messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 0, -4, 1, -5],\n [0, -7, -10, 11, 4],\n [-4, -10, 12, -2, 10],\n [1, 11, -2, -11, 2],\n [-5, 4, 10, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 892 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 6, 10, 1, 12],\n [6, -2, -10, -7, -6],\n [10, -10, -9, -5, 1],\n [1, -7, -5, 7, 0],\n [12, -6, 1, 0, -12]]\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... | 632 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 8, 10, 7, 10],\n [-11, -4, 9, -1, 7],\n [0, 6, 5, -5, 13],\n [0, -6, -6, -13, -5],\n [-2, -12, 0, -13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 92 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -5, -6, -4, 14],\n [-5, -10, -3, 2, -4],\n [-15, 4, 11, 7, 15],\n [-5, 7, 13, 2, -8],\n [4, 1, -4, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 734 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -6, -11, 9, 1],\n [-7, 14, 5, 3, -5],\n [-13, -12, -1, -9, -9],\n [10, 1, -3, 3, -2],\n [0, -6, 6, -13, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 570 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, 2, 2, 4],\n [0, -5, 0, -2, -4],\n [2, 0, -11, 2, -10],\n [2, -2, 2, -13, 0],\n [4, -4, -10, 0, -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": "... | 329 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, -4, -10, -2],\n [-5, 15, 8, 3, 12],\n [-12, 12, -3, 9, -12],\n [13, 14, -9, -15, 0],\n [-1, -9, 1, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 839 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -12, -2, -11, 12],\n [0, 15, 14, -15, -13],\n [0, 0, -14, 11, 12],\n [0, 0, 0, 11, -3],\n [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": "u... | 530 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 6, -4, 11, -9],\n [0, -3, -7, -13, 5],\n [3, 2, -12, -9, 15],\n [-8, -6, 7, 0, 10],\n [10, -2, 4, 2, -15]]\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... | 21 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, -12, 6, 8, 14],\n [15, 0, -6, 5, 14],\n [14, -4, -13, 6, 15],\n [-13, 0, -4, -2, -5],\n [-5, 6, -5, 2, 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... | 80 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 2, -10, -3, 14],\n [2, 13, 0, -2, -1],\n [-10, 0, 15, 4, 2],\n [-3, -2, 4, 3, 9],\n [14, -1, 2, 9, 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": "... | 203 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -4, -10, 13, 7],\n [7, -15, -10, -5, 8],\n [-13, 5, 10, 5, -1],\n [-13, -11, 4, -2, 13],\n [7, 3, 11, 7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 938 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 15, 9, -14, 13],\n [0, 5, -6, -8, 13],\n [0, 0, -15, 6, -2],\n [0, 0, 0, 5, 4],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 875 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -15, 12, -6, -4],\n [-3, 3, 0, -3, -8],\n [-2, 14, 4, 6, 0],\n [-11, 12, -4, 3, -4],\n [-10, -4, 6, 4, 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"... | 776 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -1, 6, -5, 1],\n [-1, -8, 4, 2, 8],\n [6, 4, 0, 5, -10],\n [-5, 2, 5, 3, 5],\n [1, 8, -10, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 103 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, -11, -7, 4, 8],\n [0, 12, -3, -15, -5],\n [0, 0, 10, 5, 6],\n [0, 0, 0, -11, 1],\n [0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -2, 0, 2, 2],\n [-2, -5, -2, -6, 2],\n [0, -2, -6, 7, -3],\n [2, -6, 7, -15, 7],\n [2, 2, -3, 7, -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": "us... | 416 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -7, 12, 4, 12],\n [5, 4, 4, 11, 13],\n [14, -12, 3, 0, 2],\n [-6, 5, 13, 15, 10],\n [8, -1, -8, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 793 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 0, -8, -2, -11],\n [-6, 0, 3, 7, -8],\n [-9, 7, 4, 10, -13],\n [-10, 12, -8, -11, -10],\n [13, -7, 9, 15, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 710 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 7, -10, -1, -1],\n [0, 9, -12, 0, 9],\n [0, 0, 7, -14, -13],\n [0, 0, 0, -12, 8],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -15, 12, 6, 8],\n [0, -11, -13, 4, 13],\n [0, 0, -1, -6, -7],\n [0, 0, 0, 6, -4],\n [0, 0, 0, 0, -15]]\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": "u... | 90 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[14, -3, 10, -10, 6],\n [0, -14, -12, 14, 12],\n [0, 0, -4, 14, 11],\n [0, 0, 0, -14, 10],\n [0, 0, 0, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 3, 2, 6, 7],\n [2, -11, 13, 14, -14],\n [6, 4, 3, 2, 2],\n [10, -10, 0, -2, 8],\n [-8, -10, -1, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 760 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -2, -1, -3, 13],\n [-10, -13, 5, -7, 4],\n [6, 9, -4, -13, -10],\n [-9, -14, 6, 8, -2],\n [-9, -3, 4, 11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 118 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -8, 10, 2, -10],\n [-8, -11, 3, -10, 9],\n [10, 3, -2, 9, 0],\n [2, -10, 9, 7, 4],\n [-10, 9, 0, 4, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 750 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 2, 12, 1, -6],\n [6, 13, -13, 0, 7],\n [3, -15, -10, 2, -8],\n [7, -8, 15, 6, -4],\n [12, -11, 6, 2, 0]]\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": ... | 661 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -8, 6, -3, 0],\n [-8, 9, 6, 0, -6],\n [6, 6, -7, -8, 2],\n [-3, 0, -8, -1, 2],\n [0, -6, 2, 2, -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... | 873 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 8, -1, 14, 6],\n [0, 6, -12, -11, 8],\n [0, 0, -6, 13, 11],\n [0, 0, 0, 1, -2],\n [0, 0, 0, 0, -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": "use... | 856 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 4, 6, 14, 8],\n [4, -4, 0, -8, -3],\n [6, 0, 12, -11, -2],\n [14, -8, -11, -1, -1],\n [8, -3, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 11, 6, -10, 11],\n [0, -1, 6, 0, 13],\n [0, 0, 7, -15, -9],\n [0, 0, 0, 4, 13],\n [0, 0, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -2, 0, -4, -12],\n [-2, 0, 0, -9, 4],\n [0, 0, 15, 0, 2],\n [-4, -9, 0, 3, -1],\n [-12, 4, 2, -1, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, 1, -15, -6, -1],\n [0, 10, -1, -10, -15],\n [0, 0, 15, -9, -13],\n [0, 0, 0, 6, -11],\n [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"
}
] | 800 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 13, -8, 3, -4],\n [-6, 10, -8, 12, 3],\n [-7, -11, 2, 14, -6],\n [-2, -14, -2, 11, 7],\n [7, -8, -13, 14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 394 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -13, -8, -10, 13],\n [0, -4, 11, 12, -1],\n [0, 0, 1, -5, 6],\n [0, 0, 0, 14, 2],\n [0, 0, 0, 0, -15]]\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 |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 4, 9, 5, 7],\n [7, -4, 10, 15, 4],\n [-5, -12, -12, 13, -8],\n [-12, 0, -13, 5, 1],\n [6, -4, 2, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 232 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -12, -15, 13, 8],\n [0, 15, 10, 0, -12],\n [0, 0, -6, -7, 6],\n [0, 0, 0, -11, -6],\n [0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 1, -15, -13],\n [14, -4, -11, -4, 10],\n [4, 0, -15, -8, -15],\n [-5, -1, 10, -6, -3],\n [-4, 9, -11, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 495 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 7, -13, -6, -13],\n [-15, -9, -6, 8, 2],\n [11, -2, 7, -6, 11],\n [-4, -5, 2, -7, 11],\n [12, -2, 3, 10, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 692 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 6, 0, 0, -2],\n [6, -3, 4, -1, -2],\n [0, 4, -15, 0, -2],\n [0, -1, 0, 10, -4],\n [-2, -2, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 758 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -7, 12, -2, 0],\n [6, 9, 15, -7, -8],\n [-9, 4, -10, -12, -14],\n [-8, 1, -13, 0, 11],\n [12, -14, 14, 6, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 98 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 2, -15, -14, 3, -6],\n [-1, 5, 1, -9, 8, 0],\n [-2, -2, 7, 6, -11, -4],\n [4, 10, 3, 2, 10, 8],\n [10, -2, 11, -11, -1, -10],\n [9, -12, 3, -13, 14, -1]]\n\nPresent the answer in LaTex ... | 256 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -2, 8, 4, -8, 6],\n [-2, 11, 6, 2, 5, 9],\n [8, 6, 15, 1, 0, 7],\n [4, 2, 1, -9, 6, -2],\n [-8, 5, 0, 6, 13, -10],\n [6, 9, 7, -2, -10, 15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format:... | 10 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, -15, 7, -4, 10, 13],\n [0, -3, 5, -12, -1, 9],\n [0, 0, -1, -9, 14, -14],\n [0, 0, 0, -6, 13, 1],\n [0, 0, 0, 0, 11, -8],\n [0, 0, 0, 0, 0, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 808 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 3, -2, 4, -15, -14],\n [0, 6, -15, -11, 7, -5],\n [1, -12, 4, 13, -1, -3],\n [-8, 4, -4, -9, -13, -14],\n [8, -6, -1, 12, 5, 9],\n [14, 5, -1, 15, -5, -4]]\n\nPresent the answer in LaTex ... | 583 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -11, -2, -6, -7, 5],\n [13, 7, 3, 1, 9, -14],\n [-5, -11, 5, -7, -15, 1],\n [6, -8, -11, -15, -10, -7],\n [14, -2, 12, -5, -8, 11],\n [1, 5, -14, 13, 9, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 268 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -5, 2, -6, 0, 4],\n [-5, -1, -2, -8, 2, -5],\n [2, -2, 14, 10, -4, -2],\n [-6, -8, 10, -4, 4, -7],\n [0, 2, -4, 4, 12, 8],\n [4, -5, -2, -7, 8, 11]]\n\nPresent the answer in LaTex format:... | 896 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 6, 1, 3, -12, 8],\n [0, -3, -10, -1, 12, -6],\n [0, 0, -6, 14, -11, 13],\n [0, 0, 0, -3, -10, 3],\n [0, 0, 0, 0, -1, 15],\n [0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex fo... | 296 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 0, -2, -2, 2, 10],\n [0, -6, 4, 0, 3, 2],\n [-2, 4, 2, 0, -6, -2],\n [-2, 0, 0, -4, -5, 10],\n [2, 3, -6, -5, -4, 5],\n [10, 2, -2, 10, 5, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 996 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 13, 2, -6, -5, 3],\n [0, -15, -4, 12, 6, 4],\n [0, 0, 7, 15, 7, -15],\n [0, 0, 0, -6, 13, -4],\n [0, 0, 0, 0, 12, 11],\n [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 an... | 280 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 8, -2, -6, 12, -1],\n [0, -5, -5, 14, 5, 11],\n [0, 0, 9, -4, -7, -5],\n [0, 0, 0, -1, -1, 1],\n [0, 0, 0, 0, -4, -6],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, 10, -6, -9, 9, 1],\n [0, -10, -1, -7, -14, 1],\n [0, 0, -2, -4, -12, 4],\n [0, 0, 0, -11, 3, 7],\n [0, 0, 0, 0, 6, -13],\n [0, 0, 0, 0, 0, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 7, 15, 14, -8, -1],\n [0, 2, 5, 7, -3, 1],\n [0, 0, 5, 5, -14, 15],\n [0, 0, 0, 13, 12, -7],\n [0, 0, 0, 0, -4, -14],\n [0, 0, 0, 0, 0, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex forma... | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 10, 0, -1, -4, 0],\n [10, 7, 8, -8, 2, -2],\n [0, 8, -15, -7, -8, -2],\n [-1, -8, -7, -1, 0, 4],\n [-4, 2, -8, 0, 8, -2],\n [0, -2, -2, 4, -2, 1]]\n\nPresent the answer in LaTex format: ... | 624 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 15, 1, 12, -4, 4],\n [0, 7, 14, -13, 9, 14],\n [0, 0, -13, -8, -6, -14],\n [0, 0, 0, 4, 14, 9],\n [0, 0, 0, 0, -11, 2],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format... | 128 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 5, 14, -14, -13, -15],\n [-6, 3, -10, 7, 11, -10],\n [-7, 14, 7, 8, 10, 1],\n [12, -15, 8, 4, 0, 12],\n [11, -9, 2, 0, -1, 5],\n [9, -6, 3, 13, 11, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex... | 21 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, -2, -4, 2, 4],\n [-6, -4, -2, 2, 6, 0],\n [-2, -2, 8, 3, -7, 6],\n [-4, 2, 3, 0, 1, 3],\n [2, 6, -7, 1, 5, -6],\n [4, 0, 6, 3, -6, 8]]\n\nPresent the answer in LaTex format: \\... | 828 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 9, 15, -15, -9, -5],\n [8, 2, 11, 2, -15, -4],\n [11, 2, 7, -12, -4, 10],\n [4, -1, 11, 6, 12, 1],\n [-6, 1, -3, 3, 14, -13],\n [-2, 4, -2, -2, 1, -13]]\n\nPresent the answer in La... | 8 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 15, -15, 9, -1, -10],\n [-11, 11, -2, -12, 8, 2],\n [-15, 2, 9, 3, -7, 4],\n [14, -5, 10, 8, -11, -3],\n [10, 10, 2, 4, 10, 13],\n [15, 13, 2, -13, 13, -12]]\n\nPresent the answer in LaTe... | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 1, -15, -8, -8, -13],\n [0, -2, 1, 9, 11, 3],\n [0, 0, 10, 9, 14, 7],\n [0, 0, 0, 15, -2, 5],\n [0, 0, 0, 0, -14, 7],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\box... | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 11, 6, 6, 5, 11],\n [0, -2, 8, 4, -4, -9],\n [0, 0, -14, 0, -14, -10],\n [0, 0, 0, 3, 7, -3],\n [0, 0, 0, 0, -8, -10],\n [0, 0, 0, 0, 0, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex form... | 96 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 7, -1, -4, 13, 13],\n [0, 11, 3, -5, -11, -7],\n [0, 0, -2, -12, 7, -6],\n [0, 0, 0, 15, 10, -3],\n [0, 0, 0, 0, 2, -8],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex forma... | 360 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -8, 1, -3, 10, -6],\n [-2, -1, -2, -7, 8, -1],\n [7, 6, 13, 11, 12, -4],\n [8, -3, 9, 7, 6, 4],\n [4, 7, -8, -3, -7, 6],\n [-5, 3, -5, -8, 4, 2]]\n\nPresent the answer in LaTex format: \\... | 333 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, 12, -7, -7, 0, 15],\n [1, -8, 1, -15, 11, 5],\n [5, -9, 5, -6, -5, 14],\n [-14, -8, -10, -2, 15, 11],\n [2, 7, 6, -2, 3, 12],\n [7, -12, 2, 6, -3, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 279 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 10, -2, 3, 14, -8],\n [3, 14, 15, -9, -2, -4],\n [13, 13, -6, -8, 0, -13],\n [-6, -14, -3, -9, 15, -7],\n [5, -11, -7, 15, -2, -9],\n [9, -8, -8, 6, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 411 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 0, -10, 14, 9, -8],\n [0, 9, 15, 11, -5, 13],\n [0, 0, -13, -6, 11, -11],\n [0, 0, 0, -1, -2, -15],\n [0, 0, 0, 0, 8, -4],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex fo... | 752 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -7, 0, -8, -2],\n [4, 8, 3, -4, 2, -10],\n [-7, 3, 2, 2, 3, -8],\n [0, -4, 2, -3, -2, 12],\n [-8, 2, 3, -2, -4, -2],\n [-2, -10, -8, 12, -2, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex fo... | 368 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -6, 2, 1, -3, 4],\n [-6, 14, 0, 5, 4, 4],\n [2, 0, 10, 4, -1, 13],\n [1, 5, 4, 11, 3, -4],\n [-3, 4, -1, 3, -10, 0],\n [4, 4, 13, -4, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 175 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, 0, -2, 7, -7, 8],\n [0, 3, -2, 2, 0, 4],\n [-2, -2, -4, -2, -4, 7],\n [7, 2, -2, -7, -2, -12],\n [-7, 0, -4, -2, 3, -6],\n [8, 4, 7, -12, -6, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex forma... | 537 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 13, 2, -5, -10, -1],\n [0, -1, -2, -1, 9, -6],\n [0, 0, -9, -1, 9, 12],\n [0, 0, 0, -12, 0, -10],\n [0, 0, 0, 0, 2, -8],\n [0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: ... | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, 14, 5, 2, -9],\n [-8, 2, 5, 0, 8, -2],\n [-5, -6, -7, -15, -8, 8],\n [9, -13, -3, -5, 8, -12],\n [-6, 14, -8, 5, -5, 9],\n [-4, -5, 0, 1, -9, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 790 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -15, 6, 6, -13, 0],\n [-6, 8, 0, -8, 5, 4],\n [-3, -3, 12, 10, 7, 8],\n [-1, 14, 5, 9, -10, 1],\n [13, 11, -5, 8, 0, 12],\n [2, -5, 2, -7, -10, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed... | 872 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 9, -5, 13, 7, 11],\n [0, -2, -14, 5, 2, -13],\n [0, 0, -1, 0, 4, -15],\n [0, 0, 0, -4, 12, -10],\n [0, 0, 0, 0, 10, -5],\n [0, 0, 0, 0, 0, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 520 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -14, -9, 2, -5, 11],\n [14, 7, 6, 12, 13, 1],\n [-10, -14, 8, -13, 8, 13],\n [11, -3, -8, 5, 11, 7],\n [11, -14, 1, 6, 10, 4],\n [-7, 6, -13, -1, -9, 10]]\n\nPresent the answer in L... | 679 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 7, 6, 10, 10, -10],\n [0, -11, 3, -4, 4, -2],\n [0, 0, 3, -9, -4, 14],\n [0, 0, 0, -1, -4, 13],\n [0, 0, 0, 0, 1, 9],\n [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:... | 310 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 6, -8, -8, 8, -14],\n [2, -1, -14, 11, -13, -12],\n [13, 15, 15, 0, -8, 13],\n [13, -11, 15, 3, 2, 14],\n [13, -6, -7, 12, 4, 14],\n [12, 7, -13, 10, -13, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the an... | 480 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 11, 2, 2, -1, 6],\n [11, 15, -4, 0, -6, 6],\n [2, -4, 4, 4, 2, -2],\n [2, 0, 4, 9, 1, -2],\n [-1, -6, 2, 1, -1, -6],\n [6, 6, -2, -2, -6, 14]]\n\nPresent the answer in LaTex format:... | 252 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 2, -4, 6, -2, 4],\n [2, 11, 10, -4, 2, 2],\n [-4, 10, 4, -4, -1, 6],\n [6, -4, -4, -10, -4, -6],\n [-2, 2, -1, -4, -12, 0],\n [4, 2, 6, -6, 0, 5]]\n\nPresent the answer in LaTex fo... | 258 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 8, 3, 11, 1, 2],\n [15, 10, 14, -8, 13, 14],\n [-12, 6, 4, 8, 5, 13],\n [-12, 2, -7, -5, 7, -14],\n [1, -10, -2, -6, 5, 8],\n [14, 13, -3, -2, 0, -12]]\n\nPresent the answer in LaTe... | 132 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -7, 8, 2, -7, 8],\n [0, 14, -12, -10, 14, 9],\n [0, 0, 9, -11, 1, 0],\n [0, 0, 0, -4, 15, -3],\n [0, 0, 0, 0, 3, 3],\n [0, 0, 0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 208 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -11, 10, 1, 13, 2],\n [0, -4, 1, 10, 12, 1],\n [0, 0, -13, -15, -8, -8],\n [0, 0, 0, 3, -12, 3],\n [0, 0, 0, 0, -6, -13],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\... | 520 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 2, 8, -4, -1, 6],\n [2, 4, 4, -3, -2, -2],\n [8, 4, -5, 4, 0, -6],\n [-4, -3, 4, -11, -4, 14],\n [-1, -2, 0, -4, 12, 4],\n [6, -2, -6, 14, 4, -11]]\n\nPresent the answer in LaTex f... | 299 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 9, 5, -2, -4, -8],\n [0, 3, 7, -13, 3, 15],\n [0, 0, -14, -7, -7, -6],\n [0, 0, 0, -1, 7, 4],\n [0, 0, 0, 0, 13, 15],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\box... | 30 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -5, -3, 10, -10, 7],\n [0, 2, -3, -7, 11, -9],\n [0, 0, -5, 1, -12, 14],\n [0, 0, 0, -14, 14, -13],\n [0, 0, 0, 0, 6, -6],\n [0, 0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 320 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 2, 4, 8, -5, 14],\n [1, -1, -9, -4, 6, -2],\n [6, 12, -2, -9, 8, -5],\n [-2, 0, -4, 15, 10, -6],\n [1, 5, 4, 10, -3, 8],\n [-10, -5, 8, -13, 3, -3]]\n\nPresent the answer in LaTex format... | 879 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -4, -14, 0, 8, 2],\n [-4, -2, -5, -4, -2, -2],\n [-14, -5, -14, 1, 0, 6],\n [0, -4, 1, -13, 3, -2],\n [8, -2, 0, 3, -13, -2],\n [2, -2, 6, -2, -2, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in La... | 272 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 6, 11, 4, -9, 11],\n [-11, 0, 11, -11, 9, 14],\n [3, -2, -3, 6, -8, 1],\n [-1, -5, -1, 9, -3, 14],\n [-7, 0, -11, 15, 13, 5],\n [9, 12, 10, 8, -5, -3]]\n\nPresent the answer in LaT... | 992 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 2, -9, -11, -6, -1],\n [2, -5, 6, 4, 5, -7],\n [-9, 6, -9, -4, -6, 8],\n [-11, 4, -4, -12, -10, 6],\n [-6, 5, -6, -10, -1, -4],\n [-1, -7, 8, 6, -4, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in... | 493 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -10, -5, -3, 2, -3],\n [0, -6, -11, 12, 13, 15],\n [0, 0, -3, -7, 3, -5],\n [0, 0, 0, 3, -8, -3],\n [0, 0, 0, 0, 11, 4],\n [0, 0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \... | 760 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-15, -11, 6, -15, -8, -12],\n [0, -5, -7, 15, 1, -3],\n [0, 0, 11, 4, 4, 5],\n [0, 0, 0, 5, 8, -2],\n [0, 0, 0, 0, 2, 1],\n [0, 0, 0, 0, 0, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, -12, -2, 6, -6],\n [-2, -12, 10, 4, 6, -3],\n [-12, 10, 2, -8, -4, 2],\n [-2, 4, -8, -1, 0, 9],\n [6, 6, -4, 0, 9, -6],\n [-6, -3, 2, 9, -6, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex fo... | 748 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, -9, -3, 2, -12],\n [0, -13, -15, 14, 9, 9],\n [0, 0, 10, 7, -12, -7],\n [0, 0, 0, 15, 6, -6],\n [0, 0, 0, 0, 3, 6],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\box... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -10, -11, 9, 10, -11],\n [12, -10, 1, -3, -12, -9],\n [-13, -4, -10, -10, 10, 13],\n [-13, 3, -1, 2, -7, -5],\n [-9, 15, -7, -15, -14, 3],\n [-15, 7, -10, 2, 11, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaT... | 729 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 10, 10, 2, 12, 2],\n [10, 7, -2, -6, -8, -4],\n [10, -2, -5, -2, -12, -5],\n [2, -6, -2, -2, -2, -4],\n [12, -8, -12, -2, -7, -4],\n [2, -4, -5, -4, -4, 1]]\n\nPresent the answer in LaTe... | 144 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 6, 4, 3, -3, 8],\n [6, 2, 0, 0, 4, 6],\n [4, 0, -9, 3, 2, -10],\n [3, 0, 3, -11, 2, 0],\n [-3, 4, 2, 2, -2, -2],\n [8, 6, -10, 0, -2, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 952 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 8, -12, 3, 2, 3],\n [8, -6, 8, -8, -4, 0],\n [-12, 8, 4, 0, 4, -6],\n [3, -8, 0, 12, -6, 4],\n [2, -4, 4, -6, 12, -5],\n [3, 0, -6, 4, -5, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\... | 336 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -9, -4, 0, -2, -6],\n [-9, -11, 4, -2, -2, 10],\n [-4, 4, 2, -1, 0, 2],\n [0, -2, -1, -13, -2, -2],\n [-2, -2, 0, -2, 8, 4],\n [-6, 10, 2, -2, 4, 14]]\n\nPresent the answer in LaTex forma... | 432 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, -6, 2, -11, 2],\n [-4, 5, -13, 2, 4, 8],\n [-6, -13, -12, -6, -7, -10],\n [2, 2, -6, 6, -7, -6],\n [-11, 4, -7, -7, 15, -8],\n [2, 8, -10, -6, -8, 8]]\n\nPresent the answer in LaTex f... | 996 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 8, 5, -10, 7, -2],\n [0, 2, -2, 9, -10, -14],\n [0, 0, 11, 8, -11, -12],\n [0, 0, 0, -10, 12, -7],\n [0, 0, 0, 0, -6, -11],\n [0, 0, 0, 0, 0, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 480 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-13, 2, -9, 11, -15, -13],\n [0, -1, -12, 4, -4, 14],\n [0, 0, -7, -4, -15, 3],\n [0, 0, 0, 2, 7, 4],\n [0, 0, 0, 0, 3, 14],\n [0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 730 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, 4, -8, 10, -1, 11],\n [9, -9, 14, 2, 13, 5],\n [4, -5, 6, 8, -12, 0],\n [-11, 0, 2, -14, -14, -12],\n [15, -13, -15, -11, 7, -11],\n [-1, 3, -3, 7, 14, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in L... | 828 | MATH |
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