id
string | setting_key
string | difficulty
string | level
int64 | messages
list | ground_truth
string | dataset
string | omega_split
string | __index_level_0__
int64 |
|---|---|---|---|---|---|---|---|---|
math_arithmetic_matrix_determinant_level_6_6_100
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, 23, -6, -10, -18, -10, -16, 0, -26, -10],\n [0, -22, 29, 19, 14, -22, -22, -22, -17, 27],\n [0, 0, 27, -27, 12, -1, -19, 6, -2, -15],\n [0, 0, 0, -16, 29, 15, 2, -23, 10, -3],\n [0, 0, 0, 0, 10, -18, 28, 2, -9, 11],\n [0, 0, 0, 0, 0, 17, 22, -6, -5, -6],\n [0, 0, 0, 0, 0, 0, -21, 30, 0, -29],\n [0, 0, 0, 0, 0, 0, 0, -19, -2, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
math
|
train
| 411,332 |
math_arithmetic_matrix_determinant_level_6_6_101
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, 12, -27, -16, 13, -16, 6, 24, -5, -14],\n [12, -23, 10, 14, -21, 19, -13, 2, 8, -26],\n [-27, 10, 23, 6, 22, -25, 3, 16, 8, 12],\n [-16, 14, 6, 14, -12, -17, 20, 12, 8, -4],\n [13, -21, 22, -12, 22, -16, 8, 24, 10, -4],\n [-16, 19, -25, -17, -16, 15, 10, 26, 12, 6],\n [6, -13, 3, 20, 8, 10, 11, 5, 4, -2],\n [24, 2, 16, 12, 24, 26, 5, 3, 4, -10],\n [-5, 8, 8, 8, 10, 12, 4, 4, -27, 7],\n [-14, -26, 12, -4, -4, 6, -2, -10, 7, -26]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
417
|
math
|
train
| 411,333 |
math_arithmetic_matrix_determinant_level_6_6_102
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[27, -12, -12, 6, 10, 6, -12, -12, -4, 10],\n [-12, -7, -23, -6, -8, 14, 18, 4, 10, 9],\n [-12, -23, -13, -20, -6, -15, -8, 26, 0, 0],\n [6, -6, -20, -14, -19, -6, 22, 18, -10, 24],\n [10, -8, -6, -19, 23, -10, 5, -6, 12, -12],\n [6, 14, -15, -6, -10, 21, -17, 14, -5, 6],\n [-12, 18, -8, 22, 5, -17, 13, 11, 10, -16],\n [-12, 4, 26, 18, -6, 14, 11, -1, 4, -1],\n [-4, 10, 0, -10, 12, -5, 10, 4, 14, 11],\n [10, 9, 0, 24, -12, 6, -16, -1, 11, 19]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
854
|
math
|
train
| 411,334 |
math_arithmetic_matrix_determinant_level_6_6_103
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -9, 12, -4, 4, 1, 20, 4, -10, -7],\n [-9, -18, 10, -24, 28, -10, 16, 1, 16, 10],\n [12, 10, -25, -3, 22, -20, -14, -8, 6, -13],\n [-4, -24, -3, -21, 2, 1, 9, 25, 4, 3],\n [4, 28, 22, 2, 6, -20, 19, 12, 0, 8],\n [1, -10, -20, 1, -20, 10, -5, 4, 2, -24],\n [20, 16, -14, 9, 19, -5, 8, 16, 21, -16],\n [4, 1, -8, 25, 12, 4, 16, 18, -12, 13],\n [-10, 16, 6, 4, 0, 2, 21, -12, -28, 5],\n [-7, 10, -13, 3, 8, -24, -16, 13, 5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
217
|
math
|
train
| 411,335 |
math_arithmetic_matrix_determinant_level_6_6_104
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -5, 4, 13, 30, -30, 0, -1, -12, 28],\n [-2, 27, 29, -5, -8, 22, -8, 6, -12, 8],\n [1, -3, -28, -12, -7, 25, -4, -9, -23, -14],\n [-17, 0, 20, 29, -13, 30, -9, -24, -4, 6],\n [20, -14, 18, 4, 14, -28, -29, -28, -10, 28],\n [6, -20, 28, -30, 29, -12, -10, 21, -3, -13],\n [-21, 12, 6, -12, 22, -17, 29, -30, -4, -19],\n [12, 24, 6, 12, -6, -24, 12, 29, 17, -1],\n [-3, -23, -8, -19, -6, -22, 15, 1, -14, 19],\n [7, 9, 13, -27, 26, 19, 7, -1, -7, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
math
|
train
| 411,336 |
math_arithmetic_matrix_determinant_level_6_6_105
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[18, 8, 27, -22, -7, -7, -16, -24, 25, 25],\n [-11, 20, 29, 5, -16, 14, 9, 13, -8, -26],\n [-13, -22, 11, -9, 3, 28, -30, 23, 12, -1],\n [-12, -28, -3, -21, -22, -3, -20, -15, -8, 4],\n [23, -20, -7, 4, 22, -10, -17, -4, 14, -30],\n [-4, 14, 6, -5, 19, 26, 7, 28, 19, -20],\n [27, 23, 16, -20, -26, -26, -15, -17, 25, 2],\n [21, -7, -26, 11, 15, 0, 20, 4, -14, 30],\n [-19, 13, 5, 8, -24, 29, -17, 25, -15, 0],\n [16, -10, 14, 5, 20, 12, -9, 12, -5, 22]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
237
|
math
|
train
| 411,337 |
math_arithmetic_matrix_determinant_level_6_6_106
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -27, -4, 15, -29, 12, 5, 24, 7, 5],\n [-26, -3, -22, 30, -17, -10, 27, 25, 29, -19],\n [22, 20, 16, 10, -16, 16, -3, -20, -11, -4],\n [1, 26, 18, 26, 18, 25, 19, -18, -27, 17],\n [29, -17, -25, -28, -1, 11, -19, -25, -6, 29],\n [-4, 21, 4, 18, 4, 29, -24, -11, 12, -21],\n [-20, 29, 10, -24, -15, -28, -6, -8, -3, 21],\n [-10, -27, 25, 20, 12, 14, 12, -23, 19, -1],\n [5, 29, 0, 1, 6, 5, 19, 5, 28, 7],\n [21, 3, -1, -4, 20, -23, 3, -16, 22, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
364
|
math
|
train
| 411,338 |
math_arithmetic_matrix_determinant_level_6_6_107
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-23, -3, 27, 7, -24, 21, -2, -2, -1, 12],\n [0, 11, 14, 1, -12, 23, 19, -25, 12, 11],\n [0, 0, 7, -24, -13, 0, -26, 29, -25, -12],\n [0, 0, 0, -21, 17, 9, -3, 20, 9, -21],\n [0, 0, 0, 0, -5, 30, -4, -21, 19, 7],\n [0, 0, 0, 0, 0, 10, 16, -23, -8, 9],\n [0, 0, 0, 0, 0, 0, 24, 9, -19, 13],\n [0, 0, 0, 0, 0, 0, 0, -5, 7, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, -12, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,339 |
math_arithmetic_matrix_determinant_level_6_6_108
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-29, -22, -1, -6, 0, -2, -17, -3, -23, 8],\n [0, 6, -4, 22, -22, -18, 10, -11, 25, -15],\n [0, 0, -28, -16, -30, 18, 25, -16, 25, -15],\n [0, 0, 0, -12, -21, -23, -11, 26, -22, -24],\n [0, 0, 0, 0, -8, 8, 10, 5, -5, 9],\n [0, 0, 0, 0, 0, 11, 2, 20, 13, 5],\n [0, 0, 0, 0, 0, 0, -13, -1, 26, -12],\n [0, 0, 0, 0, 0, 0, 0, 16, 8, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
math
|
train
| 411,340 |
math_arithmetic_matrix_determinant_level_6_6_109
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-29, -18, -21, -6, 2, 10, -4, -2, 26, 21],\n [-4, 8, -15, 22, 12, -2, 4, 15, -15, -16],\n [-4, 2, -6, 2, -19, -17, -21, 11, 6, -19],\n [30, 16, -10, 5, -24, -19, -11, 3, 0, -25],\n [14, 11, -27, -15, 9, -1, 1, -3, -28, 17],\n [28, 19, -28, -4, 25, 20, 10, -2, 14, -18],\n [14, 16, 21, -20, -23, 13, 6, -2, -21, 24],\n [24, 16, 8, -24, -23, 7, -5, -29, 5, 4],\n [-20, 19, -7, -2, 22, -8, -26, -7, -17, -14],\n [8, 13, -30, 25, -19, 7, 22, 13, -15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
812
|
math
|
train
| 411,341 |
math_arithmetic_matrix_determinant_level_6_6_110
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-30, 14, 21, -18, 2, 12, -7, -20, -26, 12],\n [0, 1, 4, 21, 20, -12, 30, -30, -16, -12],\n [0, 0, 15, 5, -23, 14, 18, -5, 5, -13],\n [0, 0, 0, -26, 23, 5, 20, -3, -14, -17],\n [0, 0, 0, 0, -28, -28, -12, 24, 2, 5],\n [0, 0, 0, 0, 0, -7, -2, 9, 14, -4],\n [0, 0, 0, 0, 0, 0, -27, 6, 3, -24],\n [0, 0, 0, 0, 0, 0, 0, -11, 26, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,342 |
math_arithmetic_matrix_determinant_level_6_6_111
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -28, 24, 2, -22, -25, -22, -13, 9, -23],\n [-14, 24, -6, -6, 22, -22, 28, -22, -27, -16],\n [-21, -16, -14, 7, 6, -28, -12, 30, -10, 23],\n [23, 8, -30, -7, -13, -14, 1, -2, 17, -29],\n [10, -28, 29, -24, -9, 7, -23, 4, -27, 12],\n [12, -10, 6, 23, -16, 14, -3, 27, 11, 16],\n [-26, 2, 29, -27, -26, 14, 22, -28, 29, 24],\n [-10, -25, -20, -6, -23, 22, -3, 21, -30, 22],\n [21, -5, 1, -27, 16, -7, 12, 3, 16, -7],\n [16, 0, 27, -22, 18, 27, 20, -16, -2, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
943
|
math
|
train
| 411,343 |
math_arithmetic_matrix_determinant_level_6_6_112
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 2, 12, 21, -29, -2, -23, -27, -30, 28],\n [-30, 16, -2, 13, 7, -6, -13, -19, -20, -26],\n [30, -24, 28, 22, 6, 12, 30, 4, 22, 2],\n [-22, -14, 29, 16, 16, -28, 9, -14, 8, -18],\n [-28, -12, 6, 15, -25, 3, 4, 8, -17, 23],\n [-19, -3, 8, -29, 8, 18, 7, -6, -4, 30],\n [25, 28, 3, 26, -3, 12, 11, 15, -4, -22],\n [-2, -23, 23, 21, 8, -29, 25, -14, 8, 7],\n [5, -17, -8, -30, -30, -28, 9, -8, -3, -15],\n [-2, 2, 1, 24, 16, -8, 16, 16, 30, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
164
|
math
|
train
| 411,344 |
math_arithmetic_matrix_determinant_level_6_6_113
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, 4, 23, -9, 22, 26, -2, -12, -13, 25],\n [-13, 13, 30, 16, 18, -15, 13, 27, 28, 25],\n [-12, 18, 21, -22, 2, 25, -18, -20, 30, 2],\n [6, -1, 8, 15, -22, -8, -7, 1, 18, 7],\n [-27, 13, 10, 15, -4, -20, -10, -17, -13, 28],\n [30, -7, -11, 10, -5, 0, 21, -15, 10, 17],\n [11, 8, -12, -24, 21, -15, -7, -25, 9, -15],\n [26, 5, 8, -16, 9, 19, -27, 25, -29, -17],\n [29, -9, -29, -11, -27, 21, 3, -13, 19, 17],\n [24, 16, 18, -11, -5, -24, 23, -12, -7, -20]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
825
|
math
|
train
| 411,345 |
math_arithmetic_matrix_determinant_level_6_6_114
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -30, 5, -3, -18, -20, 23, -25, 28, -1],\n [21, 27, 6, 3, 19, -3, -22, 0, -25, 29],\n [27, -25, 5, -11, 9, 1, 16, 18, 1, -26],\n [7, 6, -21, 6, 16, -29, -24, -20, -30, -17],\n [-10, -25, 17, -5, -14, -5, -24, 17, -30, -16],\n [0, 5, -25, -12, -25, -1, 4, 14, 26, -14],\n [-15, -21, 5, 14, -13, -21, 21, 6, -27, 29],\n [-23, -7, 16, 3, -19, -7, 27, 11, 13, -4],\n [26, 7, 21, -14, 19, -15, 16, 10, -4, 4],\n [18, -5, 17, 23, -25, 14, 15, -30, 5, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
313
|
math
|
train
| 411,346 |
math_arithmetic_matrix_determinant_level_6_6_115
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[17, -1, 2, -14, 20, 8, 6, 8, 13, -22],\n [0, -27, 13, 24, -14, -27, 13, 17, 27, 10],\n [0, 0, -21, 14, 16, -10, 25, 25, 1, -1],\n [0, 0, 0, -11, 9, 25, 23, 18, -3, -22],\n [0, 0, 0, 0, 23, -11, -25, 20, -6, 6],\n [0, 0, 0, 0, 0, -26, 25, 6, 21, -30],\n [0, 0, 0, 0, 0, 0, -25, 26, 12, -4],\n [0, 0, 0, 0, 0, 0, 0, -26, 16, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, -23, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
900
|
math
|
train
| 411,347 |
math_arithmetic_matrix_determinant_level_6_6_116
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-23, 25, -17, -14, -20, -25, 0, -19, 10, 20],\n [7, -4, 27, -26, -2, 18, -1, -18, -18, 29],\n [26, 25, 26, -2, 14, -26, -17, -9, 20, -14],\n [-12, 15, 22, 14, 10, 23, 5, 17, 24, -19],\n [-6, 24, -8, -14, 4, 8, -7, 7, 9, 24],\n [-19, 27, 12, 7, 27, -17, -17, -21, 16, -30],\n [-8, 29, -3, -24, 30, 1, 12, -20, -22, -7],\n [9, -27, -14, 28, -10, -6, 2, -28, -27, 12],\n [-18, 23, 29, -2, 20, 5, -25, 4, -17, -30],\n [-24, 0, 17, 7, 10, 13, -11, -2, -4, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
255
|
math
|
train
| 411,348 |
math_arithmetic_matrix_determinant_level_6_6_117
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[29, -30, 17, 0, -1, -19, -17, 6, -25, 29],\n [-1, 27, -14, 24, -18, 27, 17, 7, -15, 17],\n [26, -3, -19, 5, -15, -19, -30, -12, -25, -25],\n [-13, 17, -3, -19, 0, -4, 15, 18, -23, -20],\n [-24, 29, -9, -11, -12, -29, 18, 14, -4, 25],\n [-6, 15, -20, -22, 27, -5, 0, 10, 18, 18],\n [25, -20, -19, 30, 12, -21, -5, -22, -13, -6],\n [-13, 12, 18, 29, 13, 23, 30, -17, -4, -9],\n [28, 5, -14, -19, -17, -25, -21, 12, 14, -17],\n [-9, 14, -28, -23, 7, 22, 5, -26, 3, -30]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
504
|
math
|
train
| 411,349 |
math_arithmetic_matrix_determinant_level_6_6_118
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[4, 14, -27, -15, 28, 19, 9, 1, -7, -11],\n [0, 8, 23, -28, -23, 3, -17, -11, -10, 6],\n [0, 0, -5, -12, 20, -14, 1, -28, 25, -7],\n [0, 0, 0, -18, -6, -1, 8, -18, 1, 17],\n [0, 0, 0, 0, -26, -4, 22, -21, 30, 21],\n [0, 0, 0, 0, 0, -27, -21, -30, -28, -10],\n [0, 0, 0, 0, 0, 0, -11, -11, 7, 9],\n [0, 0, 0, 0, 0, 0, 0, -29, -27, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, -10, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
math
|
train
| 411,350 |
math_arithmetic_matrix_determinant_level_6_6_119
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[7, 30, 25, 20, -26, 15, 26, -25, -30, -11],\n [-4, 2, -10, -20, 15, -30, 12, 19, -17, -12],\n [-28, -16, -2, 22, 23, 17, -30, -13, -1, -21],\n [-4, -28, -15, -21, 26, -23, 12, -3, 25, 8],\n [30, 22, 27, -2, 10, -18, 18, -5, 18, 25],\n [27, 26, -27, 3, -13, -9, -20, -22, 3, 10],\n [-13, -9, 10, -21, -3, -8, -28, 28, -24, -23],\n [1, 30, 13, -30, 29, -6, -5, 4, -18, -3],\n [-20, 23, -19, 20, 28, 12, -3, -6, -2, 23],\n [28, 21, -30, 9, -8, 20, -6, -14, -24, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
math
|
train
| 411,351 |
math_arithmetic_matrix_determinant_level_6_6_120
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[27, 0, -26, -10, -9, -16, -6, -12, 2, 25],\n [0, 15, 12, 4, -4, 10, -4, -19, 8, -18],\n [-26, 12, 29, -8, -15, -8, -26, -3, 15, 12],\n [-10, 4, -8, -24, 0, 0, -13, 13, 14, -18],\n [-9, -4, -15, 0, -26, 20, 30, -22, 20, 12],\n [-16, 10, -8, 0, 20, 15, 24, -12, 5, -6],\n [-6, -4, -26, -13, 30, 24, -20, 6, 6, 2],\n [-12, -19, -3, 13, -22, -12, 6, -11, 1, -12],\n [2, 8, 15, 14, 20, 5, 6, 1, -3, -24],\n [25, -18, 12, -18, 12, -6, 2, -12, -24, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
522
|
math
|
train
| 411,352 |
math_arithmetic_matrix_determinant_level_6_6_121
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 1, -28, -13, -10, 0, -7, 3, 11, -26],\n [1, -10, 15, -4, 2, -28, -12, 26, -30, 14],\n [25, -27, 27, -4, 24, 22, 11, -8, -27, -11],\n [-19, 0, -22, -18, 3, 2, 9, 23, 15, -1],\n [16, 28, 15, -9, -24, 20, 5, -14, -22, 12],\n [-27, 7, 24, -3, 1, -13, -26, 22, -29, -20],\n [-1, 13, -4, 17, -16, -7, -12, 9, 23, -30],\n [21, -3, -23, -9, 29, -6, 28, -13, -22, -23],\n [12, 22, -9, 26, -29, 30, 26, 6, 4, -25],\n [-20, -8, 12, -16, 24, -12, 20, 11, -7, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
583
|
math
|
train
| 411,353 |
math_arithmetic_matrix_determinant_level_6_6_122
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[17, 7, -27, -28, 10, -6, -27, -14, -28, -14],\n [0, -27, -25, -2, 5, -17, 30, 21, 18, 1],\n [0, 0, 16, -26, 20, -30, -9, -11, 20, 29],\n [0, 0, 0, 14, 25, 30, 26, 22, 21, -28],\n [0, 0, 0, 0, 29, -19, 19, 30, -12, -22],\n [0, 0, 0, 0, 0, 1, 14, 8, -20, -18],\n [0, 0, 0, 0, 0, 0, 9, -25, 15, -12],\n [0, 0, 0, 0, 0, 0, 0, -9, 17, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 15, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
math
|
train
| 411,354 |
math_arithmetic_matrix_determinant_level_6_6_123
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 0, -12, -12, -7, -8, -18, 25, -18, 0],\n [0, 16, -12, 6, 6, -18, -10, -16, -2, 16],\n [-12, -12, -19, -10, 12, -20, 14, 21, -24, 9],\n [-12, 6, -10, -3, 3, -4, 12, 8, 4, 9],\n [-7, 6, 12, 3, -10, -16, -6, -21, 24, -6],\n [-8, -18, -20, -4, -16, 21, -6, -24, -10, -20],\n [-18, -10, 14, 12, -6, -6, -10, 16, -4, -3],\n [25, -16, 21, 8, -21, -24, 16, 9, -8, -26],\n [-18, -2, -24, 4, 24, -10, -4, -8, -14, -8],\n [0, 16, 9, 9, -6, -20, -3, -26, -8, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
707
|
math
|
train
| 411,355 |
math_arithmetic_matrix_determinant_level_6_6_124
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-19, -4, 10, 17, -4, -8, 1, 22, 4, 4],\n [-4, 26, 2, 0, 18, -2, -6, -14, 0, 30],\n [10, 2, -18, 10, 24, 14, -4, 8, -20, -1],\n [17, 0, 10, -8, 2, -4, 15, 4, -4, 15],\n [-4, 18, 24, 2, 24, -16, 8, 20, -18, -18],\n [-8, -2, 14, -4, -16, -10, -14, -8, 8, -4],\n [1, -6, -4, 15, 8, -14, 18, -16, 18, -9],\n [22, -14, 8, 4, 20, -8, -16, 30, 15, 2],\n [4, 0, -20, -4, -18, 8, 18, 15, 8, 10],\n [4, 30, -1, 15, -18, -4, -9, 2, 10, -21]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
57
|
math
|
train
| 411,356 |
math_arithmetic_matrix_determinant_level_6_6_125
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[16, -29, 6, -19, -9, 29, -27, 10, -16, 15],\n [0, 1, 0, 4, 12, 18, -7, 18, 27, -3],\n [0, 0, 9, -25, -5, 10, -15, -17, -2, -8],\n [0, 0, 0, 1, 4, -30, 12, 28, -18, -24],\n [0, 0, 0, 0, -17, -5, 20, -14, -2, 23],\n [0, 0, 0, 0, 0, -29, 17, 24, 19, 28],\n [0, 0, 0, 0, 0, 0, -24, 9, -4, 3],\n [0, 0, 0, 0, 0, 0, 0, 26, 2, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
672
|
math
|
train
| 411,357 |
math_arithmetic_matrix_determinant_level_6_6_126
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -19, -30, 29, 26, 24, -13, -15, 17, -6],\n [0, 21, -18, 23, 9, 5, -10, -24, -26, -11],\n [0, 0, -29, -14, 10, -28, 1, -5, -22, 7],\n [0, 0, 0, 8, -11, -3, -3, 19, -6, -5],\n [0, 0, 0, 0, 20, -7, 9, -27, 26, 23],\n [0, 0, 0, 0, 0, -12, -8, 17, -25, 6],\n [0, 0, 0, 0, 0, 0, 15, 0, 8, 28],\n [0, 0, 0, 0, 0, 0, 0, 14, 27, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, -3, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,358 |
math_arithmetic_matrix_determinant_level_6_6_127
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[15, -16, -6, -28, -11, -18, 16, -28, 23, 0],\n [18, -22, -4, -13, 17, 0, 19, 5, -30, -1],\n [20, 15, 11, -25, 29, 2, -4, 29, 6, -26],\n [-27, -16, -17, 19, 5, -29, 11, 20, 16, 18],\n [-12, 2, -23, 18, 28, -30, -21, -18, -8, -29],\n [15, -27, -30, 23, 20, 14, -12, 26, 30, -24],\n [26, -22, -6, 24, -27, 6, -17, -9, -19, 17],\n [-21, -3, -21, 14, 28, 30, 17, 9, 3, -24],\n [-26, -10, -24, 29, -30, 2, -6, 21, 13, 11],\n [-7, 11, -23, -1, -17, -1, -22, -7, -30, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
930
|
math
|
train
| 411,359 |
math_arithmetic_matrix_determinant_level_6_6_128
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 5, -30, -15, 6, 8, -1, 21, -20, -19],\n [0, -12, -7, -6, 17, -15, 3, 17, -13, -2],\n [0, 0, 23, -20, 0, -20, 6, 18, -21, 23],\n [0, 0, 0, 11, -17, 12, -29, 22, 19, -2],\n [0, 0, 0, 0, 10, 3, -19, -2, -25, -5],\n [0, 0, 0, 0, 0, -19, -22, 17, 10, -2],\n [0, 0, 0, 0, 0, 0, 25, -19, 29, 1],\n [0, 0, 0, 0, 0, 0, 0, 4, -2, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,360 |
math_arithmetic_matrix_determinant_level_6_6_129
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -29, 22, -5, -20, 7, 25, 21, 15, 17],\n [-28, 1, 12, -11, 11, 8, -11, -23, 20, -8],\n [-9, -1, 18, -6, -10, 6, -28, -7, -9, 11],\n [-11, 27, -29, -27, -14, 18, 15, -3, 9, -11],\n [16, 26, 17, -25, -5, 21, -22, 29, 0, 0],\n [27, 18, -27, -3, -8, -28, -4, 27, 7, 11],\n [-27, 10, 11, -11, -27, 27, 10, -13, 19, 15],\n [-11, -13, 0, -18, 19, -25, -11, 11, -15, -28],\n [5, -8, 24, 4, -4, -6, -5, 19, 19, 4],\n [-2, 7, -1, -18, 7, -24, -18, 8, -30, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
math
|
train
| 411,361 |
math_arithmetic_matrix_determinant_level_6_6_130
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[25, -29, 15, -17, -22, -13, -20, -14, -4, 23],\n [-26, 5, 3, 23, -4, -13, 22, 10, -30, -15],\n [14, 29, 8, 19, -12, 13, 2, -1, -4, 1],\n [-2, -23, 13, 11, 4, 4, 26, -17, 6, 7],\n [9, 9, 7, 24, 1, 18, -21, 21, -2, 0],\n [23, 13, -23, -8, 27, 28, -25, 16, -10, -26],\n [6, -26, -25, -26, 22, -30, 20, 18, -4, -19],\n [17, -28, 18, 23, -25, 23, 24, 27, -30, -21],\n [-21, -23, -19, 21, -6, 19, 3, -7, -30, -27],\n [-18, -8, 13, -20, 5, 10, -12, -26, -12, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
math
|
train
| 411,362 |
math_arithmetic_matrix_determinant_level_6_6_131
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[19, -4, 3, -2, 21, 21, 28, 10, -13, -21],\n [0, 24, 15, 18, 6, 23, -26, -15, 21, 27],\n [0, 0, 1, 14, 30, -3, 3, -4, 19, 9],\n [0, 0, 0, -12, 17, 18, 19, 19, -9, -8],\n [0, 0, 0, 0, -28, -26, -1, -22, -17, -30],\n [0, 0, 0, 0, 0, 27, 3, -4, -12, 4],\n [0, 0, 0, 0, 0, 0, 11, 7, -23, 0],\n [0, 0, 0, 0, 0, 0, 0, -24, 21, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
112
|
math
|
train
| 411,363 |
math_arithmetic_matrix_determinant_level_6_6_132
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-16, -8, -6, -11, -16, 15, -28, 12, 27, 18],\n [19, 10, 29, -24, 12, -30, -18, -18, 24, -15],\n [5, 19, 7, 27, -4, -9, 30, -23, -15, 1],\n [30, -15, 6, 22, -25, -6, 27, 11, -8, -12],\n [-6, -30, -22, 1, 14, 23, 19, -14, -18, -7],\n [21, -1, 12, 9, 24, -10, 13, 5, -17, 21],\n [-8, -15, -7, -17, 25, 24, 2, 18, -14, 15],\n [28, 4, -28, 2, -3, -3, -26, -23, 14, 19],\n [-24, 28, 4, -21, -13, -25, 27, 6, 27, 30],\n [25, -15, 24, 8, 0, 18, 7, 15, 23, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
419
|
math
|
train
| 411,364 |
math_arithmetic_matrix_determinant_level_6_6_133
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 11, -30, 2, 5, 10, 3, 9, -24, -8],\n [-13, -30, -20, 21, -11, 19, -11, 1, 29, 1],\n [20, -11, -4, 10, -27, 2, 18, -10, -8, 4],\n [20, 28, -26, -25, 1, 28, -25, 11, -5, 28],\n [-22, -30, -10, -9, -7, 6, 28, -10, -16, -21],\n [-5, 25, -21, 12, -5, -24, -22, 25, -18, 1],\n [21, 5, -7, -14, 8, -29, 1, 19, -25, 16],\n [13, 26, -5, 11, -13, -15, -26, 22, 4, 29],\n [2, -11, 12, -27, 22, 3, 3, 27, -24, 20],\n [3, 1, -5, -2, -13, 7, -6, 12, -3, -30]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
539
|
math
|
train
| 411,365 |
math_arithmetic_matrix_determinant_level_6_6_134
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-27, 3, -6, 0, 1, -6, 5, -8, 10, -3],\n [3, 6, 22, -24, 1, -17, -22, 4, 12, 6],\n [-6, 22, -11, 0, -6, -14, 11, 8, -12, 19],\n [0, -24, 0, 21, 3, -6, -8, 6, -2, 22],\n [1, 1, -6, 3, 24, -8, 12, -7, 12, -14],\n [-6, -17, -14, -6, -8, 16, 6, 23, -11, 10],\n [5, -22, 11, -8, 12, 6, -23, 13, 2, -6],\n [-8, 4, 8, 6, -7, 23, 13, 19, 6, 10],\n [10, 12, -12, -2, 12, -11, 2, 6, 16, 1],\n [-3, 6, 19, 22, -14, 10, -6, 10, 1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
274
|
math
|
train
| 411,366 |
math_arithmetic_matrix_determinant_level_6_6_135
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-28, 5, -17, -29, -27, 26, 30, 6, -8, -20],\n [4, 3, -10, 30, 28, 23, 4, 11, -22, -17],\n [-1, -29, -14, 30, -16, -20, 18, -2, -20, 23],\n [26, -11, -28, -24, -30, -18, 20, 10, 16, 28],\n [29, -12, -1, -15, -13, 0, 4, -3, 22, 27],\n [10, 25, -6, -19, 17, 13, -7, 1, -8, -5],\n [10, -26, -18, -29, 26, 21, -4, 26, 17, -7],\n [-27, 23, -11, -22, 8, -6, 27, 30, 19, 28],\n [11, 6, -28, 26, 30, -10, -22, 12, 12, -8],\n [-9, -14, -18, -22, -11, -8, -12, 19, -13, 23]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
math
|
train
| 411,367 |
math_arithmetic_matrix_determinant_level_6_6_136
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 12, -6, 10, 7, 3, 29, 6, 13, -13],\n [0, 9, 26, 6, -19, -23, -8, 1, -9, 24],\n [0, 0, 14, 2, 21, -28, -20, -19, 10, -5],\n [0, 0, 0, -18, -16, 11, 18, -8, 11, 11],\n [0, 0, 0, 0, 7, -6, -8, 16, -9, -16],\n [0, 0, 0, 0, 0, -28, -17, -20, -29, 12],\n [0, 0, 0, 0, 0, 0, 29, 23, -8, -22],\n [0, 0, 0, 0, 0, 0, 0, 18, 5, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 2, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
math
|
train
| 411,368 |
math_arithmetic_matrix_determinant_level_6_6_137
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-30, 14, -12, 3, 12, -28, -2, 27, -1, -21],\n [-29, 18, -20, -26, 0, 5, 18, 30, 30, -28],\n [-5, -3, -26, 8, 0, -1, 18, -22, -24, 4],\n [27, -10, -26, -8, 0, 3, -11, -10, 20, -15],\n [-6, -24, -23, 0, 27, -29, -9, -29, 22, 0],\n [-16, -25, -27, -8, -7, 15, 8, 1, -3, 27],\n [-6, 22, 22, 15, 20, 8, -17, 25, 11, 4],\n [-18, 23, -10, 11, 6, 24, -20, -27, 17, -27],\n [-22, 7, 27, -26, -18, -20, -24, -17, -16, 2],\n [8, 25, 26, 12, 3, 16, -12, -18, -2, -27]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
426
|
math
|
train
| 411,369 |
math_arithmetic_matrix_determinant_level_6_6_138
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -27, -29, 11, 8, -30, 8, 26, 16, -17],\n [26, 3, 11, 13, 21, -27, 21, -27, -8, -7],\n [25, 29, 16, -7, -5, 20, 5, -29, -24, -13],\n [17, -7, -3, 3, 30, 26, -21, -1, 21, -10],\n [24, -4, -26, 4, -7, -5, -30, 1, -21, 27],\n [26, -7, -15, -7, 11, -2, -10, -5, 14, -26],\n [-27, 18, -2, -23, -23, -20, 5, 20, -18, 12],\n [25, 17, 27, 27, 8, -6, -12, 5, 15, -6],\n [17, 2, -11, -18, -3, 1, 14, 28, 15, 18],\n [-2, 30, -21, -11, 1, -3, 28, -19, 7, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
330
|
math
|
train
| 411,370 |
math_arithmetic_matrix_determinant_level_6_6_139
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 30, -4, 10, -29, -21, -8, 10, -10, -22],\n [-4, -7, -24, 27, -21, 30, 17, 25, -29, 15],\n [-1, 10, 5, 15, -17, 2, -27, 21, 21, 23],\n [2, 20, 27, -7, 26, 25, -17, -19, 18, 1],\n [1, -18, -25, 6, 8, 10, -27, -21, 11, 30],\n [-7, -19, 1, 16, 2, -17, 7, 8, 14, -21],\n [-22, -29, 9, 5, -17, 6, -7, -24, -12, -3],\n [6, -20, 5, -1, 29, 18, 1, 1, 27, -14],\n [-22, -26, -5, -12, 14, 13, -14, -13, -29, -15],\n [22, 6, -30, 1, -16, 3, -11, 15, 23, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
99
|
math
|
train
| 411,371 |
math_arithmetic_matrix_determinant_level_6_6_140
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -8, 4, 1, -4, 5, 8, 6, -2, -24],\n [-8, 11, 16, 22, 8, 10, -2, 16, 12, 0],\n [4, 16, 5, -8, 5, -22, 14, -10, 8, -4],\n [1, 22, -8, -7, -3, 28, -22, 18, -20, 2],\n [-4, 8, 5, -3, 12, -28, 2, 5, -10, -4],\n [5, 10, -22, 28, -28, -17, 0, -12, -2, 10],\n [8, -2, 14, -22, 2, 0, -2, -6, 8, 16],\n [6, 16, -10, 18, 5, -12, -6, -9, 10, 26],\n [-2, 12, 8, -20, -10, -2, 8, 10, 22, -12],\n [-24, 0, -4, 2, -4, 10, 16, 26, -12, 28]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
math
|
train
| 411,372 |
math_arithmetic_matrix_determinant_level_6_6_141
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -2, 20, 18, -22, 11, -4, -10, 10, 16],\n [-2, 30, -14, -12, 0, -14, 12, 2, -8, 0],\n [20, -14, -5, -16, 8, -19, -2, -8, 14, -12],\n [18, -12, -16, -9, 4, 10, -18, 2, 10, 9],\n [-22, 0, 8, 4, -5, 4, 18, 10, 4, -10],\n [11, -14, -19, 10, 4, -26, 8, 7, -19, -12],\n [-4, 12, -2, -18, 18, 8, 14, -14, -28, 15],\n [-10, 2, -8, 2, 10, 7, -14, 11, -1, -16],\n [10, -8, 14, 10, 4, -19, -28, -1, 4, -20],\n [16, 0, -12, 9, -10, -12, 15, -16, -20, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
918
|
math
|
train
| 411,373 |
math_arithmetic_matrix_determinant_level_6_6_142
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-29, 22, 0, 6, 28, 5, 1, 14, 15, 10],\n [22, 10, 12, 1, 26, 12, -23, 0, 12, 8],\n [0, 12, 12, -4, 10, 18, -26, -8, 7, -4],\n [6, 1, -4, 21, -18, -4, 0, 10, 2, -15],\n [28, 26, 10, -18, -20, 4, -28, 4, 10, 6],\n [5, 12, 18, -4, 4, 15, -7, -10, -23, -6],\n [1, -23, -26, 0, -28, -7, -17, -2, 4, 16],\n [14, 0, -8, 10, 4, -10, -2, 20, -2, 0],\n [15, 12, 7, 2, 10, -23, 4, -2, 21, -8],\n [10, 8, -4, -15, 6, -6, 16, 0, -8, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
math
|
train
| 411,374 |
math_arithmetic_matrix_determinant_level_6_6_143
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 3, 24, -2, 28, -28, 26, 6, 13, -6],\n [14, 27, 9, 29, -22, -23, 12, -24, 15, -18],\n [16, 20, 2, 26, 10, 1, -10, -10, 20, 1],\n [-15, 17, 17, 26, -26, 5, -8, -10, 24, -7],\n [-25, -27, -21, -19, 11, -1, -30, -12, 18, 6],\n [-9, -29, -29, 8, 11, -12, 8, -24, 0, -13],\n [-30, -30, -13, 7, -28, -13, -9, -23, 30, 7],\n [-21, -28, 13, -14, -24, 6, -9, 16, 10, -20],\n [17, -12, -2, -3, -3, 30, 5, -7, 13, 24],\n [-20, 0, 26, -23, 17, -13, 1, 9, 0, 29]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
845
|
math
|
train
| 411,375 |
math_arithmetic_matrix_determinant_level_6_6_144
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[9, -5, -17, 17, -17, -19, -2, -5, 23, -2],\n [1, 28, 5, 16, 21, 24, -5, -23, 23, 27],\n [19, -17, 21, 28, 14, -18, 27, 1, 5, -27],\n [7, -20, -19, -30, 17, 13, -22, 18, 6, 17],\n [-5, -8, -30, -27, -17, -20, 15, 1, 8, 16],\n [13, 23, 23, 14, -10, 8, -28, 6, 0, -7],\n [-14, 11, 2, -1, -20, -29, 0, 27, -27, -24],\n [-20, 14, -4, -4, 15, -3, 9, 17, 28, -24],\n [-30, 0, -22, 28, -11, 28, 7, -16, -28, 10],\n [5, -15, -29, -17, 16, 16, 1, 3, -9, -17]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
673
|
math
|
train
| 411,376 |
math_arithmetic_matrix_determinant_level_6_6_145
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-23, -16, 9, 12, -6, 4, 18, -4, 5, 0],\n [-16, -4, -8, -12, 0, -19, 10, -2, 14, 12],\n [9, -8, 26, -10, -13, 10, 0, -8, 26, -23],\n [12, -12, -10, 24, -5, 0, -12, 2, 16, -3],\n [-6, 0, -13, -5, -15, -5, 11, 17, 26, 6],\n [4, -19, 10, 0, -5, -30, 4, 6, -20, 18],\n [18, 10, 0, -12, 11, 4, -9, 0, 3, 20],\n [-4, -2, -8, 2, 17, 6, 0, 23, -20, 8],\n [5, 14, 26, 16, 26, -20, 3, -20, -5, 2],\n [0, 12, -23, -3, 6, 18, 20, 8, 2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
651
|
math
|
train
| 411,377 |
math_arithmetic_matrix_determinant_level_6_6_146
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[12, 2, 2, -4, 10, 10, -4, 8, -22, 0],\n [2, -8, -14, 17, 18, -12, 0, -20, 16, -8],\n [2, -14, -27, -2, 12, -16, -4, 23, 6, -6],\n [-4, 17, -2, 18, -5, -10, -12, 2, 13, -4],\n [10, 18, 12, -5, -5, -1, -13, -2, 17, 1],\n [10, -12, -16, -10, -1, -21, 1, 0, -8, 5],\n [-4, 0, -4, -12, -13, 1, 24, -6, 10, -13],\n [8, -20, 23, 2, -2, 0, -6, -25, -10, 4],\n [-22, 16, 6, 13, 17, -8, 10, -10, -9, -25],\n [0, -8, -6, -4, 1, 5, -13, 4, -25, 29]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
math
|
train
| 411,378 |
math_arithmetic_matrix_determinant_level_6_6_147
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 21, 28, -22, -26, 2, 18, 2, 10, 17],\n [0, 14, -10, 29, -26, -24, 10, 29, -3, -23],\n [0, 0, -27, -7, 5, 30, -23, 3, 2, -8],\n [0, 0, 0, 5, 10, -11, -17, -14, -24, -14],\n [0, 0, 0, 0, 29, -2, 10, -12, 2, -15],\n [0, 0, 0, 0, 0, 12, -3, -29, 3, 21],\n [0, 0, 0, 0, 0, 0, 14, 22, -14, -14],\n [0, 0, 0, 0, 0, 0, 0, 25, 13, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,379 |
math_arithmetic_matrix_determinant_level_6_6_148
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-19, 10, -6, 24, 9, 19, 14, -4, -22, 1],\n [0, 13, 12, -24, -18, -15, 30, -3, -5, 27],\n [0, 0, -9, 8, -12, 9, 9, -18, 29, 17],\n [0, 0, 0, -25, 20, -9, 25, -4, -21, -30],\n [0, 0, 0, 0, -27, -12, 22, -3, 26, 1],\n [0, 0, 0, 0, 0, -8, -8, -15, -5, 25],\n [0, 0, 0, 0, 0, 0, -21, -9, -2, -9],\n [0, 0, 0, 0, 0, 0, 0, -14, 30, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, -24, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
math
|
train
| 411,380 |
math_arithmetic_matrix_determinant_level_6_6_149
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-25, 28, 28, 18, -16, -25, 14, -9, -27, -16],\n [0, -2, -8, 23, -29, -26, 23, 19, 11, -27],\n [17, -26, 1, 16, -15, 5, -27, 28, -22, 29],\n [-2, -29, -3, -17, 23, 27, -30, 7, 24, 6],\n [10, 8, 23, -11, 15, 14, 27, -14, -15, 12],\n [-28, -21, 15, -26, 21, -14, -22, 11, 23, -22],\n [-9, 7, -11, 16, 22, -21, 12, -20, -18, -3],\n [13, -25, -14, -23, -4, -16, -13, -13, 1, 18],\n [-12, -23, 1, 0, 20, -29, 7, 25, 28, 15],\n [5, -3, -9, 12, 1, -17, -27, 10, -21, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
905
|
math
|
train
| 411,381 |
math_arithmetic_matrix_determinant_level_6_6_150
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-21, -1, 8, 12, -14, 22, -7, -11, -12, -2],\n [-1, -10, -6, -7, 5, 6, 9, 12, -2, 2],\n [8, -6, -20, 0, -17, 6, -2, 6, 11, 0],\n [12, -7, 0, -5, -4, -16, 22, -2, -10, -10],\n [-14, 5, -17, -4, -21, -7, -2, 1, -25, 1],\n [22, 6, 6, -16, -7, -23, -14, -8, 1, -14],\n [-7, 9, -2, 22, -2, -14, -14, 17, 24, 0],\n [-11, 12, 6, -2, 1, -8, 17, -19, -12, -20],\n [-12, -2, 11, -10, -25, 1, 24, -12, 13, 6],\n [-2, 2, 0, -10, 1, -14, 0, -20, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
755
|
math
|
train
| 411,382 |
math_arithmetic_matrix_determinant_level_6_6_151
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 19, -6, 17, -5, 18, -29, 6, -1, 9],\n [-12, -8, 3, -4, 7, 15, 8, 25, -16, 23],\n [16, -22, -13, -6, -13, 25, -12, -13, -29, -19],\n [14, 27, 21, -2, 20, 13, -27, 11, -20, -18],\n [4, 12, -23, -16, -6, -4, 15, 23, 25, 9],\n [-15, -2, 24, 16, -16, 11, 6, -26, 30, 8],\n [10, -12, 23, -18, 23, -3, 17, 20, 29, 22],\n [-9, 3, -14, -30, 5, 8, 18, 24, 14, -9],\n [-24, 5, 24, -26, 6, -11, -15, -29, -11, 30],\n [24, 14, 19, 13, -28, -25, 3, -4, -11, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
314
|
math
|
train
| 411,383 |
math_arithmetic_matrix_determinant_level_6_6_152
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-20, 9, -1, -7, 22, -5, -29, 3, 22, -15],\n [0, -29, 27, -19, -24, 20, 28, -17, 1, -24],\n [0, 0, 23, 20, 4, -13, 1, -18, -21, 16],\n [0, 0, 0, -9, -11, -22, -21, 13, 29, 25],\n [0, 0, 0, 0, 21, 13, 17, -24, 26, -28],\n [0, 0, 0, 0, 0, 20, -24, 20, 15, -16],\n [0, 0, 0, 0, 0, 0, -17, -13, -23, 2],\n [0, 0, 0, 0, 0, 0, 0, 5, -12, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,384 |
math_arithmetic_matrix_determinant_level_6_6_153
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -22, -16, 6, 13, 13, 13, -22, 1, 27],\n [-14, 29, -28, 16, 22, 16, -19, 7, 28, 2],\n [2, -4, -16, -27, -1, -14, 10, -28, 27, 3],\n [-2, 13, 26, -15, -6, -20, -6, -18, -28, 27],\n [-11, -10, 16, 18, 13, -16, -23, 15, 28, 8],\n [24, 22, -1, -13, -23, -21, 9, 23, 16, 25],\n [28, -12, -22, -22, 20, -3, -12, 0, 17, 12],\n [-5, -3, 0, 27, -19, 7, -16, -28, -2, 23],\n [-23, -29, 23, -28, -1, 2, 5, -10, 4, -15],\n [-21, 13, -30, -30, 1, 9, -14, -25, -26, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
368
|
math
|
train
| 411,385 |
math_arithmetic_matrix_determinant_level_6_6_154
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 3, -30, 7, 24, 1, 2, 28, 25, 10],\n [24, 26, -12, -16, -21, 11, -5, -12, 6, -29],\n [-23, 10, -20, 25, 11, 22, -26, -20, -15, 26],\n [4, -4, -20, 5, -1, 19, -28, 7, 21, -7],\n [-26, -18, 12, -9, 3, -8, 13, -17, -15, 8],\n [11, -15, -25, -22, 20, -3, -29, 30, 12, 19],\n [-12, 28, 9, -4, -16, -19, 10, 25, -10, 22],\n [23, 19, -30, -14, 14, -18, -4, 2, -28, 3],\n [18, 22, -20, -10, -12, 23, -8, 19, -20, 26],\n [17, 19, -12, -17, -24, 1, 17, -21, -1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
986
|
math
|
train
| 411,386 |
math_arithmetic_matrix_determinant_level_6_6_155
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[24, 21, -2, 23, -23, -23, -2, 5, -12, 4],\n [0, -18, 30, 11, 14, -27, 1, -20, -1, 8],\n [0, 0, -24, 23, -17, -30, -13, -30, 26, -25],\n [0, 0, 0, -21, -21, 10, -3, -5, -7, 15],\n [0, 0, 0, 0, 28, -8, 10, -12, -18, -17],\n [0, 0, 0, 0, 0, 13, 9, 4, 9, 17],\n [0, 0, 0, 0, 0, 0, -21, -23, -15, -21],\n [0, 0, 0, 0, 0, 0, 0, -15, -22, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
math
|
train
| 411,387 |
math_arithmetic_matrix_determinant_level_6_6_156
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 14, 17, 21, 27, -4, 8, -3, 29, -3],\n [0, 15, -22, 29, -30, -9, 24, 24, -8, 30],\n [0, 0, 7, -1, -22, -18, 26, 3, 25, -30],\n [0, 0, 0, -24, -23, -15, -8, 28, -1, -22],\n [0, 0, 0, 0, -3, 20, 2, -5, 2, -18],\n [0, 0, 0, 0, 0, -26, 30, 28, -5, -24],\n [0, 0, 0, 0, 0, 0, 17, 0, 27, -9],\n [0, 0, 0, 0, 0, 0, 0, 18, -29, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, -22, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
math
|
train
| 411,388 |
math_arithmetic_matrix_determinant_level_6_6_157
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 17, -8, 12, -17, -10, 22, -29, 29, -6],\n [25, 13, -30, -30, -11, -17, 11, 25, -30, 19],\n [17, 3, 22, 11, -20, -10, 16, 29, -18, -6],\n [-4, -8, 26, -19, -1, -19, -25, -6, -6, -1],\n [8, -16, -19, -20, 14, 24, -11, 0, -26, -25],\n [4, 13, -10, 15, -24, -15, -29, -24, 30, 24],\n [5, 21, 25, 18, -3, -19, 23, 1, -26, -13],\n [-17, 19, -25, -7, -2, 7, -30, -28, 2, -3],\n [29, 5, 12, 21, 17, -5, -4, -11, -10, -28],\n [-17, -21, 8, 28, -14, -5, 30, 30, 28, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
261
|
math
|
train
| 411,389 |
math_arithmetic_matrix_determinant_level_6_6_158
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 0, 29, 0, -7, 10, -6, -8, -19, 20],\n [0, -15, -12, -13, -27, -30, -8, -30, 28, -10],\n [0, 0, -9, 26, -15, -13, 21, -5, -4, 30],\n [0, 0, 0, -7, 14, 8, 10, -6, 11, 25],\n [0, 0, 0, 0, -5, -13, -20, 5, 26, -14],\n [0, 0, 0, 0, 0, 12, 19, -12, 24, 20],\n [0, 0, 0, 0, 0, 0, 28, -2, 8, -27],\n [0, 0, 0, 0, 0, 0, 0, -18, -28, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 1, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,390 |
math_arithmetic_matrix_determinant_level_6_6_159
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, 26, 4, 4, 28, 7, -1, -19, 13],\n [2, -18, -10, -11, 29, -2, 11, -2, -14, -7],\n [28, 4, 28, 26, 2, -22, -10, -25, 13, 5],\n [-1, -13, -21, 25, -14, -7, 4, -11, -17, 27],\n [-27, 14, 29, 29, -16, 4, 30, 11, 20, -2],\n [-26, 17, -8, -12, -28, -9, -16, 25, -23, -15],\n [18, 13, 7, -1, -28, -6, -16, -14, -23, -19],\n [-5, 27, -17, -24, 21, 25, -6, -1, -13, -21],\n [-1, 9, 30, -10, -29, 4, -3, -14, 3, 27],\n [-27, 2, 10, 18, 11, -7, 0, -22, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
math
|
train
| 411,391 |
math_arithmetic_matrix_determinant_level_6_6_160
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[22, -29, -2, 2, -9, 3, 21, 13, -19, -21],\n [0, 22, -9, -17, 3, 28, 28, 22, 28, -17],\n [0, 0, 9, 18, 8, -16, -14, -5, 20, 11],\n [0, 0, 0, -20, 2, 25, 5, -23, 21, 27],\n [0, 0, 0, 0, 13, -30, -19, -15, -29, -10],\n [0, 0, 0, 0, 0, -4, -8, 30, -29, 4],\n [0, 0, 0, 0, 0, 0, 1, 27, -12, -13],\n [0, 0, 0, 0, 0, 0, 0, -20, -4, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
math
|
train
| 411,392 |
math_arithmetic_matrix_determinant_level_6_6_161
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[29, -16, 25, -11, -26, -10, -14, -1, 3, -27],\n [0, -26, 7, -21, -20, 5, -13, 4, -15, -7],\n [0, 0, -24, -22, -9, -16, 19, -14, -17, -2],\n [0, 0, 0, -9, -4, 19, 5, 24, -25, -1],\n [0, 0, 0, 0, -20, -8, 13, -25, 29, 18],\n [0, 0, 0, 0, 0, 3, 4, 10, 1, 5],\n [0, 0, 0, 0, 0, 0, 4, -19, -26, 1],\n [0, 0, 0, 0, 0, 0, 0, -20, -2, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
math
|
train
| 411,393 |
math_arithmetic_matrix_determinant_level_6_6_162
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 14, 14, 12, 14, 0, -2, 9, 2, -21],\n [14, 22, 20, 22, 21, -6, 0, 12, 2, -8],\n [14, 20, -10, 10, -4, 10, 10, 18, -12, -24],\n [12, 22, 10, -26, -2, 10, -10, -1, 16, -23],\n [14, 21, -4, -2, 10, -24, -24, -22, 10, -1],\n [0, -6, 10, 10, -24, 15, 24, -3, 10, 2],\n [-2, 0, 10, -10, -24, 24, 28, -20, -8, -4],\n [9, 12, 18, -1, -22, -3, -20, 12, -16, 28],\n [2, 2, -12, 16, 10, 10, -8, -16, -1, 5],\n [-21, -8, -24, -23, -1, 2, -4, 28, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
570
|
math
|
train
| 411,394 |
math_arithmetic_matrix_determinant_level_6_6_163
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -30, 13, 16, 27, 14, 29, 7, 0, -12],\n [0, -5, -26, 1, -14, 29, -19, -23, -10, -15],\n [0, 0, 30, -20, 25, -17, -24, 1, -19, 13],\n [0, 0, 0, 30, 3, -28, 27, 16, 8, 14],\n [0, 0, 0, 0, 20, -5, -14, -5, -27, 26],\n [0, 0, 0, 0, 0, -6, -23, -24, -3, -11],\n [0, 0, 0, 0, 0, 0, 11, 21, -22, -19],\n [0, 0, 0, 0, 0, 0, 0, 22, 21, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,395 |
math_arithmetic_matrix_determinant_level_6_6_164
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[20, -7, -24, 24, -11, -10, 1, -2, -17, 21],\n [0, -25, 1, -13, 30, 6, -20, 10, -27, -7],\n [0, 0, 9, 23, -18, 24, -25, -14, -4, -5],\n [0, 0, 0, 4, 25, -7, 3, -3, 4, -27],\n [0, 0, 0, 0, 1, -18, 15, -22, -10, -17],\n [0, 0, 0, 0, 0, -2, -9, 24, -5, -20],\n [0, 0, 0, 0, 0, 0, 2, -12, -4, 13],\n [0, 0, 0, 0, 0, 0, 0, -12, -15, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,396 |
math_arithmetic_matrix_determinant_level_6_6_165
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[15, -2, 29, -11, 28, -15, -20, -1, 18, -28],\n [13, -7, 2, -5, 24, 7, -4, 6, 14, 22],\n [-25, 12, -27, 4, 11, -13, 11, 20, -4, 27],\n [21, -6, -20, 11, -15, 7, 10, 24, 28, 22],\n [1, 17, -22, 24, 22, -7, -5, -30, -1, -25],\n [-22, -21, -11, 11, -19, -22, 4, 23, 13, -14],\n [14, 13, -30, -23, -8, 2, 25, 2, 6, 4],\n [-17, -18, -3, 26, -30, 22, 8, 2, -20, -13],\n [4, -30, 25, 17, -16, -4, 9, -30, 0, 27],\n [8, 23, 0, -22, 14, 20, 11, -11, 2, -29]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
846
|
math
|
train
| 411,397 |
math_arithmetic_matrix_determinant_level_6_6_166
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[13, 12, -23, -23, 27, 9, -29, 2, 17, -5],\n [5, 6, 4, 10, 0, 21, 22, 21, 24, 15],\n [1, 24, 4, 16, 29, -22, 18, 11, 4, 9],\n [-28, -8, 15, -26, -15, -27, 7, 3, -13, -6],\n [14, 29, 19, 12, -23, -16, 1, -15, 22, -22],\n [-7, 1, 24, -15, 3, -21, -8, -15, 16, 13],\n [-27, 16, -7, 30, -28, -17, 15, -3, 28, 10],\n [-29, 9, -28, -1, -26, -16, -28, 19, -5, 15],\n [-8, -16, 30, -15, -22, 26, 17, -25, -20, -18],\n [-26, 10, -7, 2, 27, -17, 14, 14, -30, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
612
|
math
|
train
| 411,398 |
math_arithmetic_matrix_determinant_level_6_6_167
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 29, 4, -6, -12, 25, 7, 19, 23, 29],\n [0, 6, 27, 5, 5, 1, -7, -1, 28, 6],\n [0, 0, -11, -29, 17, 24, -23, 21, -9, -17],\n [0, 0, 0, -24, -21, 12, 4, -24, -12, -6],\n [0, 0, 0, 0, 9, -29, -23, -14, 7, -25],\n [0, 0, 0, 0, 0, 26, -1, 0, 6, -25],\n [0, 0, 0, 0, 0, 0, 19, 19, 28, 0],\n [0, 0, 0, 0, 0, 0, 0, -10, 14, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
math
|
train
| 411,399 |
math_arithmetic_matrix_determinant_level_6_6_168
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[20, 10, 1, 0, 25, -29, -28, 25, 21, -18],\n [0, 12, 0, 26, 18, 19, 22, -20, 7, -7],\n [0, 0, -21, 9, 24, 25, -5, -5, 2, -16],\n [0, 0, 0, 23, 2, -24, -2, 7, -12, -12],\n [0, 0, 0, 0, 10, -12, 6, 29, 10, -29],\n [0, 0, 0, 0, 0, -17, -14, -29, 15, 20],\n [0, 0, 0, 0, 0, 0, -14, 22, 20, -11],\n [0, 0, 0, 0, 0, 0, 0, -30, -30, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,400 |
math_arithmetic_matrix_determinant_level_6_6_169
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 4, 15, 14, -14, -12, -9, -18, -2, 18],\n [4, -22, 20, 10, 14, -10, -4, 24, -5, 15],\n [15, 20, -15, -8, -5, -8, 6, 8, 10, -3],\n [14, 10, -8, -5, 14, 22, -6, -6, -8, -5],\n [-14, 14, -5, 14, -8, -9, -10, 2, 14, -8],\n [-12, -10, -8, 22, -9, 13, 12, 18, -26, -14],\n [-9, -4, 6, -6, -10, 12, -23, 2, -26, 7],\n [-18, 24, 8, -6, 2, 18, 2, 29, -1, 1],\n [-2, -5, 10, -8, 14, -26, -26, -1, -25, 16],\n [18, 15, -3, -5, -8, -14, 7, 1, 16, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
213
|
math
|
train
| 411,401 |
math_arithmetic_matrix_determinant_level_6_6_170
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, 22, 18, 8, 9, -18, -19, 9, -27, 6],\n [-14, -6, 16, 21, 2, -20, 26, 7, 0, 18],\n [-24, -6, -6, -24, 26, 11, -22, 24, 25, 25],\n [4, 8, -21, 24, -29, -3, 20, 0, 21, -19],\n [28, 12, 18, 15, 18, 9, 29, 20, 24, -13],\n [7, -28, -3, -3, -12, 1, -27, -9, -4, 2],\n [26, 14, -10, -28, 21, -4, 14, 30, 25, 17],\n [23, 19, 1, -27, 3, -26, 19, 26, -24, -6],\n [9, -1, 13, 2, 24, 6, 26, 22, 30, -20],\n [-23, -19, 15, -15, -30, 11, 6, 5, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18
|
math
|
train
| 411,402 |
math_arithmetic_matrix_determinant_level_6_6_171
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -21, -5, 16, 21, 0, 14, 13, 14, -7],\n [-2, -6, -6, 17, 12, -11, 12, 4, -21, 3],\n [10, 1, -15, 24, 23, 15, 27, -7, -29, -21],\n [6, -29, 29, 2, -3, -18, -1, 16, -6, -15],\n [-22, 22, 7, 3, 1, 29, 19, -23, 8, 14],\n [13, 29, -10, 24, 13, 6, -23, -25, -9, 6],\n [28, 24, 11, -25, -18, -29, -23, -6, -23, 21],\n [18, 3, 26, 12, 26, 11, -19, 25, 2, 20],\n [-10, 27, -20, 29, 26, 25, -23, 28, 20, -25],\n [-21, 6, -16, -9, 28, -1, 19, 28, -9, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
362
|
math
|
train
| 411,403 |
math_arithmetic_matrix_determinant_level_6_6_172
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-28, 14, 22, -12, 5, 20, -13, 14, -26, -1],\n [14, 22, 6, -27, 3, 2, 1, -12, 16, 20],\n [22, 6, 8, -18, 20, -6, -8, 2, -20, 12],\n [-12, -27, -18, 27, -5, -4, 22, -26, 10, -20],\n [5, 3, 20, -5, -15, 8, 22, 12, 6, 12],\n [20, 2, -6, -4, 8, -3, -6, -28, 2, -16],\n [-13, 1, -8, 22, 22, -6, -8, -4, -2, 19],\n [14, -12, 2, -26, 12, -28, -4, -20, 18, 19],\n [-26, 16, -20, 10, 6, 2, -2, 18, -14, 24],\n [-1, 20, 12, -20, 12, -16, 19, 19, 24, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
214
|
math
|
train
| 411,404 |
math_arithmetic_matrix_determinant_level_6_6_173
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-26, -23, -17, -6, -14, -20, -20, 25, 14, 2],\n [0, -15, -28, -9, -1, -30, -23, -30, -22, -14],\n [0, 0, -9, 15, 3, -7, -3, 29, -1, 19],\n [0, 0, 0, 22, 0, 9, -16, 8, -6, -17],\n [0, 0, 0, 0, -20, 9, 13, 10, 1, 30],\n [0, 0, 0, 0, 0, 23, -20, 30, -2, 11],\n [0, 0, 0, 0, 0, 0, -3, 21, 5, -15],\n [0, 0, 0, 0, 0, 0, 0, 3, -27, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
math
|
train
| 411,405 |
math_arithmetic_matrix_determinant_level_6_6_174
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 2, 19, 2, 10, 0, -3, 2, -15, -2],\n [2, 11, 10, -27, 14, 21, 16, 7, 3, 10],\n [19, 10, 4, 4, -5, 2, -4, 4, -27, 23],\n [2, -27, 4, -19, -26, 8, 6, 12, 7, 8],\n [10, 14, -5, -26, -11, -15, -12, -14, -23, -23],\n [0, 21, 2, 8, -15, 29, 22, -6, 8, -3],\n [-3, 16, -4, 6, -12, 22, 25, 4, -14, -6],\n [2, 7, 4, 12, -14, -6, 4, 30, -2, -10],\n [-15, 3, -27, 7, -23, 8, -14, -2, -13, 16],\n [-2, 10, 23, 8, -23, -3, -6, -10, 16, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
455
|
math
|
train
| 411,406 |
math_arithmetic_matrix_determinant_level_6_6_175
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[24, -18, 11, -11, -23, -6, -20, -28, -6, 26],\n [-18, 6, 13, 25, 27, 1, -30, 8, -22, 18],\n [-29, 8, -16, 28, 24, -17, -22, -5, 22, -9],\n [-2, 25, -10, -26, 5, 21, 16, 0, 16, -29],\n [19, -3, 14, 30, -11, -15, 4, 6, 7, -2],\n [15, 12, 11, -28, -16, -16, -29, 22, -25, 12],\n [26, 8, 5, -8, 6, 5, 18, -22, -14, -23],\n [25, -11, 19, 27, 5, 21, 28, 15, -29, -19],\n [-27, -19, 25, 29, 29, 7, -26, 16, 22, 0],\n [-29, -10, 18, -27, -8, 21, -26, -5, 27, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
516
|
math
|
train
| 411,407 |
math_arithmetic_matrix_determinant_level_6_6_176
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[21, 11, -4, -16, -20, 10, -11, 5, -13, -4],\n [11, -22, 12, -12, -23, 10, 21, 4, 6, -6],\n [-4, 12, 8, -6, 22, 15, 2, 1, 12, 3],\n [-16, -12, -6, 17, 2, 12, 2, 6, -9, -12],\n [-20, -23, 22, 2, -12, 0, -11, -2, 0, -22],\n [10, 10, 15, 12, 0, -12, -2, 0, 20, -6],\n [-11, 21, 2, 2, -11, -2, 1, -14, 6, -11],\n [5, 4, 1, 6, -2, 0, -14, 20, 19, -20],\n [-13, 6, 12, -9, 0, 20, 6, 19, 17, 10],\n [-4, -6, 3, -12, -22, -6, -11, -20, 10, -23]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
791
|
math
|
train
| 411,408 |
math_arithmetic_matrix_determinant_level_6_6_177
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 29, -25, -2, -25, -4, 18, 4, -22, -12],\n [0, -13, -15, 17, 19, 16, -11, 25, 0, -23],\n [0, 0, 9, -12, 19, 26, 8, -19, -15, -16],\n [0, 0, 0, 19, -11, -21, -25, -1, -3, 12],\n [0, 0, 0, 0, 8, 3, -30, 0, -20, -11],\n [0, 0, 0, 0, 0, -6, 15, 13, -8, -16],\n [0, 0, 0, 0, 0, 0, 29, -18, 12, 15],\n [0, 0, 0, 0, 0, 0, 0, 24, -7, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
104
|
math
|
train
| 411,409 |
math_arithmetic_matrix_determinant_level_6_6_178
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-22, -16, -23, 14, -9, 26, -1, 18, 5, -29],\n [2, 0, 8, -5, -26, -3, -24, 1, 22, 16],\n [-20, -4, -17, -24, -5, -22, -8, 30, 28, 23],\n [11, -5, -15, 9, -16, 19, -3, -3, -2, 29],\n [10, -24, -30, 26, -29, -14, 15, -12, 17, 17],\n [-23, -25, -25, 10, 10, 15, -21, 11, 21, 10],\n [13, -28, -12, 13, -10, -28, 6, -19, -8, 15],\n [-2, 26, -21, -3, -2, 30, -25, -4, -11, 3],\n [21, 2, 3, -16, 1, 10, 25, -29, -29, -4],\n [12, 27, -3, 24, -29, -28, 19, -9, -9, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
794
|
math
|
train
| 411,410 |
math_arithmetic_matrix_determinant_level_6_6_179
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 0, 21, 18, 25, -3, -30, 23, -13, 16],\n [-5, -15, -1, -30, -30, -13, -22, 16, -4, 12],\n [27, 28, 14, 9, -12, -29, -23, -2, 14, 27],\n [-20, -9, -26, 7, 3, -20, 16, -1, -23, -15],\n [-1, -3, -2, 26, -26, 19, 10, -17, 26, -26],\n [17, -25, -15, -21, -19, -12, -9, -20, 23, -30],\n [2, -14, 17, 5, -12, 25, -18, -12, -24, -24],\n [-10, 12, 21, -25, -12, -30, -18, 15, 0, -3],\n [-13, -30, -15, 2, -3, -8, -28, -25, 20, -8],\n [-24, 4, -16, 23, -3, 0, 3, 27, -29, 24]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
math
|
train
| 411,411 |
math_arithmetic_matrix_determinant_level_6_6_180
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-23, -10, -2, 12, -14, -10, -15, 2, 0, 0],\n [-10, -6, 2, 15, 10, 8, 0, 6, 6, -2],\n [-2, 2, 6, 8, 8, 11, 24, -13, 12, -12],\n [12, 15, 8, -22, 0, -15, 14, -4, -24, -9],\n [-14, 10, 8, 0, -27, 8, 10, 8, -9, 13],\n [-10, 8, 11, -15, 8, -2, -25, -5, -16, 3],\n [-15, 0, 24, 14, 10, -25, 1, -8, 20, -22],\n [2, 6, -13, -4, 8, -5, -8, -24, 0, -6],\n [0, 6, 12, -24, -9, -16, 20, 0, 5, 20],\n [0, -2, -12, -9, 13, 3, -22, -6, 20, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
536
|
math
|
train
| 411,412 |
math_arithmetic_matrix_determinant_level_6_6_181
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 3, -13, 19, 22, 0, -8, 0, 21, -24],\n [3, -15, 6, 3, -22, 0, -2, -16, -5, -6],\n [-13, 6, -25, 16, -2, 20, 14, -8, 12, 14],\n [19, 3, 16, 21, 16, -14, 15, 14, -4, 4],\n [22, -22, -2, 16, -21, -10, -8, 2, 15, 30],\n [0, 0, 20, -14, -10, 27, 12, -12, -18, -6],\n [-8, -2, 14, 15, -8, 12, -26, 21, -4, 23],\n [0, -16, -8, 14, 2, -12, 21, 13, -6, -12],\n [21, -5, 12, -4, 15, -18, -4, -6, -30, -6],\n [-24, -6, 14, 4, 30, -6, 23, -12, -6, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
732
|
math
|
train
| 411,413 |
math_arithmetic_matrix_determinant_level_6_6_182
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, -10, -2, -4, -8, -21, -15, 27, 20, -25],\n [-14, -26, -6, 15, -29, -6, -12, 7, 14, -22],\n [27, -5, -4, -19, 14, -19, 5, 6, 13, 30],\n [-25, -19, -12, -17, 0, 14, -19, -14, -8, -1],\n [-1, 19, -8, -4, 11, 25, 13, 18, -10, 25],\n [-17, -24, 7, -21, 13, 20, 20, 23, 7, 4],\n [-27, 12, -15, -7, -2, -22, 11, 26, -29, -1],\n [30, 24, -20, -10, -3, 1, -6, -8, -26, 15],\n [-4, -16, -18, 27, -4, -8, -16, -18, 0, 15],\n [25, -19, 8, 12, 0, -6, -16, 8, -4, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
357
|
math
|
train
| 411,414 |
math_arithmetic_matrix_determinant_level_6_6_183
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[27, 9, -8, -22, -3, 10, -26, 2, 22, -10],\n [9, -3, -14, 6, -10, -19, -15, 8, 14, 2],\n [-8, -14, 17, 2, -20, 28, -7, 12, -20, 21],\n [-22, 6, 2, 28, -6, 5, 27, 13, -2, -10],\n [-3, -10, -20, -6, 28, -16, -3, 11, -26, -12],\n [10, -19, 28, 5, -16, -15, -2, -1, 4, -11],\n [-26, -15, -7, 27, -3, -2, -25, -10, 16, 16],\n [2, 8, 12, 13, 11, -1, -10, -21, -10, 10],\n [22, 14, -20, -2, -26, 4, 16, -10, -24, 8],\n [-10, 2, 21, -10, -12, -11, 16, 10, 8, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
489
|
math
|
train
| 411,415 |
math_arithmetic_matrix_determinant_level_6_6_184
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[17, 13, 26, -22, -6, -14, 2, 0, -22, 5],\n [13, 6, -8, 2, -4, -26, 14, -16, -21, -10],\n [26, -8, 23, -10, -14, 2, 22, 0, 16, -4],\n [-22, 2, -10, 25, 0, 22, 4, -28, -6, -6],\n [-6, -4, -14, 0, -16, 0, -20, -8, 6, -6],\n [-14, -26, 2, 22, 0, 22, 28, 0, 14, 19],\n [2, 14, 22, 4, -20, 28, -17, 26, 8, -14],\n [0, -16, 0, -28, -8, 0, 26, 21, 14, -8],\n [-22, -21, 16, -6, 6, 14, 8, 14, -21, 10],\n [5, -10, -4, -6, -6, 19, -14, -8, 10, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
math
|
train
| 411,416 |
math_arithmetic_matrix_determinant_level_6_6_185
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-26, -15, 19, 20, -21, 22, 2, -27, 17, -10],\n [0, -19, 30, 19, -21, 15, -1, 8, 14, 25],\n [0, 0, 19, -4, 5, -10, 17, -15, 29, 15],\n [0, 0, 0, 11, 8, -11, -19, -29, 30, -13],\n [0, 0, 0, 0, 24, -13, 18, -7, 4, -30],\n [0, 0, 0, 0, 0, 10, 23, 4, -6, 9],\n [0, 0, 0, 0, 0, 0, -20, -22, 4, -22],\n [0, 0, 0, 0, 0, 0, 0, -18, 2, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -4, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
math
|
train
| 411,417 |
math_arithmetic_matrix_determinant_level_6_6_186
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[27, -21, 30, 10, -1, 2, 7, 18, -15, 29],\n [0, -24, -28, -14, 0, 24, 21, -23, 12, 3],\n [0, 0, 30, -30, 11, -16, 27, -11, -10, -15],\n [0, 0, 0, 17, -30, 17, -6, 18, -13, -28],\n [0, 0, 0, 0, 21, -4, -30, -22, -19, -27],\n [0, 0, 0, 0, 0, -6, -6, -17, 12, -10],\n [0, 0, 0, 0, 0, 0, 16, -23, -29, -5],\n [0, 0, 0, 0, 0, 0, 0, 24, -11, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
math
|
train
| 411,418 |
math_arithmetic_matrix_determinant_level_6_6_187
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-30, -26, 25, -12, 3, -18, 15, -11, -13, 17],\n [12, 30, -25, 18, 17, -13, 10, -25, -24, 5],\n [21, -18, 0, 12, 29, -12, -13, 10, -5, 26],\n [-8, -10, -20, 24, -16, 20, -27, 24, 7, 17],\n [13, -3, -7, 27, 4, -12, -24, -2, -1, 23],\n [29, -21, 4, 18, -24, 25, 6, -17, -5, 6],\n [27, 29, -13, 15, 14, 25, -9, -29, -30, -2],\n [25, -25, -20, -25, 11, 28, -28, 0, -16, 23],\n [-12, -6, 16, 2, -4, -3, 13, 29, 17, -1],\n [27, 24, 3, 19, 26, 30, -6, -1, -18, 30]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 411,419 |
math_arithmetic_matrix_determinant_level_6_6_188
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[21, 6, 7, -4, -6, -12, 20, 8, 18, -8],\n [6, 27, 4, -5, -28, 2, 19, -3, -24, -6],\n [7, 4, -6, 10, 12, 14, 2, -21, -8, 30],\n [-4, -5, 10, 19, -6, 12, 16, -17, 6, 8],\n [-6, -28, 12, -6, -24, -15, -2, -6, -15, 14],\n [-12, 2, 14, 12, -15, 27, -26, 0, 15, -28],\n [20, 19, 2, 16, -2, -26, 7, -4, -15, -16],\n [8, -3, -21, -17, -6, 0, -4, -10, 4, 2],\n [18, -24, -8, 6, -15, 15, -15, 4, 9, 8],\n [-8, -6, 30, 8, 14, -28, -16, 2, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
611
|
math
|
train
| 411,420 |
math_arithmetic_matrix_determinant_level_6_6_189
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -25, 7, 25, 9, -1, -27, -11, 12, 8],\n [22, -10, -17, 22, -1, -23, 18, 15, 11, -14],\n [14, 7, 12, -1, -7, -22, 13, 13, -14, 19],\n [19, -12, 12, 25, 4, 29, 25, -9, 21, 30],\n [7, 26, -28, -29, -26, -9, -4, -24, -8, -12],\n [-11, -9, -13, -3, -7, -21, 23, 10, -18, 6],\n [13, -16, 22, -7, -8, -8, -4, 23, 12, -24],\n [-15, 24, -3, -19, -15, 24, -28, -30, -30, 7],\n [25, 9, 12, -11, 0, 16, 14, -13, 11, -6],\n [-14, 11, -6, -27, 12, 21, -26, -5, 7, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
948
|
math
|
train
| 411,421 |
math_arithmetic_matrix_determinant_level_6_6_190
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[21, -17, -18, -24, 21, -21, -13, 11, -16, 2],\n [25, 8, 4, -20, -27, 22, 8, -16, 1, -3],\n [-23, 21, 21, 3, -18, 1, 18, 12, -2, 9],\n [5, -13, 8, -11, -28, -30, 9, -28, -26, -11],\n [20, -18, 13, -22, -12, 7, -13, -4, -13, -19],\n [-3, 20, -2, -23, -6, 4, -15, 17, -21, 8],\n [17, 3, 16, -4, -18, -15, -4, 17, 20, 21],\n [2, 14, 18, -5, 15, 13, -12, -13, 14, 2],\n [-25, 16, 11, -30, -4, -3, -28, -6, 9, 23],\n [-14, -19, 5, 23, 21, 27, -25, -21, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
336
|
math
|
train
| 411,422 |
math_arithmetic_matrix_determinant_level_6_6_191
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -18, -3, 11, -16, -10, -20, 21, 10, 26],\n [0, 12, 24, 22, -13, -8, 7, -8, 8, 5],\n [0, 0, -26, 17, 13, 1, -5, 29, -30, 23],\n [0, 0, 0, -1, -10, 19, -9, 15, -30, -6],\n [0, 0, 0, 0, -27, -2, 28, 4, 26, -28],\n [0, 0, 0, 0, 0, 26, 16, 5, -5, 11],\n [0, 0, 0, 0, 0, 0, 4, 9, 3, -18],\n [0, 0, 0, 0, 0, 0, 0, -18, -16, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
608
|
math
|
train
| 411,423 |
math_arithmetic_matrix_determinant_level_6_6_192
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, -18, 2, -4, -29, 27, -19, -19, 28, 6],\n [12, -29, -4, 2, -3, 24, 21, 15, -29, 11],\n [-4, -23, -1, 12, -27, -15, -28, 27, -4, -8],\n [17, 8, -28, 12, 14, 21, -24, 20, 7, -13],\n [-8, 18, 14, 6, -29, -15, -22, -20, 15, 0],\n [27, 21, -20, -23, -29, 28, 5, -21, -27, -4],\n [28, -18, -27, -1, -13, 24, 12, -16, -13, -2],\n [-8, 7, 5, 23, 18, -29, -12, 24, -18, 24],\n [-7, -11, 28, -19, -9, 5, 4, 5, -28, -27],\n [-1, 22, 12, 22, 3, -19, 5, 8, -30, -15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
429
|
math
|
train
| 411,424 |
math_arithmetic_matrix_determinant_level_6_6_193
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -15, 19, 0, 22, 14, 3, -14, -11, 26],\n [-15, -18, -7, 6, 18, 14, 12, 10, -6, 0],\n [19, -7, -1, -22, 14, -8, 0, -2, -14, -8],\n [0, 6, -22, 29, 12, 19, -4, 14, -4, 5],\n [22, 18, 14, 12, 1, -2, -8, -20, -3, -12],\n [14, 14, -8, 19, -2, -16, 1, 4, -18, 8],\n [3, 12, 0, -4, -8, 1, -8, -9, -6, -1],\n [-14, 10, -2, 14, -20, 4, -9, 5, -2, 16],\n [-11, -6, -14, -4, -3, -18, -6, -2, -29, -6],\n [26, 0, -8, 5, -12, 8, -1, 16, -6, -25]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
366
|
math
|
train
| 411,425 |
math_arithmetic_matrix_determinant_level_6_6_194
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-24, -1, -27, 26, -23, -8, -9, 19, -24, -26],\n [-24, -10, -4, 21, 6, 3, 7, 30, 20, 18],\n [-25, -9, 14, -9, -15, -11, -22, 4, -24, -19],\n [19, -9, 25, -25, 24, -29, 0, -5, -7, 6],\n [12, 11, -29, -28, -10, -27, -21, 13, 4, 0],\n [22, 0, -8, 13, -29, 19, 18, -26, -9, -26],\n [-9, -16, -8, -24, -15, 28, 9, -9, -14, -16],\n [21, -15, 1, 20, -16, 10, -27, 9, -9, -6],\n [-8, 21, -29, -9, -26, -23, -12, 14, -18, 29],\n [13, -27, 13, 12, -4, -28, 17, 10, 12, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
147
|
math
|
train
| 411,426 |
math_arithmetic_matrix_determinant_level_6_6_195
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-23, 29, -28, 25, -3, -3, -11, 1, -12, 28],\n [8, -7, 23, 19, 6, -16, 0, -12, 7, 27],\n [-29, -1, 14, 19, -18, 26, -14, 13, -21, -17],\n [5, 21, -14, -3, 24, -26, -17, -22, -30, 9],\n [17, 9, -4, -10, -29, 10, -8, 8, 2, 0],\n [30, 21, 21, 6, 3, 11, -23, 25, 25, -22],\n [18, 27, -24, -5, -13, 16, 17, 1, -10, 1],\n [21, 12, -12, 23, 26, 20, -3, 27, -7, 5],\n [0, -7, -3, 7, -16, 25, 17, 0, 26, -4],\n [-9, 22, -12, -13, 19, 21, -11, -19, -11, -29]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
math
|
train
| 411,427 |
math_arithmetic_matrix_determinant_level_6_6_196
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-30, -15, 12, 5, -29, -15, -15, 22, -30, -7],\n [0, 8, -25, -5, 18, -4, 28, 5, -6, 7],\n [0, 0, 22, -23, 1, 16, -1, -27, -8, 8],\n [0, 0, 0, 3, 27, -10, -20, -19, 26, -15],\n [0, 0, 0, 0, -1, 22, 12, 23, -27, -17],\n [0, 0, 0, 0, 0, -4, 12, -28, 0, -8],\n [0, 0, 0, 0, 0, 0, 4, 6, -7, 27],\n [0, 0, 0, 0, 0, 0, 0, -30, -26, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, -22, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
math
|
train
| 411,428 |
math_arithmetic_matrix_determinant_level_6_6_197
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[30, -2, -4, -14, 14, -9, -4, -22, -2, 5],\n [-2, -10, 9, -16, -12, -8, -6, -2, 2, 8],\n [-4, 9, 0, 24, -8, 17, 0, -10, -4, -21],\n [-14, -16, 24, -26, -4, 20, 26, 0, -2, -14],\n [14, -12, -8, -4, 8, -4, 8, -9, 6, -15],\n [-9, -8, 17, 20, -4, -2, 17, -6, 6, 22],\n [-4, -6, 0, 26, 8, 17, -30, 20, 18, -18],\n [-22, -2, -10, 0, -9, -6, 20, 28, -24, 18],\n [-2, 2, -4, -2, 6, 6, 18, -24, -18, 14],\n [5, 8, -21, -14, -15, 22, -18, 18, 14, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
477
|
math
|
train
| 411,429 |
math_arithmetic_matrix_determinant_level_6_6_198
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-20, 23, -19, 22, -30, 20, -24, 26, -8, -25],\n [-4, 24, 3, -1, -8, -22, -24, 5, 29, 20],\n [7, -18, 22, 30, -25, 6, 12, -10, -9, 4],\n [-17, 0, 25, -25, -6, 24, -7, -12, 19, 19],\n [14, -16, 5, -9, 24, -29, -14, 8, 5, -2],\n [-11, 14, 23, 10, 8, 15, 9, 21, 16, 4],\n [4, 10, 22, -18, 0, 22, 17, -5, 5, -8],\n [27, 25, -30, 22, 3, 7, 26, 22, 26, 20],\n [4, 7, -29, 7, -26, -21, -20, -21, -17, 27],\n [26, -29, 9, -30, 6, 17, 28, 11, -25, 17]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
592
|
math
|
train
| 411,430 |
math_arithmetic_matrix_determinant_level_6_6_199
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-27, -20, 8, -14, -12, 10, 4, -2, -21, -6],\n [-20, -27, 6, 12, -16, -5, 16, 4, -12, 12],\n [8, 6, 29, 2, -24, -12, 10, -18, 19, 10],\n [-14, 12, 2, 23, -3, 7, -1, -14, -8, 0],\n [-12, -16, -24, -3, 8, 20, 11, 0, 26, 5],\n [10, -5, -12, 7, 20, 15, 10, 6, 12, -5],\n [4, 16, 10, -1, 11, 10, -11, 1, 1, 10],\n [-2, 4, -18, -14, 0, 6, 1, 25, 14, 6],\n [-21, -12, 19, -8, 26, 12, 1, 14, -11, 10],\n [-6, 12, 10, 0, 5, -5, 10, 6, 10, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
math
|
train
| 411,431 |
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