5, 14, -18, 17, -23, -24, 10],\n [-6, 12, 19, 3, 10, -3, -26, -11, 1, 3, -8, -4],\n [7, 23, 10, -4, 16, -11, 14, 5, -11, 8, 0, -24],\n [-7, 0, -25, -14, -21, -13, -3, 0, -18, 23, -4, 8],\n [17, 24, 10, -13, -1, -19, 26, 18, 4, -19, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
517
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_956
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[-11, 26, 4, 4, 8, 10, -13, 20, 12, -2, -26, 2],\n [1, 2, -17, -19, 13, 3, 3, 14, -21, -12, -3, -14],\n [-18, 23, -7, 9, 25, 22, -14, 0, -9, -19, 15, 22],\n [-19, 24, 25, -3, 17, 13, 0, 24, -7, 8, -19, -3],\n [13, -15, 20, 6, -13, -6, 6, 14, 18, -26, -21, -13],\n [1, -2, 12, -4, 16, 12, -10, 4, 25, 1, -20, -9],\n [-11, -21, -25, -7, -4, -25, -2, 20, -21, 16, 13, 2],\n [-18, -18, -13, 18, -12, 19, -11, 21, 24, 18, 17, -18],\n [1, -23, 13, -15, -5, -26, 17, 13, -23, 15, 6, -7],\n [8, 20, -25, -17, -19, -13, 0, -14, -14, 2, -19, -3],\n [-22, 1, -25, -6, 11, 0, -19, -15, -17, 23, -20, 14],\n [-17, 2, -2, -1, 25, -1, -21, -5, 12, -15, -20, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
97
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_957
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-14, -9, -22, 4, -10, -12, 7, -5, -22, -11, 6, 14],\n [-23, 6, 1, -16, -22, 15, 14, -20, 24, -3, 17, 23],\n [-23, -15, -23, -2, -24, -10, -1, 23, -18, 19, -14, -22],\n [20, 26, -22, -15, 1, -17, -26, 8, 1, 24, -25, -4],\n [-22, 6, 4, -12, -26, 25, 2, -3, -18, 8, -11, -19],\n [-19, -4, 20, 17, -10, 0, 2, -16, -4, -23, -10, -16],\n [-19, 24, -1, 25, 22, -19, -19, -20, 24, 7, 5, -14],\n [9, -9, -14, 3, -26, 26, 8, -24, 3, 21, -2, 6],\n [-11, 22, -24, 20, 2, -13, 16, 18, -22, 17, -10, 26],\n [2, -6, -21, -3, 22, 1, -10, 15, -5, -3, 13, -9],\n [1, -17, -26, 10, -1, 23, -1, 6, -18, -9, -22, -5],\n [-17, -13, -15, 5, 12, 18, 9, 24, 23, 20, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
91
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_958
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, -23, 24, -24, -1, 10, 7, 15, -18, 17, -13, 20],\n [6, 21, 11, -22, 24, 20, 1, 6, -10, -6, -20, 13],\n [8, -20, -19, 24, 17, 15, 4, -22, -22, -3, -5, 17],\n [-14, -5, -1, -26, -10, -8, -25, 23, 25, -16, 3, 19],\n [-4, -12, -4, -15, 0, -21, 3, -22, 19, 11, 8, -21],\n [-13, 25, 23, -10, -18, 13, 4, 9, -17, 0, 22, 25],\n [-22, -10, 4, -13, -4, 17, 2, 12, -12, 20, -15, 6],\n [13, 3, -5, 3, 5, -7, 11, -7, -25, 4, 23, 1],\n [-24, -7, 8, -8, -21, -16, 18, -21, -9, 20, -13, -13],\n [-26, -10, -13, 4, 18, -17, 11, 6, -22, -11, -7, 21],\n [-5, 13, -10, 23, 23, -18, 11, 15, -18, -12, 25, 19],\n [-13, -18, -18, 6, 26, 4, -17, -17, 12, -22, -9, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
535
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_959
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 22, -9, 25, -15, -2, 0, 14, 26, -18, 22, -14],\n [22, -5, -25, 12, 21, -12, -4, -14, 18, 20, -7, -14],\n [0, 15, -10, 4, -1, -5, 14, 5, -5, 1, 15, 20],\n [-26, -23, -11, 16, -4, 11, 14, 21, 9, -13, 16, 16],\n [-24, -26, 17, -11, -19, -26, -6, -25, -15, -13, -5, -7],\n [-10, -20, -6, 7, -5, -5, -6, -14, 18, -21, -2, 17],\n [4, -2, 5, 2, 21, 8, -15, -11, -18, -14, -15, -1],\n [-12, -23, 22, -17, 21, 17, 11, 21, -15, -5, 11, 3],\n [-12, 9, -22, 22, -23, -1, 16, -8, -13, 0, 11, -1],\n [15, -4, 15, 23, 22, -25, -14, -15, 10, 13, 9, -24],\n [-23, 4, 14, 1, 13, -16, 20, 16, -11, 11, 2, -12],\n [-6, -13, -11, 0, 1, -13, 9, -17, 20, -18, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_960
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[-8, -14, 24, 10, 12, 25, -24, -20, 1, -13, 10, 21],\n [25, -5, 4, -26, 20, -15, -3, 3, 19, 21, 0, -11],\n [-6, -23, -25, -6, -20, 10, -20, -25, -15, -26, -24, -26],\n [8, -11, 24, -19, -6, 24, -22, 4, -1, -26, -4, -14],\n [5, -22, -7, 24, 1, -20, -14, 5, 19, -9, 19, 18],\n [-19, 2, -7, -1, -9, 19, -25, 16, 20, 15, 22, -3],\n [16, -19, -5, 7, 5, 8, -2, -20, -13, 17, 2, 10],\n [10, -20, 6, -10, -8, -2, -19, -15, -24, 4, 17, -19],\n [-23, 5, -20, -13, 7, -22, -15, 10, 0, -6, -14, -2],\n [7, 15, 17, 21, -10, -6, -12, -1, 6, 8, -1, -15],\n [-5, -17, -18, 9, 7, -6, 6, -17, 18, -20, 1, -9],\n [-12, 13, 3, -2, 23, 23, 18, 3, -11, -17, -2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
87
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_961
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -26, -18, -7, 11, -9, 2, 10, 22, -15, 10, 5],\n [-15, 10, 12, -15, 6, 16, 5, 6, -3, 4, 20, 3],\n [-1, -25, 25, -10, -26, 25, 4, 2, -16, 18, -23, 9],\n [-19, 9, 20, -6, -16, -15, -1, 0, 7, -17, -18, 12],\n [-14, -15, -10, -23, 12, 1, 14, -7, -20, -19, 8, 2],\n [20, -12, 4, -15, -6, 21, -11, 12, 5, -21, -3, 5],\n [-9, 17, -17, 2, -18, -14, 24, 0, 10, -19, 26, -25],\n [15, -23, -17, -13, -2, 14, -13, -17, -19, -21, -22, -6],\n [22, -4, 10, -8, 26, 22, -7, -17, -9, -7, 21, -16],\n [-12, 5, -16, 25, 2, 13, 12, -26, 20, 0, 8, -19],\n [-15, 1, 21, -8, 2, 15, 15, -9, 7, 24, -8, -3],\n [7, 5, -25, 5, -19, 18, 26, -18, -4, 2, -20, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
89
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_962
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[13, 5, 13, -24, -17, 13, 26, 2, 18, -8, -2, -7],\n [20, 11, 19, -17, 24, -16, -13, 24, 4, -22, 16, 1],\n [-8, 6, -25, 2, -9, 19, -17, 11, -12, -5, 0, 0],\n [-5, -6, 4, 7, -21, -14, 13, -12, 0, 4, 21, 15],\n [-4, 19, 8, -19, 6, 1, -20, 9, 16, -14, 15, 4],\n [-14, 8, 23, -20, -5, 13, 25, 7, -18, 5, 8, -24],\n [-6, -14, 6, 9, -17, 9, -9, 4, 18, 13, -26, 4],\n [-1, -11, 11, -15, 21, 16, 16, 24, 2, -15, -22, 15],\n [-25, -15, -13, 20, 3, 8, 20, -10, -24, -18, -20, -7],\n [-15, -20, 2, 2, -9, -25, 21, -16, -1, 0, -8, 11],\n [-7, -3, 12, -14, -21, 13, 10, -26, 25, -25, 11, 14],\n [3, -3, 14, 11, 0, 3, -18, 10, -11, 8, 1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
89
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_963
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, 24, -18, 2, 24, 24, -6, -10, 6, 7, -1, -9],\n [7, 11, -2, 25, 24, 7, 23, 21, 18, -12, -25, -4],\n [18, -21, 12, -8, 7, 10, 19, -4, -12, -25, 11, -2],\n [17, -19, -16, 2, -22, 10, -7, -15, -11, -6, 10, 23],\n [-6, 1, 7, 26, -19, 19, 4, -6, -24, 20, -6, 2],\n [5, 22, -1, -14, -12, -25, 22, 6, 4, -26, -12, 12],\n [26, -12, -7, 25, -20, 9, 16, -15, -14, -22, 16, -21],\n [-22, 18, 12, 16, 20, -21, -21, -16, 0, -11, 18, -24],\n [-5, 5, -2, -9, -8, 21, 3, 8, 24, 19, 0, -9],\n [-14, 17, 4, 26, -24, 4, -3, 10, -5, 6, 18, -12],\n [11, 15, -13, 21, -12, 2, -1, -5, -23, 6, -22, 1],\n [22, 8, 15, 5, 2, 19, -3, 3, -18, 21, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
84
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_964
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 10, -4, 2, -14, 5, 17, -17, 16, 21, -21, -6],\n [8, -24, -6, -7, 23, 16, 7, -24, 18, 18, 13, 10],\n [26, -22, 23, -16, 21, -10, -23, -19, 14, 20, -5, 5],\n [0, -21, 4, -23, 20, 12, 3, 16, 26, 6, 4, 1],\n [-2, 22, -10, 4, 23, 9, 19, 16, -10, -17, 24, 21],\n [-5, 4, 3, 24, -7, -13, -12, 16, -8, 26, 13, 4],\n [10, -4, 17, -13, -5, 3, 21, -19, 17, 4, -11, 12],\n [-3, -6, -19, -9, 11, -21, -13, 3, -13, -20, -23, -8],\n [-2, -2, -8, 3, 16, 3, -12, 21, 2, 8, 6, 12],\n [13, -4, -4, 16, 10, 15, 25, 3, -11, 6, 0, -17],\n [-7, -23, -7, -12, 11, -12, 20, -10, -7, 22, -10, 26],\n [-15, -16, 3, -1, 21, -2, 18, -10, 14, -26, 23, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
89
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_965
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[-24, 26, 16, -16, 20, 1, 1, 3, 8, -20, 6, 21],\n [0, 2, 0, 15, 4, 20, -22, 7, 10, -6, -1, 16],\n [-22, 6, 15, -25, -4, 24, 16, 2, -9, 8, -17, 12],\n [6, 5, 15, 10, -4, -26, -10, 19, 9, 0, 21, 12],\n [-26, 11, -13, -23, 5, -6, 20, 16, 23, -25, -2, 11],\n [21, -13, -14, 17, -8, -15, 4, 7, 14, -4, -18, -11],\n [-3, -19, 10, 4, 5, 26, 15, -4, 11, 9, 5, -4],\n [-4, 6, 14, -1, 13, -24, -26, -14, 0, 23, 0, 17],\n [-5, -16, -12, 3, -9, 17, -3, 5, -5, -22, -22, -5],\n [21, 22, 24, 12, -5, -20, 23, -6, 8, -17, 23, -15],\n [10, -4, 11, -14, -24, -21, 3, 14, -24, -25, 3, 1],\n [26, 22, 22, 16, 13, 7, 4, -10, -18, -7, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
87
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_966
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[9, -23, 0, -19, -18, -6, 8, 1, 0, -20, 23, 18],\n [7, -13, 2, 19, 2, -6, 22, -25, 24, -17, -3, 0],\n [24, 24, 5, 18, -4, 21, 25, 17, 9, -6, -5, -4],\n [-15, -14, 7, -2, -25, 14, -6, 4, -9, -11, -13, 6],\n [19, -20, 11, -7, -23, -16, -21, 12, 23, -20, 18, 3],\n [15, -4, 1, 11, 8, -26, -3, 21, 1, 7, -10, -3],\n [4, -7, 2, 1, -13, 15, -1, 14, 17, -16, -11, 9],\n [2, 0, 2, 1, 5, 0, -16, 18, -19, 22, 26, 16],\n [-23, 25, -15, 5, -15, 24, -2, -3, -7, 23, 15, -20],\n [5, 24, -21, -8, 25, -9, -15, 16, 20, 10, -17, -4],\n [-9, -6, 20, -14, -25, -25, -9, 8, 21, 7, 14, -17],\n [10, 5, -2, -3, -6, 18, 12, 7, -1, 15, 12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
91
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_967
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 5, 14, 5, -19, -9, -26, -3, 20, -10, -9, -7],\n [-1, 23, 3, 10, 0, 12, -4, -1, -22, -13, 8, 26],\n [5, 18, -23, -5, 22, 6, -14, -19, 11, 19, -18, 17],\n [1, -26, -12, -20, -10, -15, 2, -13, -14, 26, 5, 15],\n [26, -2, 0, -3, -14, 2, 3, 0, -20, -14, -20, 8],\n [-21, -5, -13, -6, -9, 21, 2, -1, 12, 10, 23, 18],\n [9, 1, -16, -10, -15, 1, -3, 4, 10, 22, 2, -22],\n [8, -14, 24, 18, -18, 4, -4, -11, -7, 26, 20, -19],\n [21, -10, 23, -8, 16, 10, 18, 0, -12, -3, -22, 26],\n [20, 11, -18, -2, -12, 17, 0, 18, 26, -21, 12, -11],\n [24, 2, 6, -9, 9, 14, -26, -14, -21, -7, 11, 7],\n [-9, -20, 10, -11, -13, -13, -23, -13, -26, 6, -19, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
85
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_968
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, -7, -21, -26, -18, 5, 6, -9, 10, -8, 6],\n [-22, -15, -26, -21, -10, -19, -22, 8, 1, -12, 1, -3],\n [-1, -19, 8, -11, -20, -10, 24, 8, 4, -20, 24, -24],\n [-9, 26, 0, -10, 5, -16, -15, 19, 9, -15, -15, -7],\n [15, -24, 4, -22, -7, 13, 16, 20, 15, -26, -16, 18],\n [14, 9, 4, -3, -12, -25, 2, 14, -5, 14, -16, 4],\n [-7, 16, 12, -12, 8, -10, -23, 25, 4, 2, 3, -22],\n [2, -7, -18, 26, 10, -13, 17, -9, 22, -10, -10, -21],\n [-6, 19, 15, -17, 17, 1, 10, 18, -6, -26, 14, -23],\n [10, 18, 25, 21, -21, -2, -26, 9, 15, 8, -24, 17],\n [13, -3, -4, -1, -22, 7, 26, 25, -13, -3, 11, 6],\n [26, -10, 6, 17, 17, -12, 8, -13, -26, 19, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
90
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_969
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[18, 10, -15, 26, 8, 5, -25, 6, -9, 20, -11, -2],\n [-1, -22, -11, 17, -11, -16, -19, -24, 26, -11, -20, 1],\n [-25, 24, 8, 4, -16, 14, -16, -26, 3, 3, 6, -15],\n [-17, 17, 19, 16, -23, 15, 22, 6, 11, 4, 4, -22],\n [-6, -9, -9, -23, 23, -7, 26, -7, 21, 1, 20, -14],\n [8, -9, 6, 10, 9, -18, -1, -26, -2, -3, 3, 15],\n [-15, 17, -12, -7, 0, 2, -25, -12, 8, -17, -1, 7],\n [-19, -26, -12, -23, -24, 18, 15, -25, -8, -8, 19, 14],\n [-8, -7, 22, 10, -25, -2, 12, -5, 7, -5, -15, 19],\n [12, 19, -15, 21, 19, 26, 4, 26, 5, 9, -13, -1],\n [1, -26, -17, -4, 8, -12, 26, 18, -19, -25, -7, 14],\n [16, 2, -25, 13, 14, 17, 24, -12, 26, -23, 15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
90
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_970
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 13, 16, 10, -6, -12, 6, 26, 22, -15, 3, -23],\n [12, -16, 17, 0, 21, -9, -13, -12, 22, 7, -4, 8],\n [-22, -26, -1, -17, -12, 5, 15, -3, 9, 18, -11, -17],\n [7, 13, -13, -22, -9, -19, 4, 17, -9, -14, 10, -16],\n [-24, -11, -19, -10, 11, -14, 22, 8, 18, 13, -19, -8],\n [15, -12, -20, 23, -26, -14, 22, -8, -25, -5, -19, 16],\n [-2, -1, -15, -24, -6, -22, -15, 0, -26, 16, -24, 25],\n [26, -17, -14, -8, 4, -14, 25, 3, -13, 5, 15, 22],\n [11, 10, -13, 19, 10, 1, -7, -2, -16, 0, 2, -22],\n [-4, 24, 20, 22, -10, -24, 24, -22, -19, 6, -13, 15],\n [4, -19, -26, -22, 24, 12, -22, 7, 20, -26, -17, 11],\n [11, -13, -19, -2, 2, 23, 10, -6, 4, 19, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
89
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_971
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[14, -6, 26, -24, 5, -21, -20, 24, -12, 7, 19, 19],\n [-15, -9, -2, 11, -25, -6, -4, 6, 0, 16, 2, 20],\n [11, -10, -19, -6, -4, 25, -9, 17, -19, 25, -3, -18],\n [2, -16, 18, 9, -19, -23, 19, -3, 22, -25, -15, -15],\n [-1, -8, 23, -1, -3, 15, -2, 14, -11, -26, 5, 21],\n [-3, 13, 24, 7, 23, -7, -4, 1, 25, -9, 5, 26],\n [19, 12, 12, 1, 10, 25, -1, 0, 17, 0, 18, -10],\n [-12, 21, -14, -5, 16, 8, -4, -26, 11, -19, 26, -22],\n [12, 8, 14, -13, -25, -24, -8, -17, -25, 18, -13, -8],\n [18, -20, -24, -26, 25, -4, -14, 11, 17, -17, 8, 4],\n [6, -3, -14, 7, 26, -8, -7, -24, -8, 20, 4, -8],\n [15, 0, -16, 20, 13, -16, -10, 7, 23, -18, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
84
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_972
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -19, -14, 7, 15, -10, 21, 17, 11, -12, 4, 20],\n [21, -24, 18, 23, 8, 9, -22, -1, -1, 25, -3, -21],\n [-20, 25, 1, 18, -13, 12, -6, -16, -15, 23, 23, 7],\n [8, 25, -20, 26, -4, -26, -7, 5, 7, 23, -7, -13],\n [-22, -3, -6, -15, -25, -17, -14, 4, 19, -3, -1, 6],\n [14, -3, -26, -18, 4, -3, 16, -1, 12, 26, -5, 6],\n [5, 6, -18, -12, -5, -11, 8, -2, 8, -2, 19, 10],\n [22, 26, -17, -11, -9, 18, 23, 2, -10, -23, -23, 26],\n [-12, -23, -14, 23, 26, -21, -22, 6, -21, 7, -22, 21],\n [9, -14, 1, -20, -18, -1, 6, -4, 10, -1, 25, -16],\n [22, -14, 25, 0, -25, -11, 24, 2, -7, 5, -4, -18],\n [5, -23, 23, 15, 20, 18, 21, -17, -23, 21, -16, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
570
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_973
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -15, 13, -6, 18, 7, 7, 9, 23, -24, 12, -21],\n [-26, 14, -15, 12, -26, -7, 9, 11, 21, 20, -24, 23],\n [24, 18, -7, 19, 19, -19, -16, 17, -26, 3, 14, 25],\n [-13, -7, 19, 3, 18, -15, -15, 25, 12, -25, -4, -16],\n [21, -14, -9, -8, 0, -16, 26, 3, -26, -14, -19, -5],\n [-7, -13, -13, -11, -8, 12, 2, 11, -18, 23, -21, -1],\n [22, 9, -7, 14, -2, -19, 20, 13, 0, -6, -16, -8],\n [-14, 20, -22, -1, -20, -14, 21, -3, 21, -3, 7, 12],\n [-23, -7, -14, 26, 3, 10, -4, 17, -14, 14, 21, 11],\n [18, -13, 9, 14, -22, -16, -11, -15, -10, 4, -19, -15],\n [-19, -14, -4, -22, -19, -24, 16, -22, 21, 15, 15, -2],\n [5, -11, -16, -3, 14, -3, 12, 19, 19, -5, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
87
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_974
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[-26, -15, -4, -19, 6, -15, -10, 3, 12, 16, -14, -6],\n [-18, 1, -20, -9, 23, 15, 6, 19, -4, 26, -26, 12],\n [-8, -8, -23, -20, 2, 21, 12, -16, 2, -19, 18, -18],\n [-22, 4, -17, 16, -3, -10, 20, -16, 7, -3, -19, 17],\n [12, -3, -25, -19, 4, 20, 17, 8, -23, -15, 12, -11],\n [-5, -10, -2, 24, -12, -7, 4, 23, -22, 3, 0, 19],\n [-13, 19, -10, 3, 19, -23, 15, -23, -24, -20, 25, 12],\n [8, -14, 9, 24, 9, 20, 1, 25, 5, 17, -13, 9],\n [8, 11, 20, -22, -21, -15, 12, 25, 16, 22, -15, -19],\n [18, -9, 24, -9, -17, -21, -22, 18, -4, -2, -20, 16],\n [18, -22, 4, -8, 24, 9, 17, 23, 8, 16, -18, -3],\n [-9, 17, -18, 26, 11, 7, 6, -23, -7, -4, 23, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
532
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_975
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 16, -26, 12, 16, 5, 21, 24, 1, -3, -14, 6],\n [-15, 6, -13, -14, 21, 10, 0, -23, -23, 13, 20, -11],\n [12, 13, -9, -11, 20, 4, -1, -4, 25, 21, 21, -25],\n [11, -16, -22, 20, -13, -11, 21, 14, 24, 10, -6, -19],\n [-13, -18, -15, -12, -2, -6, 19, 7, -1, -23, -2, 13],\n [5, 2, -5, 7, -8, 23, -21, -7, -11, 6, -18, -5],\n [7, 20, -8, 14, 14, 10, -23, -22, -15, 6, 24, -18],\n [17, 2, 3, 2, 18, 25, -10, 8, -14, 19, 9, -23],\n [-26, 11, 16, 0, 1, -2, -3, -25, -4, 24, -5, -9],\n [25, -11, 5, -24, -26, 7, 18, -1, 19, 13, 19, -21],\n [17, 9, -18, -20, 4, 6, -23, -21, -16, 13, -14, -18],\n [24, -9, -1, -4, -4, 24, -22, -17, 20, 13, -8, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
102
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_976
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-12, -8, -23, 8, 10, -15, 4, -11, 13, -6, -7, 23],\n [-5, 17, -22, -19, -19, 6, 0, 3, 1, 13, 24, -9],\n [25, -17, 13, -14, 10, 16, 13, 24, -4, -8, -4, 14],\n [-11, -15, 9, -23, -15, 0, -13, -11, 26, 2, -15, 26],\n [-12, -26, 1, -19, 5, -2, 8, -15, -21, 4, -18, 25],\n [-2, -7, 11, -12, 9, -1, 10, 22, 14, -16, 0, 12],\n [-6, 26, -21, -16, 19, 4, -16, 24, 18, -19, -8, 5],\n [-1, 19, 10, 16, 26, 7, 20, -11, 6, 8, -17, 9],\n [-4, 21, 14, -23, -8, -8, 15, 15, -13, 6, 21, 25],\n [10, 19, -9, -19, -17, 4, 8, -2, -2, 13, 20, 19],\n [-24, -12, 5, -6, 6, 12, 0, -13, 9, 19, 14, -17],\n [-3, -17, 4, 12, 20, 1, -23, 23, 21, -8, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
515
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_977
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -21, 24, -17, 18, -11, -25, -19, 14, 12, -22, 3],\n [-19, 2, -24, -14, 25, 0, 24, -15, 24, 13, 24, -21],\n [12, 22, -12, 19, 20, -19, 13, 25, -3, 5, 4, 11],\n [-24, 21, 8, -14, 20, 15, 14, -12, -1, -15, -2, 1],\n [-8, -18, 8, 18, 9, 5, -24, -22, 25, 14, -9, 15],\n [24, -12, -2, -9, -20, -5, -3, 8, -5, 0, -25, -16],\n [20, -1, -20, -8, 10, -8, -17, 20, 4, -26, -10, -17],\n [9, -6, -10, 15, 17, 16, -24, 24, 23, -5, 3, 23],\n [9, -22, -24, -26, -10, 22, 25, -5, 0, 6, -6, -26],\n [-23, 14, -21, 1, -15, 18, 25, -4, 16, -15, 15, 21],\n [22, 18, 6, -6, 14, 13, 0, 23, 5, -26, 5, -24],\n [6, -26, -3, -8, -9, 5, 17, -21, -10, -15, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
94
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_978
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, -25, -7, -7, 20, 12, 24, 5, -24, -1, 14, -15],\n [23, -24, 1, -18, -1, -21, -22, -18, 19, 7, 1, -1],\n [8, -26, -23, -14, 13, 26, -6, -9, -7, -23, 5, 0],\n [-2, -20, 18, 3, -4, 2, -6, 6, -9, 0, -13, 13],\n [4, 15, -19, -24, 8, 11, -16, 9, 25, 21, 16, 25],\n [7, -4, -22, 3, 10, -11, -13, -20, 26, 6, -25, 19],\n [-22, 18, 18, 12, -12, 15, -25, -3, 2, 2, -6, -2],\n [-5, -8, -14, 11, 6, 6, -15, 19, -4, 2, 2, 16],\n [-26, -3, -22, 8, 18, -22, -14, 5, 15, 0, -3, -24],\n [-26, 2, 18, -5, -22, 16, -6, -15, 1, -16, -12, 11],\n [8, 21, 18, -11, 10, -12, 5, -11, 6, 13, -7, 10],\n [12, 5, -17, -11, -22, -7, 0, 16, 23, -7, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
85
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_979
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, 23, -12, 11, 0, 15, -10, -17, 9, 13, -22, 24],\n [23, 21, 0, 1, -23, -20, -19, -12, 14, 2, 12, -18],\n [-7, -26, -20, 7, 20, -17, 14, 21, -21, -2, -15, 13],\n [14, 12, -13, -16, -15, -8, 15, 1, 26, -8, 2, 18],\n [8, -4, -11, 10, -6, 13, -26, 19, 25, 10, -2, -11],\n [6, -2, -5, -24, -24, -16, 16, 25, -22, 17, -2, 11],\n [26, -11, 5, 2, -21, -5, -18, -17, -13, 20, 12, -7],\n [-22, -20, 13, -13, -12, -10, -7, -11, 14, -6, -16, -23],\n [-2, -25, -25, 0, 4, 20, -19, 21, -19, -22, -5, 16],\n [-22, 13, 21, -21, 11, -20, -9, -2, -24, -2, -6, 4],\n [19, 22, 15, -11, 25, -5, 24, 2, -15, 19, 16, -26],\n [-1, -17, -2, -2, 16, -23, -9, 16, -19, -20, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
571
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_980
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[15, 17, -6, -25, -14, 5, -14, 2, -22, -1, 11, 5],\n [21, -9, -10, -7, -12, -12, 20, -23, -18, 17, 19, 6],\n [-17, 20, 16, -26, 13, 26, -18, -5, -1, 8, 6, -17],\n [11, -8, -23, -8, -20, -15, 0, 5, 0, -6, -22, -8],\n [24, 25, 26, -20, -13, -18, 10, 23, -18, -22, 21, -18],\n [25, 16, 3, -13, -24, 25, -3, 1, 12, -16, -10, -9],\n [24, -10, -2, 14, -13, -6, -16, 20, 0, -23, 24, 14],\n [7, 13, -20, -9, -8, -9, -12, -16, -15, 8, 9, 26],\n [23, -15, -11, 1, 17, 12, 17, 9, 3, -11, -11, 22],\n [-7, -18, 19, -22, 4, -9, 17, -5, 12, -25, 23, -24],\n [20, 1, -16, -17, -7, 4, 26, 24, 18, 21, 25, -5],\n [-9, -15, -12, 7, 18, 1, 17, -12, 8, -10, 11, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
565
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_981
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 25, -2, -23, 0, 15, -5, -3, 26, -8, 14],\n [0, -8, 20, 14, -14, 4, -25, 0, -19, -15, 2, 2],\n [-5, 3, -18, -22, 9, -14, 20, -25, 6, -23, -17, 6],\n [-25, -15, -11, 8, -18, -24, 1, 25, -11, 13, -8, -16],\n [11, 19, 4, -26, 17, 3, -6, -12, -11, -23, -3, 13],\n [-4, -10, 8, -1, 8, -12, -12, 0, -19, 26, -12, 26],\n [-19, 24, -23, -26, -2, 8, -19, 22, -10, 1, -21, 16],\n [-21, -26, -24, 25, -18, -12, 13, -7, -11, -17, -13, -11],\n [-12, 14, -1, -17, 13, -15, 10, -13, -2, 3, 26, 3],\n [8, -12, 4, 11, 24, -9, -20, -24, -22, -2, -11, -12],\n [-7, 14, -5, 8, 0, -15, 6, -3, -1, 25, 11, 7],\n [-14, 1, -7, -19, 23, -11, 7, 5, 21, 3, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
517
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_982
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, -18, 4, -8, 16, 7, -11, -3, -11, -12, 4, 25],\n [-20, 17, -12, -25, 12, 25, -5, -3, -2, -15, 25, 24],\n [-13, 7, 19, -7, -13, -9, 8, -10, 21, 18, -4, -5],\n [22, 4, 2, -2, 5, 4, -21, 10, -10, 20, 4, -6],\n [-25, -20, 0, -5, -23, 0, 24, 18, 5, -6, 8, -18],\n [1, -17, 23, -4, -3, 21, -23, -10, 21, -3, -26, 10],\n [-25, 13, 21, 26, -21, -13, 9, -6, -2, -19, 25, 0],\n [-13, -23, 19, -19, 0, -8, 3, 1, 0, 10, 17, -24],\n [22, 1, -8, 11, 0, -4, -8, -14, 3, 14, 23, 19],\n [-19, 2, 16, 23, 23, 20, -21, -10, 2, 13, 25, 21],\n [-25, 6, 18, 12, 24, 8, 4, -15, 4, -1, 17, 5],\n [22, 22, 23, -24, -7, 26, 20, -25, 12, 18, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
551
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_983
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[24, -21, 15, -19, -1, -17, 11, 17, -26, -25, 16, 8],\n [-26, -23, -24, -3, -10, 0, -2, -7, 12, 17, 24, 3],\n [-21, -20, 0, -22, -1, 9, -16, 15, -4, -24, 23, -12],\n [17, 26, -2, -11, 5, -1, -22, -17, -16, 6, 1, -11],\n [17, -25, 2, 17, -25, -5, -16, 8, 5, 10, 20, -22],\n [0, 24, -15, -19, -24, 5, -5, 1, -1, 18, -6, -16],\n [0, 16, -20, 11, 16, -18, 20, 21, 7, 16, -1, -21],\n [-15, 10, 23, 17, 13, -26, 8, -23, 13, 23, -19, -25],\n [-15, 24, -19, 14, 4, -6, 4, 5, -7, 20, -8, 20],\n [3, 24, -18, -7, -9, 21, -14, 3, 20, 2, 25, 24],\n [3, 20, -22, -23, 23, 19, 4, 15, 6, 22, -26, -8],\n [-12, -25, -23, -24, -4, 13, 16, 26, -21, 3, -4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
99
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_984
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[22, -12, 18, 20, 23, -10, -18, -25, 23, 26, 14, 2],\n [24, 15, 19, 4, 5, -26, 3, 1, -1, -9, -26, 14],\n [25, 21, -8, 8, 6, -19, 25, 22, 0, 10, 15, -19],\n [17, 21, 5, -8, 3, 9, -17, 9, -11, -24, -5, 24],\n [-5, -6, 3, 0, -25, -19, 16, -4, 12, 11, 14, 9],\n [-13, 26, 4, 20, 24, -8, 3, -11, -15, -3, 15, 11],\n [5, 23, -8, 13, 20, -22, 18, 19, 20, -25, 24, 5],\n [0, -25, 10, 10, -5, 7, 0, -10, 12, -4, -17, -5],\n [-12, 23, 13, 9, 16, 12, -11, 1, 8, 5, 25, 20],\n [-3, -6, 14, -8, 5, 19, 7, 25, -9, -16, -16, -9],\n [-26, 13, -26, -3, 14, -5, -20, -10, 22, -15, -26, -24],\n [20, 3, -4, -19, 17, -10, -21, -15, -6, -16, -25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
546
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_985
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[21, -7, 4, 9, -3, -5, -18, 22, -10, 7, 26, -16],\n [-21, 24, 22, -4, 21, 22, 20, 18, 22, 13, -1, -18],\n [-19, 22, 25, 19, -1, 25, -15, 6, 18, -20, -11, -1],\n [-2, 8, 16, 2, 23, 15, 1, -11, -8, 13, -21, 0],\n [-24, 7, -10, 5, -3, 8, 8, 5, 26, -12, 10, -2],\n [-6, -13, -4, -20, -22, -13, -8, 16, -20, -19, -23, -21],\n [10, -17, 23, 22, -13, -14, 11, 21, 15, -20, -6, 6],\n [-16, -21, 9, -16, 7, 3, -18, -20, 19, 10, -9, 22],\n [2, -6, -13, -11, -1, 26, 4, 24, -16, 5, -1, 6],\n [10, -16, -7, -14, 7, 6, 16, -23, -19, 23, -16, -25],\n [-5, -23, 15, -2, 25, 17, 23, -12, -15, 6, 5, -21],\n [16, -26, 11, 13, 11, -7, 17, 23, -22, 10, 13, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
559
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_986
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded sum of all singular values from the SVD of:\n[[-25, -13, -10, 23, -9, -10, 13, 4, 15, 4, 9, -8],\n [5, -10, -3, 18, 13, -23, -22, 25, 26, 20, 25, 14],\n [-26, -1, 15, -24, -4, -14, -5, 4, -19, 3, 19, -15],\n [-5, 16, -12, 3, -3, 22, -2, 26, -25, -26, -7, 18],\n [17, -1, -19, -8, 4, -12, 15, 25, -25, -25, 23, 2],\n [6, -17, 21, 19, -6, -6, 16, -14, 24, -11, -8, -3],\n [-4, -23, 4, -19, 15, -2, -4, -16, 1, 18, -4, 18],\n [26, 18, 16, 21, 20, 9, 7, 21, -16, 22, -19, 7],\n [-19, 25, -10, -5, -19, -26, -13, -22, 0, 21, 22, -4],\n [-15, 25, 3, -19, 13, -25, -22, -14, -10, 8, -12, -15],\n [8, 15, 21, 24, -24, -17, -25, -12, -20, -7, -19, 20],\n [-1, -19, 3, 18, -7, 4, 2, 26, 3, 4, -23, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
590
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_987
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 3, -5, 5, -15, 3, -22, -25, -21, 16, 16, 8],\n [-17, -11, 21, -5, 24, -13, 13, -11, 21, 12, -26, -11],\n [-7, 5, -25, -5, -22, -25, 22, 12, 17, 14, 5, -16],\n [-1, 24, 4, -12, -15, -1, 20, 22, -16, 22, -5, 1],\n [-5, -6, 17, -17, 26, 11, -2, 12, -13, 21, 8, -18],\n [11, 10, -23, -12, 2, -17, 6, -20, 26, -10, -23, -17],\n [-26, 15, -7, -20, -18, 5, 1, 1, -25, -23, -10, -21],\n [-19, 19, -15, -8, 2, 5, 1, -22, 16, 22, -15, -22],\n [6, 26, 4, -2, -20, 12, -2, 2, -16, -6, -4, -21],\n [11, -4, -17, 8, -22, -9, -6, -12, -15, 13, -20, 1],\n [8, -20, -9, 21, -7, -1, 7, 12, 10, -13, -12, -11],\n [-4, 7, -7, -8, -17, 23, 7, 13, 11, 24, -19, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
543
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_988
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -26, 18, 22, 15, -9, 22, -4, -11, 20, 15, -2],\n [-22, -16, 16, 19, -21, 20, -13, 17, -1, 0, -13, 16],\n [2, -9, -9, -13, -20, 1, -22, 22, 13, 22, -12, 22],\n [7, -22, 25, -23, -10, -26, -17, 7, 23, 6, 15, 0],\n [-3, 24, 26, 16, 1, -8, -25, -26, 18, -2, -24, -20],\n [-2, -12, 25, -23, -25, -21, 8, 7, -6, -5, 25, 14],\n [2, 22, -13, 19, 15, 22, -20, -22, -12, 25, 21, -13],\n [10, 8, 22, 1, 10, -1, -21, 21, 20, -19, -17, 19],\n [-5, -17, -8, 5, -13, -3, -9, 0, -9, -23, 2, 4],\n [-24, -10, -24, -20, 4, 0, 11, -24, -14, -9, -5, 18],\n [-15, 12, 23, -8, 19, 3, 26, 17, 4, -10, 1, 14],\n [-23, -22, 8, -20, -11, -1, -7, -23, 5, -18, -24, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
574
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_989
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[24, 5, 18, 23, 26, -25, 1, -22, -13, 18, -17, 17],\n [5, 11, 20, 1, -26, -24, 12, -2, 3, 9, 11, 3],\n [-12, 4, 16, -2, -4, 19, -1, 23, -5, -11, -10, 0],\n [-10, -10, -7, -25, 9, -4, 1, -1, 16, 23, 18, 24],\n [-15, -10, 14, 1, -16, 11, 18, -16, -12, -1, 2, -1],\n [-4, -16, -23, 25, -17, 15, 13, 6, -23, 9, -19, -5],\n [-6, 3, 3, -11, 19, -25, -4, 7, 3, 1, -22, 8],\n [-18, 11, 19, -8, 14, -20, 26, -1, -13, 5, 12, 3],\n [-17, -25, 11, -22, -21, 1, -12, 2, 3, 17, 17, 4],\n [4, 8, -1, -18, 26, 21, 26, -20, -14, -7, 24, 1],\n [20, 3, 24, 14, 0, 22, 3, 14, -3, 3, -26, -3],\n [-7, -19, -10, 4, -23, 7, 6, 2, 25, -8, -13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
86
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_990
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-26, -5, 19, -23, 25, 8, 23, 25, 12, 6, -11, 18],\n [8, -15, 9, 24, 19, -20, -23, -15, -20, 19, -12, -21],\n [-10, -10, 17, -23, -20, 9, -20, 11, 9, 15, 6, -4],\n [1, 1, 6, -5, 12, -5, -23, -3, -11, 23, 19, -14],\n [-12, 6, 3, -4, 15, 23, -22, 26, 12, 7, 14, -22],\n [23, 17, -23, -11, -16, 24, 0, -4, 6, -4, -14, -22],\n [5, 13, -17, -12, -12, -4, 18, 7, -23, -14, 2, -18],\n [-22, -15, 7, 25, -19, -7, -11, -3, -7, -19, 2, -8],\n [25, 15, -2, 10, -24, -8, 25, 7, -20, -18, -19, -8],\n [10, -19, 20, -3, -25, 2, -15, 22, 21, -22, -26, -14],\n [12, -19, -8, 19, 1, -17, 22, 23, 7, -17, -9, -17],\n [-6, -25, -18, 21, 11, -20, -24, -1, -20, 25, 13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
101
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_991
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, 8, 19, 0, 11, 8, -20, 11, -7, -4, 23, 2],\n [26, -5, -6, 15, -22, 13, 26, 20, 21, 16, -17, 6],\n [-26, 22, 9, -11, -8, -22, -4, -24, 19, 23, -9, -24],\n [15, 24, -24, -13, -19, 5, 3, -8, -21, -18, 21, 3],\n [-21, 21, 4, 15, 26, -6, 13, -12, 16, -6, 16, -13],\n [11, -15, -12, 10, -16, 3, 8, 8, 15, 15, 25, 10],\n [1, 14, -17, -16, -25, -25, 19, -10, 13, 22, -14, 11],\n [-25, 25, -1, 0, 26, 23, 26, 12, 10, 6, -9, 2],\n [-23, 21, 3, 11, -10, 21, 13, -14, -7, 9, -22, 0],\n [-4, -16, 8, -9, 17, 26, -24, 4, 16, -12, 8, 12],\n [-21, 2, 0, 1, -24, -4, -1, 0, -21, 6, -13, 26],\n [25, -24, -8, 13, -8, 0, 23, 10, 24, 15, 21, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
552
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_992
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[13, 14, -25, 18, -13, 22, 1, -17, 11, 1, -14, 1],\n [18, -10, -22, 20, -22, -8, 7, 14, 16, 12, 4, -2],\n [24, -26, 23, -5, 11, 21, 2, -25, 14, 15, 3, -10],\n [9, 25, -13, -10, 1, 26, -21, -18, -16, -19, 20, 25],\n [-4, -21, -6, -10, 12, -16, 12, -22, 4, -11, -15, 3],\n [-2, -15, -24, -10, 26, -23, -21, 23, 21, -12, 5, -6],\n [-25, 19, 21, -24, -2, 0, 0, -4, -18, 9, -16, 12],\n [-20, -14, -20, 15, 20, 16, -14, 26, -21, -23, 16, -2],\n [-7, -18, -2, 10, -18, 14, 17, -8, -15, 8, -23, -8],\n [23, 17, 19, -21, 4, 20, 24, 5, -18, 21, -1, -21],\n [10, 16, 7, 13, 24, -6, 15, 0, 25, -8, 0, -24],\n [-2, 7, 24, -6, -16, 0, 1, -23, 17, 14, 26, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
95
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_993
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, 12, -23, 10, 22, 16, -23, 23, -4, -18, 13],\n [-3, 2, -20, -9, -25, 1, 16, 14, 2, 18, -10, 4],\n [-10, 4, -4, -17, -21, 11, 20, 0, -16, -7, 19, -22],\n [5, -22, -5, -26, -7, 24, -12, -16, 5, 1, 1, -10],\n [7, -3, -25, 0, -18, 25, -8, 9, 2, -16, 5, 0],\n [25, 12, -3, 0, 0, 13, 5, 18, 17, -5, 22, 15],\n [5, 21, 19, 8, -26, 26, 7, -26, 15, 8, 2, -9],\n [-21, -21, 0, 12, 26, -8, 11, -24, 26, 24, 11, -7],\n [-25, -20, -22, -2, 15, 26, -14, -15, -22, -15, -9, -24],\n [-23, 16, -8, -6, -2, -24, -20, -18, -23, -4, -16, -8],\n [-26, -23, -18, 15, -20, -1, -6, 21, -17, -17, -26, 9],\n [-24, 8, 18, -15, 0, -10, -8, -17, 16, -1, -19, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
93
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_994
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, -25, -15, 12, 13, 4, 2, -19, -12, -1, 21, 9],\n [14, -23, 23, 6, -15, 23, 26, -16, 3, 26, 18, -1],\n [23, 3, 9, 6, 18, 4, -25, -12, -25, 26, -15, -9],\n [-19, -24, 8, 6, 4, -23, -4, 10, 18, 18, 8, 13],\n [26, 11, -26, -24, -17, 25, 3, 1, -11, -23, 26, 21],\n [18, -23, -4, 13, -4, 23, -12, -14, -26, 10, -3, 17],\n [-26, 18, 23, 18, -14, 11, -10, 24, 3, -7, 15, -22],\n [14, -22, 19, 10, -11, -6, 7, 19, 23, -21, 15, -21],\n [-17, 4, -21, -24, 17, 25, -2, -7, 8, -26, 25, 4],\n [-13, -24, -11, -13, -24, -21, -18, 6, 14, -15, -25, 16],\n [19, -24, -14, 4, -18, 13, 14, -19, -5, -1, -11, 5],\n [8, 9, -26, -20, 23, 22, 13, 15, 21, -16, -16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
590
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_995
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Calculate the rounded largest singular value from the SVD of:\n[[14, -23, -2, -24, -17, -22, -15, 7, -15, 26, 11, -12],\n [-6, -23, -16, -17, -20, -18, -9, 20, 0, 16, 1, 5],\n [-17, 7, -22, -7, 3, 6, -8, -25, -9, -13, -22, -9],\n [18, 24, -12, -4, 23, -23, 7, -3, -15, 2, -21, -3],\n [20, -5, -10, 5, -2, 26, -1, 0, -20, 8, 7, 0],\n [-19, 8, -9, -4, 3, -11, 4, 11, 23, 7, -26, -18],\n [9, 17, -23, 18, -7, 18, -10, 17, -17, 19, 16, 13],\n [-14, 11, 17, -11, 12, 6, 0, 10, 21, -11, -12, -11],\n [-21, 2, 13, -10, 13, -20, 7, 18, 9, -1, -1, -16],\n [-2, 9, 15, 21, -25, 14, 1, -26, -21, 13, 9, -26],\n [22, -12, -26, -8, -2, -13, -5, -4, -20, 7, -16, -11],\n [20, 11, -18, -23, 18, 13, 8, -4, -3, -23, 3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
92
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_996
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 25, 11, 7, 7, 4, 4, 5, 9, -5, -8, 18],\n [8, 11, 15, -12, 11, -19, 5, 9, 10, 3, 24, 21],\n [-4, 16, -20, -5, 9, 12, 1, -15, -24, 18, 11, 17],\n [9, -6, -5, -4, -20, -20, -6, 17, -13, 15, -20, -22],\n [10, -8, -2, -15, -18, -26, 25, 16, 2, 16, -8, -12],\n [9, -9, -5, -5, 3, -20, 21, -21, -14, 25, -13, -25],\n [15, -11, 12, 19, 6, -26, 3, -16, -13, 10, 10, 26],\n [8, -13, 21, -5, 4, -9, -17, -3, -3, 5, 10, 7],\n [26, -17, 19, -13, -4, 5, 20, -15, 14, -3, 7, 20],\n [-7, 2, -11, 25, 13, 23, 15, -18, 17, 23, 25, -24],\n [-17, 13, -26, -20, 4, 14, -14, -5, -11, -5, -21, 26],\n [19, -26, -25, 0, -15, -21, -25, 10, -17, -10, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
525
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_997
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, -7, -9, -18, 5, -10, -8, 22, -14, -26, 18, 11],\n [17, 11, 9, -17, 8, -1, 21, 6, 13, -19, -7, -25],\n [12, 13, 1, 2, 26, -2, -1, -19, 3, 25, -26, 1],\n [3, -14, 14, 22, -6, -6, 13, -16, 0, -22, -14, -15],\n [13, 6, 3, -24, 21, -4, 4, -21, -16, 10, 12, 20],\n [18, 10, 12, 24, -21, -9, -26, -9, 25, -16, 15, -21],\n [-22, -3, -25, 21, 8, 7, 15, -25, 25, -15, -25, 20],\n [23, 8, 2, 6, -22, 16, 25, 16, 6, 12, -14, 4],\n [9, -8, -2, 16, 8, 26, 10, 12, 6, 16, -24, 24],\n [20, 15, -3, -24, -20, -14, -3, 11, 3, -22, -4, 14],\n [17, 0, -9, 13, -7, -21, 3, 23, -21, 23, -10, 16],\n [26, 9, -12, 25, -10, -2, 17, 3, 16, 13, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
554
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_998
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 21, 21, 22, 15, 15, 8, -16, 1, 17, -7, -25],\n [14, 6, 9, -17, 18, -8, -2, 0, 8, -4, 16, 7],\n [-19, -25, -2, -18, -2, 18, 2, -5, -13, 25, 21, 16],\n [21, -16, 23, 24, 24, -14, 6, -24, 20, 25, 9, 24],\n [21, 15, 5, 9, 16, 9, 8, -22, -15, -8, 13, 0],\n [8, -17, 24, 1, 6, 20, 20, 16, 9, 8, 22, -10],\n [-16, 9, 10, -9, 4, 8, 1, -26, 4, 25, 0, 13],\n [-15, -15, 0, 0, 24, 19, -10, 25, -2, 3, -17, 13],\n [-12, -8, -23, -12, 10, -12, 6, 24, -14, -10, -8, -14],\n [-21, 13, 3, 9, 4, 26, -14, -3, 2, 22, 19, -25],\n [-11, 25, -15, 1, -1, 5, 15, -23, -22, -10, -7, 13],\n [2, -2, -9, -5, 26, -19, 13, 20, 13, -17, -10, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
527
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_999
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
{
"role": [
"user"
],
"content": [
"Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[21, -7, 0, -25, 25, 2, -21, -7, 10, -8, -16, 21],\n [-9, 12, -5, 24, -13, 15, -21, -6, -19, -9, -5, -21],\n [8, 8, 19, 18, 26, -18, -11, -16, 21, -6, 15, -4],\n [18, -7, -10, 4, 25, -9, 2, 21, 5, -19, 23, -18],\n [19, -21, -22, 18, -14, -2, 4, 7, -10, -1, -7, 23],\n [-21, 5, 6, -7, 20, -16, 20, 25, -17, 16, 12, -8],\n [0, 13, 7, 9, -7, 19, -22, -17, 5, 13, 13, 1],\n [26, 2, 21, -5, -18, -25, -14, 8, 0, 3, 2, 8],\n [10, 24, -1, -23, 8, -17, -7, 22, -17, 3, -16, -11],\n [-20, -4, 13, -26, 18, -20, 14, -23, -25, -10, 13, -18],\n [-16, 17, -8, -13, -12, 20, -19, 6, -25, -25, -7, -4],\n [-9, 3, -6, 9, -24, -10, -3, 11, -23, -18, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
86
|
math
|
train
|
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