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_200
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 28, 20, -24, 14, -22, 3, -11, 3, -9],\n [-11, 15, -23, 0, -11, 25, 1, 27, 2, -19],\n [-26, -20, -12, -3, 0, 27, -23, -25, -12, 25],\n [-11, -27, 6, 2, -22, 23, -22, 5, -14, -23],\n [5, 4, 7, 25, 13, 21, -20, -19, -16, 22],\n [-12, 29, -6, 5, 11, -26, 14, -17, -28, -11],\n [-13, -30, 30, 0, -8, -2, -10, -8, 30, 15],\n [11, 22, -16, 17, -21, 8, -13, -11, -14, 19],\n [26, -1, -3, 24, 22, -12, -5, -4, 12, -1],\n [15, -27, -5, -4, -2, 18, 30, 2, -1, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
132
|
math
|
train
| 411,432 |
math_arithmetic_matrix_determinant_level_6_6_201
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -23, 21, -28, -22, -19, 30, 3, -22, -23],\n [-10, 11, 18, 24, -3, -1, -30, 25, 24, 30],\n [0, 12, -5, 23, -10, 15, -3, -12, 26, 11],\n [1, 20, 29, -11, 23, 9, 17, 26, 23, 5],\n [-14, -14, 22, -19, 18, 22, 17, 14, 2, 27],\n [30, -17, 10, -6, -12, -21, 1, -12, -18, -15],\n [9, -4, -2, -1, 19, 28, -29, 21, 2, 24],\n [-26, 20, -12, 0, 7, 30, -30, -26, 10, 14],\n [29, 28, -19, 15, -9, 14, 21, -12, 24, 7],\n [-14, 7, -17, -25, 2, -16, -28, -9, 6, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
619
|
math
|
train
| 411,433 |
math_arithmetic_matrix_determinant_level_6_6_202
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-22, -18, 10, 22, 23, 27, 18, -22, 5, -18],\n [-1, 15, -14, 27, -4, 13, 13, 23, -8, -1],\n [20, 22, 5, -22, -13, 29, -4, 11, 16, -22],\n [-28, 26, 20, -4, 22, -29, 7, 23, 1, -23],\n [-1, 18, 1, -14, -29, 3, 25, -22, -13, 8],\n [-30, -15, 0, 12, 22, 1, -8, 28, 24, -11],\n [-9, 15, 9, 0, 19, 13, -29, -13, 30, 0],\n [-11, -28, -29, -25, -10, 1, -6, -25, 14, -11],\n [-15, -22, -1, 29, -27, 25, -14, 4, -6, 18],\n [0, 26, -11, -15, -17, -6, 23, 4, -7, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,434 |
math_arithmetic_matrix_determinant_level_6_6_203
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[8, -20, 3, 11, -25, 21, -6, 28, 2, 0],\n [0, 14, -14, 9, -1, -14, 24, 28, 10, -15],\n [0, 0, 30, 29, -8, 13, -7, 2, -18, 2],\n [0, 0, 0, 21, 5, -28, -6, 22, 16, -24],\n [0, 0, 0, 0, 13, 24, -16, 16, 18, -17],\n [0, 0, 0, 0, 0, -13, 24, 16, -26, 16],\n [0, 0, 0, 0, 0, 0, -13, 30, -2, 28],\n [0, 0, 0, 0, 0, 0, 0, -24, -23, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
math
|
train
| 411,435 |
math_arithmetic_matrix_determinant_level_6_6_204
|
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, 27, 29, -2, 17, -2, 28, 5, 6, 22],\n [0, 3, -4, -17, -4, 21, -19, -9, -7, -12],\n [0, 0, -15, 12, -21, 30, 4, -9, 17, 10],\n [0, 0, 0, -8, 30, -8, 3, -25, -10, -6],\n [0, 0, 0, 0, -14, -15, 8, -29, -7, 12],\n [0, 0, 0, 0, 0, -26, -1, -8, 20, 6],\n [0, 0, 0, 0, 0, 0, -23, 30, -25, 6],\n [0, 0, 0, 0, 0, 0, 0, 16, 4, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
math
|
train
| 411,436 |
math_arithmetic_matrix_determinant_level_6_6_205
|
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[[-12, -2, 20, 21, -13, -6, 14, -14, 12, -23],\n [4, -8, -15, 30, 3, -1, 2, 11, 25, -8],\n [-12, 11, -22, -21, -20, -29, -29, -18, -14, -2],\n [15, 15, 2, 13, 21, -28, 5, -13, -25, 10],\n [-7, -16, -20, -25, -12, 29, 11, 15, -12, 19],\n [8, 22, 7, 12, 16, 24, 12, 3, 18, 7],\n [11, -14, 2, 4, -12, 26, -16, -23, 20, -9],\n [-12, 28, -28, 30, -9, -12, 4, 27, -20, 5],\n [24, 14, -24, -26, -21, 5, -23, 8, -28, 19],\n [3, -20, 19, -29, -26, -29, -20, 27, -22, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
567
|
math
|
train
| 411,437 |
math_arithmetic_matrix_determinant_level_6_6_206
|
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[[-3, 12, -11, -4, 2, 27, 29, 10, -8, 0],\n [0, -20, -30, -20, 9, 30, 4, 13, -11, -24],\n [0, 0, 21, -22, -20, -9, 15, 30, 25, 2],\n [0, 0, 0, -30, -4, 25, 0, 25, 10, 0],\n [0, 0, 0, 0, 16, -13, -4, 21, -25, 9],\n [0, 0, 0, 0, 0, 5, -10, 16, -25, 2],\n [0, 0, 0, 0, 0, 0, 11, 12, -18, 3],\n [0, 0, 0, 0, 0, 0, 0, -11, 14, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,438 |
math_arithmetic_matrix_determinant_level_6_6_207
|
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[[20, 8, -20, -1, 30, -2, 9, -29, 23, -7],\n [0, 19, -22, -21, 7, 17, 16, 25, -7, -2],\n [0, 0, -14, 9, -12, -29, 3, 26, 21, -4],\n [0, 0, 0, 15, 24, -5, 28, -19, 17, -15],\n [0, 0, 0, 0, -28, 24, 24, -23, 5, -21],\n [0, 0, 0, 0, 0, 3, 22, -15, 22, -9],\n [0, 0, 0, 0, 0, 0, 19, 27, 8, 2],\n [0, 0, 0, 0, 0, 0, 0, -15, -25, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, -28],\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
| 411,439 |
math_arithmetic_matrix_determinant_level_6_6_208
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[16, 18, 24, -24, -6, -23, 0, 13, -6, -5],\n [18, 25, -14, -8, -10, 13, -14, 6, 27, 10],\n [24, -14, -17, -5, -19, -8, 22, 18, -10, -11],\n [-24, -8, -5, 0, -2, 22, -5, -4, -24, -3],\n [-6, -10, -19, -2, -18, 4, -4, -6, 13, -6],\n [-23, 13, -8, 22, 4, 19, 0, 10, 15, 14],\n [0, -14, 22, -5, -4, 0, -23, 4, -12, -20],\n [13, 6, 18, -4, -6, 10, 4, -30, 12, -4],\n [-6, 27, -10, -24, 13, 15, -12, 12, 3, 4],\n [-5, 10, -11, -3, -6, 14, -20, -4, 4, 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"
}
] |
296
|
math
|
train
| 411,440 |
math_arithmetic_matrix_determinant_level_6_6_209
|
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[[-19, 22, 8, -11, -21, 7, 0, 21, 20, -6],\n [0, 26, -5, -18, -23, 3, 29, -3, -11, 21],\n [0, 0, -24, -8, 11, 29, 29, -4, -1, -20],\n [0, 0, 0, -6, -27, 22, 25, -25, -23, -18],\n [0, 0, 0, 0, -16, -22, -19, 24, 20, 5],\n [0, 0, 0, 0, 0, 3, 16, -19, -9, -17],\n [0, 0, 0, 0, 0, 0, 13, 19, 5, -23],\n [0, 0, 0, 0, 0, 0, 0, 10, -10, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
math
|
train
| 411,441 |
math_arithmetic_matrix_determinant_level_6_6_210
|
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, 12, -2, -27, 6, -13, -7, -10, 4, -28],\n [12, -14, -17, 6, 7, 11, -12, 14, 26, 13],\n [-2, -17, -6, -25, -1, 2, 3, -13, -4, -1],\n [-27, 6, -25, 7, -18, -11, -23, 20, -18, -16],\n [6, 7, -1, -18, -2, 0, -16, -18, -25, 7],\n [-13, 11, 2, -11, 0, -19, -15, -18, -2, 6],\n [-7, -12, 3, -23, -16, -15, 8, 4, 1, 16],\n [-10, 14, -13, 20, -18, -18, 4, 10, -4, 6],\n [4, 26, -4, -18, -25, -2, 1, -4, -26, -8],\n [-28, 13, -1, -16, 7, 6, 16, 6, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
333
|
math
|
train
| 411,442 |
math_arithmetic_matrix_determinant_level_6_6_211
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 30, 17, -6, -7, 26, -30, -9, -22, -28],\n [0, 9, 16, -26, 22, 19, -2, -27, -9, 20],\n [16, 1, -2, 5, 12, 20, -8, 12, 18, 5],\n [21, 0, 11, -23, 14, 30, -29, 14, 3, 14],\n [18, -12, -6, -10, -24, 19, 28, 15, 6, -15],\n [20, -13, 28, -21, 26, -21, 18, 1, -15, 10],\n [-7, 15, -1, -4, -22, -6, -27, -9, -12, 15],\n [21, -19, 29, 3, 9, -7, 16, 19, 0, 18],\n [9, -20, -17, 25, 26, -13, -13, 23, 23, -16],\n [-28, -1, 30, 17, -1, -17, -25, 24, 18, -15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
541
|
math
|
train
| 411,443 |
math_arithmetic_matrix_determinant_level_6_6_212
|
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, 2, -19, -9, 8, 6, -4, 20, 8, -14],\n [2, -13, 3, 0, -16, 0, -10, 2, -18, -14],\n [-19, 3, -29, -4, 9, 22, 9, 1, 0, 22],\n [-9, 0, -4, 30, -12, -10, 15, 6, -12, -6],\n [8, -16, 9, -12, 21, -2, 2, -7, 2, 16],\n [6, 0, 22, -10, -2, 21, 11, -18, -18, 17],\n [-4, -10, 9, 15, 2, 11, -18, -10, -11, -20],\n [20, 2, 1, 6, -7, -18, -10, -5, 11, -16],\n [8, -18, 0, -12, 2, -18, -11, 11, 28, 20],\n [-14, -14, 22, -6, 16, 17, -20, -16, 20, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
math
|
train
| 411,444 |
math_arithmetic_matrix_determinant_level_6_6_213
|
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, 6, 15, -7, 0, -12, -3, 12, 1, -3],\n [6, 26, -10, -8, 4, 4, 24, 14, -6, -14],\n [15, -10, -28, 2, 10, -18, -10, -13, 7, 10],\n [-7, -8, 2, -28, 4, 18, -6, -12, 20, -8],\n [0, 4, 10, 4, 12, -8, -2, 22, 28, -9],\n [-12, 4, -18, 18, -8, 29, 10, 0, 5, 10],\n [-3, 24, -10, -6, -2, 10, -20, 4, -19, 25],\n [12, 14, -13, -12, 22, 0, 4, -17, 8, -2],\n [1, -6, 7, 20, 28, 5, -19, 8, -9, 8],\n [-3, -14, 10, -8, -9, 10, 25, -2, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
595
|
math
|
train
| 411,445 |
math_arithmetic_matrix_determinant_level_6_6_214
|
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[[-12, -11, 18, -22, -20, 1, 26, 20, -9, -6],\n [0, 29, 4, -4, 2, -9, -24, -12, -2, 3],\n [0, 0, 4, 26, -13, 22, -17, -7, -1, 4],\n [0, 0, 0, -8, -28, 3, -2, 9, 20, -23],\n [0, 0, 0, 0, 21, -23, 14, -25, -13, -6],\n [0, 0, 0, 0, 0, -30, -6, -7, -26, -7],\n [0, 0, 0, 0, 0, 0, -27, 13, -19, 21],\n [0, 0, 0, 0, 0, 0, 0, -20, -15, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
math
|
train
| 411,446 |
math_arithmetic_matrix_determinant_level_6_6_215
|
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[[-19, 22, -6, -13, -16, -15, -14, 24, -1, 15],\n [0, 8, -29, -22, 16, 20, -20, -5, 0, -7],\n [0, 0, 9, 20, 21, -16, 14, 18, 22, -5],\n [0, 0, 0, 13, -28, 1, -21, 10, 6, -15],\n [0, 0, 0, 0, -22, -10, -14, -19, 10, -25],\n [0, 0, 0, 0, 0, 26, 10, 18, 16, 26],\n [0, 0, 0, 0, 0, 0, -27, 27, 19, -14],\n [0, 0, 0, 0, 0, 0, 0, 23, 10, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
math
|
train
| 411,447 |
math_arithmetic_matrix_determinant_level_6_6_216
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-18, 6, 12, 2, -22, -9, 6, -7, 2, -6],\n [6, 20, -7, -19, 16, 0, 6, 16, 12, 24],\n [12, -7, -2, 2, 0, -9, -1, 0, -6, -22],\n [2, -19, 2, -27, -24, 14, 14, -11, 4, -16],\n [-22, 16, 0, -24, 20, -2, -10, -4, -18, -11],\n [-9, 0, -9, 14, -2, -6, -5, 17, 18, -28],\n [6, 6, -1, 14, -10, -5, 13, -10, 24, -4],\n [-7, 16, 0, -11, -4, 17, -10, 16, 4, 6],\n [2, 12, -6, 4, -18, 18, 24, 4, 0, -13],\n [-6, 24, -22, -16, -11, -28, -4, 6, -13, 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"
}
] |
607
|
math
|
train
| 411,448 |
math_arithmetic_matrix_determinant_level_6_6_217
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-20, 4, -15, -11, 8, -10, 0, -18, -14, 14],\n [4, -14, 4, 3, 10, 7, 18, -1, -14, 27],\n [-15, 4, 28, -4, 8, 5, -22, -24, -18, -10],\n [-11, 3, -4, 28, 17, 22, 0, -5, 16, 22],\n [8, 10, 8, 17, -25, 4, -4, -18, 8, -13],\n [-10, 7, 5, 22, 4, 18, 4, 8, 2, -16],\n [0, 18, -22, 0, -4, 4, -18, 17, -12, 14],\n [-18, -1, -24, -5, -18, 8, 17, 22, -21, 20],\n [-14, -14, -18, 16, 8, 2, -12, -21, -4, -2],\n [14, 27, -10, 22, -13, -16, 14, 20, -2, 8]]\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"
}
] |
190
|
math
|
train
| 411,449 |
math_arithmetic_matrix_determinant_level_6_6_218
|
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[[12, -24, 9, 12, -3, 30, 23, -15, -8, -23],\n [0, -13, -15, 29, -24, 3, -8, 26, -16, -28],\n [0, 0, -14, 21, 22, 26, -20, -2, 23, 12],\n [0, 0, 0, -4, 17, 30, 0, 2, -8, -10],\n [0, 0, 0, 0, -13, -18, 3, 30, 28, -26],\n [0, 0, 0, 0, 0, 14, -22, 19, -25, 14],\n [0, 0, 0, 0, 0, 0, -3, 9, -8, -18],\n [0, 0, 0, 0, 0, 0, 0, -24, -2, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -27, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
888
|
math
|
train
| 411,450 |
math_arithmetic_matrix_determinant_level_6_6_219
|
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[[10, -8, -22, -30, 15, 2, 27, -8, -3, 2],\n [-1, 19, 18, 8, 23, -27, -2, -11, -6, 16],\n [8, 14, -29, -21, -27, 17, 10, 16, 15, -4],\n [23, 30, 23, 22, 1, -1, -10, 10, 16, 1],\n [28, -7, 25, -5, 17, -20, 17, 7, 15, -24],\n [-30, 6, 14, 8, 0, -14, 28, 12, -27, 18],\n [22, -20, -6, 23, 13, 7, -9, 23, 3, -20],\n [17, -16, 22, 8, 21, -5, -22, 27, -22, -18],\n [26, -28, -7, 4, -17, 4, 4, -10, -7, 4],\n [-20, -8, -19, -25, -11, 7, -12, 19, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
330
|
math
|
train
| 411,451 |
math_arithmetic_matrix_determinant_level_6_6_220
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -4, -4, -24, 25, -6, 1, 7, 26, 30],\n [28, -7, -12, -26, -21, 9, 9, 4, 14, 13],\n [-28, -21, -4, -19, 4, 3, 19, -15, -30, 18],\n [-11, 29, 29, -8, 15, 17, 27, 12, -3, 13],\n [30, -7, -23, -16, -15, -8, -27, 3, -15, -5],\n [24, 25, -21, -29, 11, -23, 14, 8, 0, -22],\n [4, -2, -8, -18, 10, -15, 5, -10, 24, -29],\n [-6, -13, 6, -7, 1, 18, 19, -22, -8, -9],\n [7, -28, -18, -11, 16, 23, -14, -5, 13, 8],\n [-1, -11, 22, -8, -21, -20, 16, -2, 12, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
477
|
math
|
train
| 411,452 |
math_arithmetic_matrix_determinant_level_6_6_221
|
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[[24, -21, -27, -11, 4, -25, -9, 27, -5, 9],\n [30, 0, 12, 10, -30, -24, 6, -29, -13, 28],\n [13, -17, -24, 23, -16, -16, 7, 7, 26, 17],\n [9, -29, 21, 12, 25, 27, 11, 30, -16, -16],\n [-24, -17, -10, 13, -11, -21, 3, 1, 10, -5],\n [22, -10, -21, -3, 19, -15, 26, -7, 19, 30],\n [-4, 10, -2, 20, -3, 22, 21, -11, 29, -8],\n [23, -7, -29, 0, 4, 7, -28, -19, 2, 1],\n [25, 23, 14, 26, 6, 16, -20, 4, 20, -5],\n [-25, 20, 18, -2, 3, -24, 29, 12, -28, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
math
|
train
| 411,453 |
math_arithmetic_matrix_determinant_level_6_6_222
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 18, -12, -9, -13, -26, -2, -22, 25, -21],\n [0, -10, 15, -4, -26, 14, -22, -28, -6, 8],\n [0, 0, 16, 0, -4, 4, 2, 28, -3, 19],\n [0, 0, 0, -5, 9, 4, -28, -21, -15, 17],\n [0, 0, 0, 0, 28, 14, -18, 18, -29, -8],\n [0, 0, 0, 0, 0, -15, -16, -4, 11, 0],\n [0, 0, 0, 0, 0, 0, 17, -3, 3, -17],\n [0, 0, 0, 0, 0, 0, 0, 16, -28, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, -10, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\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
| 411,454 |
math_arithmetic_matrix_determinant_level_6_6_223
|
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, -2, 23, -4, 20, -9, -10, 12, 10, -15],\n [-2, 17, -18, 1, 9, -6, 0, 21, -6, 8],\n [23, -18, -10, 18, 3, -13, 0, -21, -18, 4],\n [-4, 1, 18, -26, 0, -2, 18, -1, -12, 18],\n [20, 9, 3, 0, 16, -14, 19, 13, 2, -6],\n [-9, -6, -13, -2, -14, -13, 4, 11, 17, 30],\n [-10, 0, 0, 18, 19, 4, 13, -11, 14, 5],\n [12, 21, -21, -1, 13, 11, -11, -23, 20, 10],\n [10, -6, -18, -12, 2, 17, 14, 20, 24, -2],\n [-15, 8, 4, 18, -6, 30, 5, 10, -2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
609
|
math
|
train
| 411,455 |
math_arithmetic_matrix_determinant_level_6_6_224
|
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, 0, 2, -7, 13, 8, -4, -14, 16, 20],\n [0, -5, 22, -26, 18, 9, -11, 14, -2, -18],\n [2, 22, 2, 17, -8, -7, -4, -10, 21, -4],\n [-7, -26, 17, 3, -8, -18, -18, -10, -2, 16],\n [13, 18, -8, -8, -9, 16, 2, 21, 22, -2],\n [8, 9, -7, -18, 16, -29, 2, 21, -26, -14],\n [-4, -11, -4, -18, 2, 2, -7, -10, -2, -16],\n [-14, 14, -10, -10, 21, 21, -10, 29, 22, -8],\n [16, -2, 21, -2, 22, -26, -2, 22, 3, -6],\n [20, -18, -4, 16, -2, -14, -16, -8, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
math
|
train
| 411,456 |
math_arithmetic_matrix_determinant_level_6_6_225
|
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, 23, 22, 0, 23, 0, 29, 14, 16, -2],\n [0, -16, 6, 23, 23, -29, -6, 3, -15, 21],\n [0, 0, 7, 15, 23, 21, 0, -12, -25, -6],\n [0, 0, 0, 12, -17, 20, -17, 24, -25, 26],\n [0, 0, 0, 0, -30, -30, 19, -22, -28, 21],\n [0, 0, 0, 0, 0, -12, 26, -30, 27, -1],\n [0, 0, 0, 0, 0, 0, 23, -23, -7, 10],\n [0, 0, 0, 0, 0, 0, 0, 20, -21, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
math
|
train
| 411,457 |
math_arithmetic_matrix_determinant_level_6_6_226
|
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[[-9, -1, 10, 10, -27, -6, -4, -12, 7, -15],\n [-1, -30, 12, -11, 2, 26, 16, -14, 16, -4],\n [10, 12, 29, -6, 2, -1, -10, -26, 7, -1],\n [10, -11, -6, 29, -25, -2, -6, 14, 8, -6],\n [-27, 2, 2, -25, -11, -5, 20, 24, 4, 20],\n [-6, 26, -1, -2, -5, 4, 6, -15, 0, 22],\n [-4, 16, -10, -6, 20, 6, -12, 6, 26, -29],\n [-12, -14, -26, 14, 24, -15, 6, 5, -2, 8],\n [7, 16, 7, 8, 4, 0, 26, -2, 1, 5],\n [-15, -4, -1, -6, 20, 22, -29, 8, 5, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
math
|
train
| 411,458 |
math_arithmetic_matrix_determinant_level_6_6_227
|
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[[-15, -20, -26, 13, -15, -14, -2, 16, 10, 14],\n [-20, -5, 14, -11, -15, 14, 2, -12, -25, -2],\n [-26, 14, 20, 4, -6, -12, 0, -4, 10, 0],\n [13, -11, 4, 20, 6, -12, -13, 20, 0, 5],\n [-15, -15, -6, 6, -13, 3, -12, 3, 1, -12],\n [-14, 14, -12, -12, 3, -14, 25, 19, -4, -8],\n [-2, 2, 0, -13, -12, 25, 11, -24, 5, -3],\n [16, -12, -4, 20, 3, 19, -24, 9, 10, 9],\n [10, -25, 10, 0, 1, -4, 5, 10, -12, 8],\n [14, -2, 0, 5, -12, -8, -3, 9, 8, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
756
|
math
|
train
| 411,459 |
math_arithmetic_matrix_determinant_level_6_6_228
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[16, 14, 27, -2, 24, 6, 26, -15, 4, -27],\n [-19, 20, -4, -4, -7, 6, 2, -14, -30, -17],\n [-11, -16, -21, 14, 23, 9, 6, -12, 18, 20],\n [8, 23, 4, 11, -11, -8, -15, 6, -25, 10],\n [-5, -21, 30, -8, 7, -16, -14, 16, -12, 5],\n [15, 8, 0, -16, -14, -29, -13, -29, -15, -27],\n [6, -21, 19, 27, 5, -3, 17, -27, -25, -8],\n [26, 10, -7, -24, -16, 16, 19, -24, 17, -1],\n [14, 20, -22, 20, 24, -2, 28, -3, -28, 19],\n [-11, 5, 10, 21, 29, 3, 26, -3, 9, -28]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
198
|
math
|
train
| 411,460 |
math_arithmetic_matrix_determinant_level_6_6_229
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-29, -16, 2, 27, 1, 8, -4, -10, 6, 11],\n [-16, -25, 2, 15, 4, -9, -4, -23, -18, -4],\n [2, 2, -19, -18, 14, 16, -8, 20, -12, 22],\n [27, 15, -18, -10, -2, -10, -17, 8, 20, -8],\n [1, 4, 14, -2, 10, 6, -4, -2, -22, 2],\n [8, -9, 16, -10, 6, 24, 1, -10, -6, 27],\n [-4, -4, -8, -17, -4, 1, -23, 5, -4, 4],\n [-10, -23, 20, 8, -2, -10, 5, 13, -2, 3],\n [6, -18, -12, 20, -22, -6, -4, -2, -7, -10],\n [11, -4, 22, -8, 2, 27, 4, 3, -10, -23]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
254
|
math
|
train
| 411,461 |
math_arithmetic_matrix_determinant_level_6_6_230
|
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[[-5, 10, -3, -21, 13, -14, -5, 24, -14, 20],\n [1, -21, -28, -14, -23, -2, -14, -25, 8, 21],\n [2, 28, 7, 13, 21, 25, -30, 29, -30, -26],\n [-27, -26, 5, -22, 19, 17, -8, 12, 8, 5],\n [15, 7, 20, 15, 20, -12, -3, -17, -24, 16],\n [27, -11, 30, -23, 10, -6, 28, 17, 16, -1],\n [6, 17, -28, -6, 1, -16, -25, 12, 27, -6],\n [11, 5, -3, -17, -19, -6, -14, 22, 12, 20],\n [28, 22, -22, 27, -22, -5, 20, -4, -18, -21],\n [11, 28, -1, -25, -20, 23, -28, -12, 22, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
271
|
math
|
train
| 411,462 |
math_arithmetic_matrix_determinant_level_6_6_231
|
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, -23, -8, -24, -26, 13, 4, 23, -10, -8],\n [10, 20, 2, 24, -25, 12, -3, -18, 29, -19],\n [-24, -16, 26, -25, 9, -16, 28, -29, 24, 6],\n [-5, 19, -11, 23, 1, -11, -7, -26, -25, 25],\n [20, -10, 28, -7, -15, 15, 12, 1, -6, 19],\n [2, -14, 18, -16, -27, 11, -15, 25, -1, 5],\n [23, 20, 6, 7, -17, 14, -24, -14, -28, -1],\n [-4, -25, 30, -15, -4, 13, 19, -25, 3, -18],\n [-9, -17, 21, 25, -17, -1, -30, -27, -8, 26],\n [11, -14, 27, -29, 0, -17, 9, 21, 27, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
435
|
math
|
train
| 411,463 |
math_arithmetic_matrix_determinant_level_6_6_232
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -8, 9, 0, -26, 16, -9, 2, -17, -16],\n [-8, 5, 0, 2, 2, -8, -25, 6, -14, -24],\n [9, 0, 23, -6, -10, 4, -22, 6, 8, 24],\n [0, 2, -6, 29, 12, -13, 4, 10, -5, 26],\n [-26, 2, -10, 12, 3, -16, 14, 5, -7, 8],\n [16, -8, 4, -13, -16, -28, -12, 2, -10, -20],\n [-9, -25, -22, 4, 14, -12, -22, -2, -18, 20],\n [2, 6, 6, 10, 5, 2, -2, -1, -20, -10],\n [-17, -14, 8, -5, -7, -10, -18, -20, 6, -12],\n [-16, -24, 24, 26, 8, -20, 20, -10, -12, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
730
|
math
|
train
| 411,464 |
math_arithmetic_matrix_determinant_level_6_6_233
|
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[[6, -5, 4, 0, -8, -12, -29, -6, 10, 0],\n [-5, 26, -11, -10, 10, 28, -6, -23, -2, 2],\n [4, -11, 8, 4, 14, -3, 2, 5, 16, -5],\n [0, -10, 4, 5, -14, -4, 26, 18, 22, 14],\n [-8, 10, 14, -14, -14, -14, 19, -10, 12, -26],\n [-12, 28, -3, -4, -14, -23, 4, 20, 6, -18],\n [-29, -6, 2, 26, 19, 4, 12, -11, 14, -14],\n [-6, -23, 5, 18, -10, 20, -11, -4, -14, 18],\n [10, -2, 16, 22, 12, 6, 14, -14, 28, -15],\n [0, 2, -5, 14, -26, -18, -14, 18, -15, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
631
|
math
|
train
| 411,465 |
math_arithmetic_matrix_determinant_level_6_6_234
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-24, -8, 8, 8, 7, -4, 22, -2, 22, 1],\n [-8, -24, 22, -4, -15, 22, -11, -26, -7, 18],\n [8, 22, 26, 20, 3, -16, 4, -12, -8, 25],\n [8, -4, 20, -3, -20, -10, -20, 13, 24, 10],\n [7, -15, 3, -20, -21, -12, 28, 0, 18, 8],\n [-4, 22, -16, -10, -12, 27, 8, -10, -20, 18],\n [22, -11, 4, -20, 28, 8, -9, -23, -8, 6],\n [-2, -26, -12, 13, 0, -10, -23, 21, -6, 21],\n [22, -7, -8, 24, 18, -20, -8, -6, 15, 26],\n [1, 18, 25, 10, 8, 18, 6, 21, 26, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
712
|
math
|
train
| 411,466 |
math_arithmetic_matrix_determinant_level_6_6_235
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -12, -8, -11, 25, 5, -9, 1, -23, 21],\n [0, 7, 21, 2, 30, 22, -10, -2, 25, 6],\n [0, 0, 22, -29, -16, 23, -29, 3, -28, 19],\n [0, 0, 0, 20, -28, -19, 30, -27, 16, -2],\n [0, 0, 0, 0, -18, 26, -13, 7, 7, -3],\n [0, 0, 0, 0, 0, -14, -16, -7, -5, 30],\n [0, 0, 0, 0, 0, 0, -26, -15, 5, 2],\n [0, 0, 0, 0, 0, 0, 0, 16, -23, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, -22],\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"
}
] |
200
|
math
|
train
| 411,467 |
math_arithmetic_matrix_determinant_level_6_6_236
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[19, 10, 16, 21, -6, 20, -12, 2, 24, 0],\n [10, -17, 2, -21, 8, -17, -2, 2, 10, -10],\n [16, 2, 3, -8, -1, -14, -14, 1, -14, 26],\n [21, -21, -8, 1, -23, -18, 20, 20, 22, -2],\n [-6, 8, -1, -23, 9, 8, 3, 6, 9, -6],\n [20, -17, -14, -18, 8, -13, -2, 10, -5, 4],\n [-12, -2, -14, 20, 3, -2, -25, 8, -2, 6],\n [2, 2, 1, 20, 6, 10, 8, 20, -28, -16],\n [24, 10, -14, 22, 9, -5, -2, -28, 0, 17],\n [0, -10, 26, -2, -6, 4, 6, -16, 17, -26]]\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"
}
] |
526
|
math
|
train
| 411,468 |
math_arithmetic_matrix_determinant_level_6_6_237
|
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[[-15, 5, -21, 10, 28, 10, -5, -10, 29, 10],\n [5, 22, 15, 2, -12, 16, -13, 6, 14, 21],\n [-21, 15, 5, 0, -6, -16, 2, 20, 20, 5],\n [10, 2, 0, 8, -18, -2, 28, 20, 6, -16],\n [28, -12, -6, -18, 19, -6, -5, 2, 0, -22],\n [10, 16, -16, -2, -6, -29, 12, -20, -21, -8],\n [-5, -13, 2, 28, -5, 12, -14, 22, 0, 4],\n [-10, 6, 20, 20, 2, -20, 22, -13, -12, 11],\n [29, 14, 20, 6, 0, -21, 0, -12, 18, -8],\n [10, 21, 5, -16, -22, -8, 4, 11, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
math
|
train
| 411,469 |
math_arithmetic_matrix_determinant_level_6_6_238
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, -7, 18, -7, -28, -26, -19, -17, -6, 10],\n [-16, -6, 2, 3, 7, -19, -9, 17, -12, -7],\n [3, -16, -10, -17, 22, 0, 11, 13, 19, -21],\n [-27, -2, -2, -14, -25, -5, -26, -6, 20, 7],\n [20, 9, 5, -29, -18, 16, -22, -27, -14, 21],\n [22, 26, -24, 7, 20, 28, 0, -29, 11, -9],\n [-2, 19, -18, -24, 17, -30, -5, 19, 4, -25],\n [12, -29, -22, -3, -19, -21, 12, 22, 26, -28],\n [29, 25, 18, 13, 4, 21, -9, -22, 28, -15],\n [-12, 16, 20, 1, 10, 6, 28, -30, 9, -23]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
629
|
math
|
train
| 411,470 |
math_arithmetic_matrix_determinant_level_6_6_239
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[27, 1, 16, -17, -11, -29, 25, 24, 16, -29],\n [-2, 14, -6, 29, 2, -1, -19, 0, 9, -29],\n [-21, -27, -7, 14, 22, 18, -1, 6, 1, -11],\n [19, 13, -24, 24, -15, 15, 13, 1, -14, 16],\n [13, 15, 9, 28, 9, -23, -8, -20, 14, -25],\n [-15, 10, 5, 14, 15, 10, 27, 17, -6, -18],\n [18, -5, 17, 30, -17, 28, -4, -14, 9, -4],\n [-20, 7, -2, 27, -22, 30, 20, -8, -8, 12],\n [25, 8, -2, 17, -8, 29, -26, 21, 6, 24],\n [-25, 22, 16, 14, -15, -12, 11, -13, -30, -5]]\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"
}
] |
732
|
math
|
train
| 411,471 |
math_arithmetic_matrix_determinant_level_6_6_240
|
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[[17, 1, -22, -21, -22, -2, -3, -6, -2, 10],\n [1, 21, 2, 6, -14, -7, -4, 13, 14, 1],\n [-22, 2, 3, -10, -2, -8, -2, -28, 0, 7],\n [-21, 6, -10, 14, -12, 13, -10, 4, 14, 3],\n [-22, -14, -2, -12, 25, -7, 28, 16, -24, -10],\n [-2, -7, -8, 13, -7, -10, -20, 3, 12, -16],\n [-3, -4, -2, -10, 28, -20, -19, -8, -6, 24],\n [-6, 13, -28, 4, 16, 3, -8, 23, 7, -2],\n [-2, 14, 0, 14, -24, 12, -6, 7, 28, 7],\n [10, 1, 7, 3, -10, -16, 24, -2, 7, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
974
|
math
|
train
| 411,472 |
math_arithmetic_matrix_determinant_level_6_6_241
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -6, 28, 0, -1, -18, -25, 16, -1, -16],\n [25, -5, 22, -2, -15, 0, 17, 0, -21, -2],\n [24, -19, -5, 3, 23, -10, 27, -25, 9, 11],\n [4, 6, 16, -8, 6, -6, 22, 29, 26, 20],\n [-30, 13, -4, 15, 2, -25, -12, -25, 29, -16],\n [25, 5, 9, 9, 26, 10, 15, 11, 8, -20],\n [-30, -26, -4, -15, 6, 4, 1, 15, 25, 28],\n [-16, -14, 13, -3, -12, -25, -27, 6, 4, 27],\n [26, 23, -7, -30, -15, 3, -16, -25, 28, 17],\n [-27, -11, 28, -13, 13, -16, 21, -20, 19, -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"
}
] |
524
|
math
|
train
| 411,473 |
math_arithmetic_matrix_determinant_level_6_6_242
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 8, 8, 20, -1, 7, 0, 22, 4, -3],\n [8, 30, 12, 0, 10, -20, -6, 8, -10, 1],\n [8, 12, -28, -4, 10, -22, -12, -4, -2, -6],\n [20, 0, -4, -25, 16, -22, 9, 12, -20, 7],\n [-1, 10, 10, 16, -10, 22, -17, -14, -16, -8],\n [7, -20, -22, -22, 22, -8, -6, 24, 0, 14],\n [0, -6, -12, 9, -17, -6, -19, 4, -4, 5],\n [22, 8, -4, 12, -14, 24, 4, 4, -3, 11],\n [4, -10, -2, -20, -16, 0, -4, -3, -24, 14],\n [-3, 1, -6, 7, -8, 14, 5, 11, 14, 27]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
652
|
math
|
train
| 411,474 |
math_arithmetic_matrix_determinant_level_6_6_243
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -29, 21, 10, -25, 12, 1, 27, -4, -6],\n [0, 7, -7, 27, -9, -29, -29, -6, -25, 6],\n [0, 0, -1, 20, 28, -14, -4, -2, 12, 6],\n [0, 0, 0, 11, -2, 24, -30, 24, 24, 0],\n [0, 0, 0, 0, 24, 21, 20, -26, -10, -26],\n [0, 0, 0, 0, 0, -27, 4, -23, -2, -26],\n [0, 0, 0, 0, 0, 0, 5, 23, 23, 27],\n [0, 0, 0, 0, 0, 0, 0, 1, -11, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, 4],\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"
}
] |
760
|
math
|
train
| 411,475 |
math_arithmetic_matrix_determinant_level_6_6_244
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-20, 10, 24, -10, 4, 8, -3, -18, 7, 5],\n [10, 0, -29, -18, 4, 16, -16, -5, -4, -12],\n [24, -29, 15, -2, 14, -4, -8, -6, -16, 2],\n [-10, -18, -2, 25, -20, 8, -2, -5, -2, 19],\n [4, 4, 14, -20, -21, 18, -10, 8, -20, 0],\n [8, 16, -4, 8, 18, -29, -19, -23, -22, 14],\n [-3, -16, -8, -2, -10, -19, 30, -2, 8, 6],\n [-18, -5, -6, -5, 8, -23, -2, -25, 8, 6],\n [7, -4, -16, -2, -20, -22, 8, 8, -16, 22],\n [5, -12, 2, 19, 0, 14, 6, 6, 22, 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"
}
] |
407
|
math
|
train
| 411,476 |
math_arithmetic_matrix_determinant_level_6_6_245
|
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[[-18, 27, -27, -11, -2, 16, 30, -10, 5, -10],\n [0, 1, 16, 1, 12, -13, -23, 24, 11, -8],\n [0, 0, -16, 14, 29, 9, -27, 25, 15, 2],\n [0, 0, 0, -25, -21, -21, -28, 12, -12, 26],\n [0, 0, 0, 0, 18, 28, 6, 27, 10, 21],\n [0, 0, 0, 0, 0, -28, -30, 5, 9, -15],\n [0, 0, 0, 0, 0, 0, -25, -20, -19, 3],\n [0, 0, 0, 0, 0, 0, 0, -11, -20, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,477 |
math_arithmetic_matrix_determinant_level_6_6_246
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[15, -23, 6, -4, 4, -16, -6, 28, 12, 4],\n [-23, -24, -4, -10, 10, 24, 9, -18, -14, -2],\n [6, -4, -30, 0, -10, 15, 5, 0, 4, -20],\n [-4, -10, 0, 22, 12, 13, 3, 2, -2, -13],\n [4, 10, -10, 12, -19, 19, -2, 10, 2, -10],\n [-16, 24, 15, 13, 19, 14, -8, -2, -12, 13],\n [-6, 9, 5, 3, -2, -8, -16, -12, -2, 18],\n [28, -18, 0, 2, 10, -2, -12, 7, 4, -27],\n [12, -14, 4, -2, 2, -12, -2, 4, -7, 11],\n [4, -2, -20, -13, -10, 13, 18, -27, 11, 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"
}
] |
666
|
math
|
train
| 411,478 |
math_arithmetic_matrix_determinant_level_6_6_247
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-23, 18, -29, -10, -22, -3, -9, 20, 8, -9],\n [-11, 30, -11, -9, 26, -27, -12, -21, 5, 17],\n [-6, -4, -6, -1, 18, -15, 22, 19, 21, -20],\n [16, -11, -13, 1, -22, 21, -15, -20, 6, -5],\n [26, 22, -21, 1, 3, 11, 6, 28, -17, 8],\n [25, 27, -20, 20, -5, -2, 30, 28, -14, 13],\n [-28, -23, -28, 15, 23, -29, -29, -2, -12, -4],\n [-18, -26, -13, -25, -22, 26, 14, 2, 28, -8],\n [-30, -30, 27, -16, 21, -19, -16, 18, -17, -28],\n [-8, -12, -11, -9, 27, 11, -5, 1, 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"
}
] |
434
|
math
|
train
| 411,479 |
math_arithmetic_matrix_determinant_level_6_6_248
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[8, 21, -5, -25, -10, 5, 22, -12, -24, 19],\n [-3, 10, -8, -18, -30, 21, -17, 5, 15, 9],\n [-13, 4, -25, 9, -25, -20, 21, -6, -17, -26],\n [10, -24, -13, -16, -3, -20, -16, -25, -14, -3],\n [-18, -11, -11, 6, -23, -21, -5, 19, 8, 28],\n [10, -30, -13, -26, 2, 3, -16, -6, -17, -15],\n [-13, -17, 18, -7, 7, -14, -23, -6, 24, 21],\n [-20, 19, -28, 10, -23, -14, -5, -26, 22, -9],\n [18, 27, 21, -29, 6, -7, 25, 1, 11, -7],\n [-1, -26, 24, -16, -10, 9, 13, 6, -3, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
972
|
math
|
train
| 411,480 |
math_arithmetic_matrix_determinant_level_6_6_249
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[17, 10, 1, 26, 30, 22, 3, 28, -5, 2],\n [23, 13, -5, 30, 16, 15, 4, 18, 18, -11],\n [-28, 17, -26, 4, 16, -20, 12, 19, -23, 14],\n [-1, -1, -9, -19, 6, 25, 23, -14, -25, 21],\n [-19, 21, 14, -14, -20, 24, 27, 30, -5, 5],\n [13, -2, 27, 15, 20, -23, 9, -13, -21, 0],\n [12, 4, -21, -5, -14, 29, -9, 21, 15, 29],\n [7, -9, -6, -19, 6, -2, 25, -26, 18, 10],\n [-1, -23, 23, 7, -1, -15, -2, -1, -17, -13],\n [-4, -25, 26, -28, -20, -27, -6, 10, -1, -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"
}
] |
104
|
math
|
train
| 411,481 |
math_arithmetic_matrix_determinant_level_6_6_250
|
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[[-19, 21, -9, 26, -12, 7, 5, -5, -2, 8],\n [0, 11, -11, -26, 26, -28, -21, -3, 10, 20],\n [0, 0, 2, 26, 28, -19, 27, -24, -17, 18],\n [0, 0, 0, 7, -7, 24, 18, -18, -7, -27],\n [0, 0, 0, 0, -27, -24, -13, -5, 12, 6],\n [0, 0, 0, 0, 0, -29, -1, -20, 2, 16],\n [0, 0, 0, 0, 0, 0, -2, 21, -4, -30],\n [0, 0, 0, 0, 0, 0, 0, 1, -29, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
math
|
train
| 411,482 |
math_arithmetic_matrix_determinant_level_6_6_251
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 6, 4, -7, 14, -20, 2, 17, -10, 2],\n [6, 12, -8, 4, 16, -22, -4, 9, 18, 8],\n [4, -8, -5, -13, 3, 2, 8, 28, 18, 14],\n [-7, 4, -13, 8, -8, 28, -22, 5, -24, 20],\n [14, 16, 3, -8, 16, -18, -26, -26, 6, -18],\n [-20, -22, 2, 28, -18, 21, -12, -3, 17, 2],\n [2, -4, 8, -22, -26, -12, -26, -11, 11, -4],\n [17, 9, 28, 5, -26, -3, -11, 12, 8, 3],\n [-10, 18, 18, -24, 6, 17, 11, 8, -5, 8],\n [2, 8, 14, 20, -18, 2, -4, 3, 8, 22]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
833
|
math
|
train
| 411,483 |
math_arithmetic_matrix_determinant_level_6_6_252
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[20, -11, -17, -23, -25, 17, 16, 26, 12, 13],\n [6, 24, -22, 19, 5, -12, 13, -5, 7, 0],\n [26, 16, 3, 27, 26, 12, -8, -19, -21, 20],\n [-22, 28, -14, -19, -24, 21, -7, 11, -16, 25],\n [3, 19, 26, 12, -27, 2, 9, 19, 22, 26],\n [21, -5, -30, -12, 1, -18, -27, 5, 9, -22],\n [2, -25, 1, -15, -6, 4, -17, -5, 15, -10],\n [30, 22, -15, -21, -19, 18, -3, -24, -4, 28],\n [4, 21, 13, 14, 11, 22, -19, -17, 28, -16],\n [29, -2, 22, -11, 8, -6, 20, -6, -7, 29]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
math
|
train
| 411,484 |
math_arithmetic_matrix_determinant_level_6_6_253
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 18, 6, 15, -9, -28, -5, 10, 18, -24],\n [0, -3, 24, 13, -1, -13, 0, 8, -8, -7],\n [0, 0, 18, 30, -4, 8, -12, 5, -5, -8],\n [0, 0, 0, -9, 10, 7, -30, 29, -28, -19],\n [0, 0, 0, 0, 27, -12, -12, -22, -20, -2],\n [0, 0, 0, 0, 0, -2, 1, -8, -10, -18],\n [0, 0, 0, 0, 0, 0, 28, -6, -30, 25],\n [0, 0, 0, 0, 0, 0, 0, 15, -15, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, -24, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
math
|
train
| 411,485 |
math_arithmetic_matrix_determinant_level_6_6_254
|
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[[-13, 16, 20, 15, 1, 9, -23, -15, -22, 14],\n [0, -20, 25, -24, 13, 28, 22, -22, -3, 28],\n [0, 0, 27, -2, -14, -2, -24, 1, 8, 20],\n [0, 0, 0, 2, 26, 23, -27, 4, -30, -9],\n [0, 0, 0, 0, -16, 11, 27, -23, -5, -4],\n [0, 0, 0, 0, 0, 11, -30, 25, -27, -16],\n [0, 0, 0, 0, 0, 0, -21, 10, -17, 20],\n [0, 0, 0, 0, 0, 0, 0, -17, 20, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
math
|
train
| 411,486 |
math_arithmetic_matrix_determinant_level_6_6_255
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -21, -27, 21, -10, 21, 15, -20, 1, -2],\n [0, -5, -22, 21, 10, 9, 30, -12, -7, -1],\n [0, 0, 8, -16, -9, 8, 27, -1, -8, 8],\n [0, 0, 0, 30, 9, -10, 29, -1, 25, 4],\n [0, 0, 0, 0, -19, -9, -8, -11, 3, -23],\n [0, 0, 0, 0, 0, -17, -18, 13, 0, 7],\n [0, 0, 0, 0, 0, 0, 1, -27, 11, 18],\n [0, 0, 0, 0, 0, 0, 0, -12, 27, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, -30, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\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
| 411,487 |
math_arithmetic_matrix_determinant_level_6_6_256
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[29, -13, -13, -26, -24, -13, -21, -3, 11, -26],\n [0, 2, 8, -24, -30, -19, -6, -11, -23, -9],\n [0, 0, 13, -6, -23, 24, -25, 21, 5, 29],\n [0, 0, 0, -6, -11, 19, -16, 7, 27, 16],\n [0, 0, 0, 0, 26, 2, -13, 28, 10, -3],\n [0, 0, 0, 0, 0, -22, 29, 27, 3, -28],\n [0, 0, 0, 0, 0, 0, 5, -6, 22, 1],\n [0, 0, 0, 0, 0, 0, 0, -18, 5, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, -20],\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"
}
] |
720
|
math
|
train
| 411,488 |
math_arithmetic_matrix_determinant_level_6_6_257
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[11, -19, -30, 14, -11, 29, 18, -15, 17, 1],\n [0, 23, -13, -17, 19, 5, 27, 14, 1, 25],\n [0, 0, -12, 4, 3, 5, -8, -9, -27, -13],\n [0, 0, 0, -10, 28, 25, -20, -29, -19, 4],\n [0, 0, 0, 0, -8, 25, -1, -16, 4, 25],\n [0, 0, 0, 0, 0, -21, 20, 12, 4, -8],\n [0, 0, 0, 0, 0, 0, 12, -30, 17, -28],\n [0, 0, 0, 0, 0, 0, 0, -30, -15, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 14, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]? 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
| 411,489 |
math_arithmetic_matrix_determinant_level_6_6_258
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[6, 26, -20, 7, 1, -14, -6, 22, 1, -18],\n [26, 26, 4, 18, 10, -6, -16, 3, 22, 18],\n [-20, 4, -28, -6, 22, -17, -20, -9, -3, -6],\n [7, 18, -6, 20, 12, 16, 10, 0, -2, -14],\n [1, 10, 22, 12, 10, 30, -18, -26, -20, 1],\n [-14, -6, -17, 16, 30, -15, 25, -6, -26, -8],\n [-6, -16, -20, 10, -18, 25, -4, 11, 17, -24],\n [22, 3, -9, 0, -26, -6, 11, -24, -16, -4],\n [1, 22, -3, -2, -20, -26, 17, -16, -5, 18],\n [-18, 18, -6, -14, 1, -8, -24, -4, 18, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
266
|
math
|
train
| 411,490 |
math_arithmetic_matrix_determinant_level_6_6_259
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-26, -10, -18, -12, 29, 13, -26, 5, -10, -30],\n [0, 28, -15, 16, -11, 22, -13, -28, -6, -2],\n [0, 0, -4, -15, 27, 3, 4, 19, 21, -24],\n [0, 0, 0, 9, -11, -29, -26, -1, -14, -22],\n [0, 0, 0, 0, 8, 28, 18, -23, 14, 28],\n [0, 0, 0, 0, 0, 21, -19, -29, 11, 1],\n [0, 0, 0, 0, 0, 0, -17, 21, -9, 20],\n [0, 0, 0, 0, 0, 0, 0, -20, 1, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -29, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
math
|
train
| 411,491 |
math_arithmetic_matrix_determinant_level_6_6_260
|
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, -1, 20, 17, -9, -1, -15, 8, -9, 2],\n [0, -19, 23, -25, 29, 5, -9, 17, -24, -16],\n [0, 0, -19, -22, 16, -15, 19, 9, 14, 8],\n [0, 0, 0, -9, 6, -16, -10, -16, -20, -13],\n [0, 0, 0, 0, 5, -21, -6, 10, -9, -27],\n [0, 0, 0, 0, 0, -22, 27, 9, -17, -23],\n [0, 0, 0, 0, 0, 0, -20, -28, 26, 20],\n [0, 0, 0, 0, 0, 0, 0, -21, 25, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,492 |
math_arithmetic_matrix_determinant_level_6_6_261
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-27, 19, 22, -15, -23, -11, -15, -26, -12, 19],\n [-8, 28, -14, -13, 19, 29, 8, 10, -8, 3],\n [18, -21, 29, -2, 24, 7, 24, 25, 27, 11],\n [16, 28, -23, 30, -30, -27, -7, -26, -6, -14],\n [-29, -27, 21, -22, 24, 13, 11, -1, 18, -19],\n [20, 25, 3, -30, 28, -26, 0, -26, -17, -22],\n [-7, 27, 14, -14, -15, 4, -15, -2, -11, -30],\n [11, 15, -10, -21, -2, 13, 9, -9, -14, -20],\n [-5, 18, 23, 15, 11, 27, -20, 6, 17, 25],\n [-28, -7, 23, -21, 4, -26, 15, 28, 24, -28]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
math
|
train
| 411,493 |
math_arithmetic_matrix_determinant_level_6_6_262
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-18, -29, -18, 1, 17, -12, 9, 9, 26, 27],\n [0, 10, -10, -26, -17, 4, 13, 9, -2, 27],\n [0, 0, 29, 30, -18, 8, 15, 18, 12, -16],\n [0, 0, 0, -20, -4, -6, -14, 24, -5, -1],\n [0, 0, 0, 0, -26, 3, -4, -19, -13, -19],\n [0, 0, 0, 0, 0, -15, -20, -17, -29, -20],\n [0, 0, 0, 0, 0, 0, -7, 4, -24, 25],\n [0, 0, 0, 0, 0, 0, 0, -4, -30, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 1, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,494 |
math_arithmetic_matrix_determinant_level_6_6_263
|
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[[-20, 28, -5, 13, 4, 27, -12, -13, 29, -19],\n [0, 21, -10, 22, -8, 12, -16, 10, 23, -27],\n [0, 0, -12, -20, 23, -27, 3, 19, 8, -11],\n [0, 0, 0, 27, -9, 23, 2, 6, 22, 6],\n [0, 0, 0, 0, 18, -30, -7, 28, 26, -10],\n [0, 0, 0, 0, 0, -10, -12, 13, 8, 11],\n [0, 0, 0, 0, 0, 0, 30, 20, -22, 18],\n [0, 0, 0, 0, 0, 0, 0, -2, 23, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, -24],\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
| 411,495 |
math_arithmetic_matrix_determinant_level_6_6_264
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -11, -23, 5, -7, -6, 8, 12, 14, -26],\n [0, 2, -21, 5, -22, 26, -27, 3, 13, 6],\n [0, 0, -14, 1, 29, 4, 6, 5, -1, -19],\n [0, 0, 0, 8, -17, -14, -24, -21, -17, -10],\n [0, 0, 0, 0, 17, 13, 13, -29, 7, -17],\n [0, 0, 0, 0, 0, 18, 16, 0, 15, 4],\n [0, 0, 0, 0, 0, 0, -8, 4, 14, 29],\n [0, 0, 0, 0, 0, 0, 0, 21, -2, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -8]]\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"
}
] |
960
|
math
|
train
| 411,496 |
math_arithmetic_matrix_determinant_level_6_6_265
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[1, 8, -20, -24, -5, -24, -9, -18, -22, 5],\n [8, 20, -5, -6, 10, -28, 5, -7, -10, -4],\n [-20, -5, 12, -9, -24, 2, 6, -25, 8, 0],\n [-24, -6, -9, -4, 3, -5, -12, 14, -6, 20],\n [-5, 10, -24, 3, 7, 7, 8, -7, 24, -20],\n [-24, -28, 2, -5, 7, 8, -2, 24, -11, -17],\n [-9, 5, 6, -12, 8, -2, -3, -24, 21, 14],\n [-18, -7, -25, 14, -7, 24, -24, -23, -6, -5],\n [-22, -10, 8, -6, 24, -11, 21, -6, -26, -10],\n [5, -4, 0, 20, -20, -17, 14, -5, -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"
}
] |
882
|
math
|
train
| 411,497 |
math_arithmetic_matrix_determinant_level_6_6_266
|
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, 3, -17, -27, 29, 30, -29, -2, 1, -6],\n [0, 9, 24, 14, 30, 17, 1, 25, 9, -5],\n [0, 0, 28, -21, -24, 9, 24, -6, 8, -10],\n [0, 0, 0, 1, -11, 24, 1, 30, 20, -6],\n [0, 0, 0, 0, -22, 10, 27, 9, 7, -29],\n [0, 0, 0, 0, 0, -29, 21, 0, 4, 22],\n [0, 0, 0, 0, 0, 0, 21, 8, -11, 15],\n [0, 0, 0, 0, 0, 0, 0, -16, 26, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
math
|
train
| 411,498 |
math_arithmetic_matrix_determinant_level_6_6_267
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[16, 1, 0, -2, 8, 16, -10, 4, -3, -11],\n [1, -27, 3, 16, -5, 8, -21, -16, 10, 13],\n [0, 3, 21, 19, 6, -14, 14, 0, -1, 2],\n [-2, 16, 19, -7, -16, 5, -6, 15, -23, 20],\n [8, -5, 6, -16, 18, 20, 0, -10, 20, -7],\n [16, 8, -14, 5, 20, -27, -15, 2, 10, -9],\n [-10, -21, 14, -6, 0, -15, -5, -10, 3, -2],\n [4, -16, 0, 15, -10, 2, -10, 30, 20, 22],\n [-3, 10, -1, -23, 20, 10, 3, 20, -15, 16],\n [-11, 13, 2, 20, -7, -9, -2, 22, 16, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
134
|
math
|
train
| 411,499 |
math_arithmetic_matrix_determinant_level_6_6_268
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[23, 6, 26, 0, -27, 19, 4, -29, 30, 21],\n [-18, -3, 27, 8, -8, -22, 8, -25, -13, -28],\n [15, -2, 24, -5, -30, -29, 7, -24, 24, 1],\n [-25, 24, 14, -23, 12, -3, 30, 11, -24, -27],\n [-4, 17, -28, 18, 8, 12, -14, -9, -30, -15],\n [-23, -21, 14, -8, -17, 14, -27, 23, -25, 25],\n [6, 30, -21, -5, -22, -25, 9, -14, 8, 18],\n [-20, -4, -16, 5, 9, 25, -1, 19, -14, -21],\n [10, -16, 30, -17, 29, 30, -14, -27, 25, -30],\n [11, 4, -11, -2, -22, 10, 16, -23, -13, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
math
|
train
| 411,500 |
math_arithmetic_matrix_determinant_level_6_6_269
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[24, 2, 7, 0, -3, -7, -11, 30, 15, -1],\n [0, -20, -19, -22, -7, 22, 4, -18, -28, 21],\n [0, 0, 26, -22, -22, -22, 19, -13, 24, -17],\n [0, 0, 0, -17, -25, -5, -4, -20, 11, -29],\n [0, 0, 0, 0, 18, 23, -10, 2, 5, -18],\n [0, 0, 0, 0, 0, 27, 25, -1, -25, 30],\n [0, 0, 0, 0, 0, 0, 21, 30, 24, 17],\n [0, 0, 0, 0, 0, 0, 0, 20, 6, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -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"
}
] |
0
|
math
|
train
| 411,501 |
math_arithmetic_matrix_determinant_level_6_6_270
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -3, 23, -3, 4, 11, 11, -12, 30, -2],\n [0, 18, 23, -27, 25, -28, 7, -28, -19, 24],\n [0, 0, -29, -14, 3, -27, -18, -21, -25, -10],\n [0, 0, 0, 1, 2, 25, -5, 17, 16, -23],\n [0, 0, 0, 0, -29, -25, -10, -2, -23, -17],\n [0, 0, 0, 0, 0, -15, -12, -22, 7, 25],\n [0, 0, 0, 0, 0, 0, -1, -13, 26, -1],\n [0, 0, 0, 0, 0, 0, 0, -24, 2, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -7, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
math
|
train
| 411,502 |
math_arithmetic_matrix_determinant_level_6_6_271
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[21, -21, -18, -8, 12, -6, -19, -24, 22, 5],\n [-21, -26, 16, -11, -4, -8, -7, 1, 8, -6],\n [-18, 16, -12, -22, 16, 10, -10, -13, 6, 10],\n [-8, -11, -22, 12, 13, -4, -28, 9, -14, -21],\n [12, -4, 16, 13, -24, -12, -17, -2, -22, 2],\n [-6, -8, 10, -4, -12, -14, 10, 14, 10, 11],\n [-19, -7, -10, -28, -17, 10, -13, -21, 16, 8],\n [-24, 1, -13, 9, -2, 14, -21, -20, 20, 8],\n [22, 8, 6, -14, -22, 10, 16, 20, 13, 0],\n [5, -6, 10, -21, 2, 11, 8, 8, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
math
|
train
| 411,503 |
math_arithmetic_matrix_determinant_level_6_6_272
|
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[[-19, -10, -11, -10, -20, -22, 8, 4, 13, -20],\n [-10, -19, -10, -2, -4, -6, -2, 0, 14, 4],\n [-11, -10, -7, 10, 24, -24, 21, -4, 6, -17],\n [-10, -2, 10, -20, 12, 24, 14, 4, 9, 5],\n [-20, -4, 24, 12, -17, 9, -16, 0, -10, 2],\n [-22, -6, -24, 24, 9, 16, -8, 22, -4, 2],\n [8, -2, 21, 14, -16, -8, 22, 12, 18, -15],\n [4, 0, -4, 4, 0, 22, 12, -2, 10, -26],\n [13, 14, 6, 9, -10, -4, 18, 10, -25, 20],\n [-20, 4, -17, 5, 2, 2, -15, -26, 20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
982
|
math
|
train
| 411,504 |
math_arithmetic_matrix_determinant_level_6_6_273
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[26, 24, 9, 16, -9, -6, -10, 27, -22, 5],\n [0, 16, 3, -29, -13, 29, -18, -21, 10, -21],\n [0, 0, 3, -25, 9, 20, -2, 18, -26, 14],\n [0, 0, 0, -5, -1, -15, -15, -8, 20, -22],\n [0, 0, 0, 0, -7, -17, -7, 15, 23, 22],\n [0, 0, 0, 0, 0, 23, -5, 22, 14, 8],\n [0, 0, 0, 0, 0, 0, -9, -23, -30, 22],\n [0, 0, 0, 0, 0, 0, 0, -3, -7, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
math
|
train
| 411,505 |
math_arithmetic_matrix_determinant_level_6_6_274
|
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[[5, 19, -5, 2, -22, 4, 10, 18, 25, 21],\n [0, 9, -7, -20, -10, 27, 28, 24, -21, 30],\n [0, 0, -10, 27, -14, -17, -20, 0, 19, 15],\n [0, 0, 0, 26, -2, 26, -9, -5, 1, -17],\n [0, 0, 0, 0, 22, -21, 27, 3, -22, 4],\n [0, 0, 0, 0, 0, -2, 10, -30, -20, -28],\n [0, 0, 0, 0, 0, 0, -21, 22, 25, -28],\n [0, 0, 0, 0, 0, 0, 0, -8, -21, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
math
|
train
| 411,506 |
math_arithmetic_matrix_determinant_level_6_6_275
|
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, 23, -4, 23, 21, -16, 6, 20, -9, 0],\n [0, 15, 19, 1, -14, -13, -21, -8, 6, -29],\n [0, 0, 26, -25, -7, 2, 7, 11, 11, -9],\n [0, 0, 0, 12, 19, 18, 9, 20, 13, -16],\n [0, 0, 0, 0, -11, -25, 18, 10, 9, -3],\n [0, 0, 0, 0, 0, 2, 23, -8, 26, 19],\n [0, 0, 0, 0, 0, 0, -30, -6, 24, 18],\n [0, 0, 0, 0, 0, 0, 0, 10, 5, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
math
|
train
| 411,507 |
math_arithmetic_matrix_determinant_level_6_6_276
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -20, 22, 7, -1, -8, -19, 19, -8, 12],\n [-20, 7, 4, -4, 14, -12, -4, 10, -12, 14],\n [22, 4, -3, -24, -20, 6, -3, 19, -21, 14],\n [7, -4, -24, 9, -5, 8, 9, 8, 13, -2],\n [-1, 14, -20, -5, -1, 23, 5, -20, -13, -14],\n [-8, -12, 6, 8, 23, 12, 11, -19, -7, 8],\n [-19, -4, -3, 9, 5, 11, 11, -12, -3, -12],\n [19, 10, 19, 8, -20, -19, -12, 27, -16, -13],\n [-8, -12, -21, 13, -13, -7, -3, -16, 17, 6],\n [12, 14, 14, -2, -14, 8, -12, -13, 6, -26]]\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"
}
] |
613
|
math
|
train
| 411,508 |
math_arithmetic_matrix_determinant_level_6_6_277
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[30, 1, -29, 4, 24, -12, -6, -8, 7, -10],\n [0, 30, 18, 12, -12, 12, -27, -25, 23, 18],\n [0, 0, -8, -18, 3, 8, -19, -4, -11, -14],\n [0, 0, 0, -21, -16, -24, -28, 23, -25, -25],\n [0, 0, 0, 0, 24, 28, 16, -29, -24, 13],\n [0, 0, 0, 0, 0, -10, -16, -15, -2, 26],\n [0, 0, 0, 0, 0, 0, -3, 11, 20, -28],\n [0, 0, 0, 0, 0, 0, 0, -27, -30, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, -22],\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"
}
] |
0
|
math
|
train
| 411,509 |
math_arithmetic_matrix_determinant_level_6_6_278
|
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, -7, 25, -24, 0, -13, -12, -9, -16, -6],\n [-7, 30, -8, 8, -3, 4, -9, 18, -19, 1],\n [25, -8, 12, 2, -5, 7, -15, -2, 4, -16],\n [-24, 8, 2, 10, -28, 6, 12, -4, 17, 4],\n [0, -3, -5, -28, -22, 11, -16, 16, -16, -12],\n [-13, 4, 7, 6, 11, -13, 2, 4, 10, -14],\n [-12, -9, -15, 12, -16, 2, -25, -25, -12, -24],\n [-9, 18, -2, -4, 16, 4, -25, 17, 6, 10],\n [-16, -19, 4, 17, -16, 10, -12, 6, -19, -14],\n [-6, 1, -16, 4, -12, -14, -24, 10, -14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
196
|
math
|
train
| 411,510 |
math_arithmetic_matrix_determinant_level_6_6_279
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Compute |A| for the matrix A =\n[[-16, 24, 3, -23, -3, 8, -13, 22, 20, -10],\n [-20, -12, -5, -28, 28, -21, -20, -13, 17, -5],\n [2, 21, -11, 8, 10, -5, 0, 19, 5, 29],\n [19, 11, -28, -5, 1, 17, -19, -24, 13, -3],\n [-23, 27, 5, -28, 23, 0, -21, 17, -12, -20],\n [-14, -20, 4, 22, 17, -25, 29, -1, 26, -14],\n [11, 9, 28, 27, 2, -23, -21, 9, 28, 5],\n [17, 25, 25, 14, 27, -28, 14, -19, -10, -27],\n [-4, 17, 26, -24, -12, 22, 15, -9, 15, 10],\n [-13, 5, -13, -22, 26, -11, 17, 3, 24, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
686
|
math
|
train
| 411,511 |
math_arithmetic_matrix_determinant_level_6_6_280
|
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, -28, -7, -15, 28, -19, 16, 14, 10, 13],\n [20, 2, 13, -14, 24, 8, -5, -30, 30, 6],\n [23, 7, 16, -10, -23, 17, -4, -2, -29, -14],\n [-30, 7, -8, -5, 2, -29, -28, 19, 19, 15],\n [-1, 5, -29, 29, 5, 20, -2, -18, 23, 0],\n [-3, 16, 28, 0, -21, 23, -11, -27, -10, 25],\n [-19, 30, -14, 17, 12, 17, 10, -18, 11, 27],\n [-9, 11, -21, 8, -8, -4, 25, -2, 10, 12],\n [-14, 28, 4, -21, -27, 30, -21, -18, 24, -17],\n [-25, 18, 25, -18, -21, -15, -29, -18, -18, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
math
|
train
| 411,512 |
math_arithmetic_matrix_determinant_level_6_6_281
|
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[[-17, 18, -21, 10, 20, 27, 8, -21, 19, 3],\n [-4, -7, 27, 3, -26, -21, -27, 26, 20, -27],\n [-14, 15, 4, 2, 4, 3, 3, -9, 18, 13],\n [13, -30, 7, -19, -10, 7, -21, 17, -21, 8],\n [-18, -21, -13, 8, -26, 6, -17, 13, -4, 28],\n [-16, 3, -2, -11, -17, -19, 15, 8, -30, -2],\n [0, 9, -14, 17, 2, 24, 29, 26, -22, 2],\n [-15, 1, -22, -24, 28, 6, -3, -24, 3, -25],\n [0, -29, 14, 25, -23, -8, -6, 24, -5, -6],\n [-12, -12, -24, -25, -10, 11, 8, 10, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
939
|
math
|
train
| 411,513 |
math_arithmetic_matrix_determinant_level_6_6_282
|
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, 13, -10, -4, 13, -26, 26, -28, 5],\n [25, 23, 0, 16, -25, -18, 20, 5, 16, 25],\n [-30, -29, -21, 14, -13, 11, 30, 30, 4, -30],\n [9, -7, 5, 5, -7, -12, -17, 14, 2, -23],\n [26, -2, 2, -20, 9, 10, -19, -4, -30, 28],\n [2, -24, -16, -17, -5, -21, -25, 2, 10, -20],\n [-3, -13, 28, 12, -29, 2, 27, 7, -2, 2],\n [28, -19, -16, 12, 24, -14, -22, 26, 5, 7],\n [-15, 11, -24, -21, -10, -3, -28, -14, -18, -11],\n [-10, -30, -25, 4, -6, 19, -19, -1, 4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
math
|
train
| 411,514 |
math_arithmetic_matrix_determinant_level_6_6_283
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[29, 10, 2, -3, 12, -8, -14, -6, 2, 16],\n [10, -24, 0, -5, 0, -4, -20, 6, -20, -24],\n [2, 0, -15, 25, 0, -4, 12, 16, 12, -4],\n [-3, -5, 25, -25, 20, 12, 0, 0, -16, 10],\n [12, 0, 0, 20, 4, 12, 3, -11, -18, -8],\n [-8, -4, -4, 12, 12, -6, -10, 5, 18, -17],\n [-14, -20, 12, 0, 3, -10, -29, 21, -15, -4],\n [-6, 6, 16, 0, -11, 5, 21, 18, 11, -24],\n [2, -20, 12, -16, -18, 18, -15, 11, 28, -12],\n [16, -24, -4, 10, -8, -17, -4, -24, -12, -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"
}
] |
391
|
math
|
train
| 411,515 |
math_arithmetic_matrix_determinant_level_6_6_284
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[24, -27, 24, 6, 16, 2, 3, -15, 30, -30],\n [-22, -30, -24, 29, -11, -22, -7, -15, 7, -18],\n [-8, 5, 14, -16, 7, 9, 3, 8, 28, -30],\n [-20, -7, -25, -7, 30, -26, 10, -20, 7, 3],\n [0, 27, 19, 18, 7, -19, -9, 3, 14, 10],\n [-7, 24, -19, 17, -24, 6, 15, 10, 23, -28],\n [-20, 1, 0, -14, 3, 2, -8, -12, 26, -24],\n [-25, 0, -16, 29, -21, 20, 29, -21, -12, -30],\n [-19, -20, -19, -12, 10, -3, 30, -21, 20, -17],\n [-16, 26, 17, -4, 22, 19, -28, 26, 12, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
314
|
math
|
train
| 411,516 |
math_arithmetic_matrix_determinant_level_6_6_285
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -14, 22, -2, -17, 8, 5, -16, 4, -2],\n [-14, 15, 3, 18, 28, -8, 4, 10, 14, -11],\n [22, 3, 4, 4, 7, 8, 0, -7, 18, -10],\n [-2, 18, 4, 2, -1, 14, -3, -4, -18, -6],\n [-17, 28, 7, -1, -21, -20, 4, 4, 22, -2],\n [8, -8, 8, 14, -20, -23, 8, -16, -4, -10],\n [5, 4, 0, -3, 4, 8, -19, 20, -1, -11],\n [-16, 10, -7, -4, 4, -16, 20, -30, -11, 14],\n [4, 14, 18, -18, 22, -4, -1, -11, -26, -13],\n [-2, -11, -10, -6, -2, -10, -11, 14, -13, -16]]\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"
}
] |
330
|
math
|
train
| 411,517 |
math_arithmetic_matrix_determinant_level_6_6_286
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[18, 24, 11, 27, 9, 4, -25, 0, -29, 25],\n [15, 19, 14, 9, 15, -9, 13, -11, -13, 25],\n [12, 4, -25, -8, 0, 26, 7, 14, -18, 2],\n [26, -14, -16, 29, -16, -30, -18, 3, 12, -29],\n [23, 10, 28, -12, 11, -16, -23, 27, 10, 9],\n [-22, 11, 8, 10, 13, -24, 30, 11, 18, 26],\n [13, 16, -29, 10, 8, -6, 24, 8, 20, 2],\n [-3, -30, 16, 19, 16, -7, 17, 27, -5, 22],\n [29, 23, 27, 4, -25, 12, -3, 3, 28, 23],\n [-6, 0, 21, 8, -30, -13, 18, 29, 9, -24]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
math
|
train
| 411,518 |
math_arithmetic_matrix_determinant_level_6_6_287
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-25, -15, 6, 0, -25, 20, -12, 11, 10, 18],\n [-15, 9, -10, -20, -20, -8, -16, -11, -17, 0],\n [6, -10, -10, -28, 4, 16, 6, 9, 3, -12],\n [0, -20, -28, 27, -7, -14, -28, -4, -12, -4],\n [-25, -20, 4, -7, 13, -9, -2, -20, 8, -4],\n [20, -8, 16, -14, -9, -6, 16, 7, -18, 14],\n [-12, -16, 6, -28, -2, 16, -17, -12, 2, -2],\n [11, -11, 9, -4, -20, 7, -12, 22, 0, -14],\n [10, -17, 3, -12, 8, -18, 2, 0, -1, 18],\n [18, 0, -12, -4, -4, 14, -2, -14, 18, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
620
|
math
|
train
| 411,519 |
math_arithmetic_matrix_determinant_level_6_6_288
|
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[[-26, 5, -23, -3, -29, -13, 25, 25, 9, 28],\n [9, 19, -17, -24, 26, -11, -23, -5, -26, -16],\n [14, -17, 25, 25, -30, -11, 17, -22, -3, 16],\n [27, 1, 28, 30, 17, -23, 23, -21, 21, 28],\n [-11, -9, -12, -17, 12, -21, -5, 28, 20, 7],\n [-7, -19, -24, 20, -13, 28, -7, 15, 29, -21],\n [-5, -18, -24, 1, -30, 14, 11, -30, -24, -4],\n [-21, -28, 27, -30, -1, 21, -23, 2, 30, 29],\n [-11, 22, -16, -8, 28, 5, 9, -14, 7, -26],\n [26, 9, -11, -13, 7, -3, 18, 3, -8, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
math
|
train
| 411,520 |
math_arithmetic_matrix_determinant_level_6_6_289
|
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, -5, -18, -19, -27, -13, 27, -21, -27, 18],\n [0, 11, -3, 5, 4, -8, -24, 30, 9, 18],\n [0, 0, 19, -22, 3, -15, -26, -8, 17, -1],\n [0, 0, 0, 27, -12, -5, -28, 10, -20, -16],\n [0, 0, 0, 0, -16, 20, 6, -9, 15, -20],\n [0, 0, 0, 0, 0, 26, -15, -26, 30, -14],\n [0, 0, 0, 0, 0, 0, -20, 18, -21, -6],\n [0, 0, 0, 0, 0, 0, 0, -12, 23, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
math
|
train
| 411,521 |
math_arithmetic_matrix_determinant_level_6_6_290
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-19, -27, 14, 1, -18, -19, 5, 30, 24, -3],\n [-21, 24, -26, 22, 23, 3, -18, 28, 28, 26],\n [10, -23, 6, 20, -18, -12, 28, -23, 28, 3],\n [-26, -17, 15, 13, -19, 21, -28, -10, 4, -6],\n [22, -5, -17, -13, 9, 28, 26, 22, 3, -13],\n [11, -14, 12, -27, -30, 0, -11, 23, 30, -23],\n [14, -18, -21, 18, -27, -9, -26, -16, -9, -7],\n [6, 29, -30, 25, 9, 16, -7, 17, -22, 17],\n [-23, 18, -9, 27, -8, -24, 13, 10, 27, 20],\n [5, -13, 7, 29, 5, -5, -6, 24, 30, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
756
|
math
|
train
| 411,522 |
math_arithmetic_matrix_determinant_level_6_6_291
|
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, 3, -19, -29, -21, 9, 27, 11, -27, 23],\n [-14, 11, 24, 9, 25, 1, -28, -7, -19, -2],\n [20, 9, 17, 20, -20, -21, 4, -23, 29, 17],\n [16, -25, 13, 9, -14, -21, -9, 20, -11, 28],\n [18, -16, -21, -9, 8, -10, -7, -4, -26, 8],\n [-23, 30, -15, -10, 27, -15, -25, -1, 20, -27],\n [24, -3, 13, -19, -9, -7, 4, 26, -25, -23],\n [19, -7, 30, -27, -12, -3, -13, -13, -15, 22],\n [-8, 0, -30, -16, -4, 17, 18, 22, -30, -30],\n [-19, -27, 1, -13, 13, -25, 14, 17, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
373
|
math
|
train
| 411,523 |
math_arithmetic_matrix_determinant_level_6_6_292
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-26, -7, 21, -25, -6, 14, -26, 3, 25, 17],\n [0, 5, -2, -4, 11, 19, 2, -8, -30, 0],\n [0, 0, 6, -8, -2, 9, 23, 28, -20, 10],\n [0, 0, 0, 25, 25, -13, -5, -25, 10, -8],\n [0, 0, 0, 0, 26, 5, -8, -12, -6, 30],\n [0, 0, 0, 0, 0, 29, 29, -20, 1, 3],\n [0, 0, 0, 0, 0, 0, 12, 23, 30, -5],\n [0, 0, 0, 0, 0, 0, 0, 5, 11, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 5, -9],\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
| 411,524 |
math_arithmetic_matrix_determinant_level_6_6_293
|
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[[12, 2, 26, -10, -3, -22, -10, 18, 4, 14],\n [2, 25, -23, 24, 10, -14, -2, 24, -10, -2],\n [26, -23, -5, -16, 4, -14, -4, -7, 2, -4],\n [-10, 24, -16, -10, -13, -6, -3, 0, 3, 27],\n [-3, 10, 4, -13, -12, 20, 6, 8, 10, -10],\n [-22, -14, -14, -6, 20, 0, 4, 8, 24, 4],\n [-10, -2, -4, -3, 6, 4, -6, -16, -8, -24],\n [18, 24, -7, 0, 8, 8, -16, 12, -25, -19],\n [4, -10, 2, 3, 10, 24, -8, -25, 13, -9],\n [14, -2, -4, 27, -10, 4, -24, -19, -9, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
773
|
math
|
train
| 411,525 |
math_arithmetic_matrix_determinant_level_6_6_294
|
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[[-24, 24, -26, 14, -23, 19, -19, 23, 24, 15],\n [0, 2, -4, 4, -10, 15, -14, 0, -15, -26],\n [0, 0, -21, -1, -29, 6, -25, -25, -4, 30],\n [0, 0, 0, 27, -25, 0, -23, -13, -6, 16],\n [0, 0, 0, 0, -21, 23, -21, 19, 13, 23],\n [0, 0, 0, 0, 0, -22, -27, 7, 12, 11],\n [0, 0, 0, 0, 0, 0, -1, -14, -19, 1],\n [0, 0, 0, 0, 0, 0, 0, 26, -29, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 5, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
math
|
train
| 411,526 |
math_arithmetic_matrix_determinant_level_6_6_295
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[21, 23, 2, -15, -25, 5, 20, 7, 30, -17],\n [-29, -14, 25, -27, 3, 5, -10, -7, 13, -19],\n [-24, -1, 15, -10, -8, 8, 7, 24, 14, -8],\n [-29, -15, 11, -8, -25, -16, 6, 16, -13, 24],\n [4, -26, -21, 10, -29, 15, -22, -13, 9, -18],\n [-29, -17, 15, 26, 6, 9, 3, -20, 15, 16],\n [25, -11, -1, 3, 22, 5, 18, 6, -20, -2],\n [27, -10, -1, -14, -7, 19, 30, -26, -23, -26],\n [27, 22, 26, -9, 3, -18, -23, 4, -29, 20],\n [22, -20, -2, -11, -4, 15, -6, 9, -5, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
608
|
math
|
train
| 411,527 |
math_arithmetic_matrix_determinant_level_6_6_296
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -8, -4, 18, 4, -10, -29, -15, -19, -17],\n [21, -23, 22, -5, 25, 28, 26, -5, -20, 24],\n [4, 14, 23, -24, -9, 16, 10, 6, -23, -5],\n [-23, 5, 21, 24, -19, -10, 8, 15, -19, -23],\n [-22, -2, 30, 9, 10, -24, -18, -3, -2, 20],\n [-20, 10, -8, 29, 12, -30, -27, -3, -30, -13],\n [16, 13, -12, -4, -24, 5, -22, -18, 17, 16],\n [-26, 9, -8, -2, -21, 5, -7, -18, -1, -13],\n [23, 24, -17, 10, 11, -2, 28, -22, 22, -19],\n [-25, -12, 16, -14, -12, -17, -1, 10, 18, 21]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
613
|
math
|
train
| 411,528 |
math_arithmetic_matrix_determinant_level_6_6_297
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 17, -16, 16, -18, 10, -29, 11, 17, 7],\n [0, -24, -16, -16, -21, 21, -7, 17, 16, -3],\n [0, 0, -17, -18, -10, 27, 12, 2, -25, -20],\n [0, 0, 0, -24, -8, 24, 8, 19, -14, -28],\n [0, 0, 0, 0, 30, 16, -30, -29, 14, 16],\n [0, 0, 0, 0, 0, -20, -1, -12, 30, -4],\n [0, 0, 0, 0, 0, 0, 14, -4, -13, -12],\n [0, 0, 0, 0, 0, 0, 0, -15, 14, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -12, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\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
| 411,529 |
math_arithmetic_matrix_determinant_level_6_6_298
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "Determine the value of det(A) where A =\n[[19, 20, 3, -10, -6, -23, -3, -18, 19, -8],\n [0, 26, -5, -4, 1, 24, -23, 15, -29, 7],\n [0, 0, -18, 11, -23, -6, -12, 26, 2, -1],\n [0, 0, 0, -28, -17, -3, 17, 16, 22, 28],\n [0, 0, 0, 0, 26, -23, -1, 3, 14, -30],\n [0, 0, 0, 0, 0, 22, -10, 19, 13, 19],\n [0, 0, 0, 0, 0, 0, 7, -23, 7, -13],\n [0, 0, 0, 0, 0, 0, 0, 26, 3, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -21, 14],\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"
}
] |
824
|
math
|
train
| 411,530 |
math_arithmetic_matrix_determinant_level_6_6_299
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6 |
[
{
"content": "What is the determinant of the matrix:\n[[-26, 2, 19, 17, 3, -15, -10, 3, -10, 8],\n [2, 21, -8, -22, 19, 0, 12, -27, -16, -10],\n [19, -8, 12, -12, 23, 18, 5, 25, -14, -6],\n [17, -22, -12, -14, 2, -8, 17, -22, -21, -14],\n [3, 19, 23, 2, 22, 24, 9, -14, 12, 12],\n [-15, 0, 18, -8, 24, 19, 6, -14, -10, -10],\n [-10, 12, 5, 17, 9, 6, 24, -1, 2, -28],\n [3, -27, 25, -22, -14, -14, -1, 17, -10, -2],\n [-10, -16, -14, -21, 12, -10, 2, -10, 1, -10],\n [8, -10, -6, -14, 12, -10, -28, -2, -10, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
923
|
math
|
train
| 411,531 |
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