messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, -10, 3],\n [0, 3, 6, 2],\n [0, 0, 4, 10],\n [0, 0, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -9, -8, 10],\n [0, 2, -1, 12],\n [0, 0, -2, -5],\n [0, 0, 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": "user"
}
] | 576 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 1, 10, 6],\n [-6, 1, 0, 12],\n [6, -10, 11, 8],\n [-5, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 412 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, 0, 4],\n [2, 5, -5, -2],\n [0, -5, -2, -4],\n [4, -2, -4, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -7, 3, -5],\n [0, -3, -4, -5],\n [0, 0, -2, -1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 210 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 4, 4, 7],\n [4, 3, -2, -5],\n [4, -2, -4, 0],\n [7, -5, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 584 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, -4, 10],\n [7, 0, 6, 10],\n [3, 6, 8, 5],\n [-6, -3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -5, 4, 10],\n [-5, 2, -1, -3],\n [4, -1, -9, 6],\n [10, -3, 6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -8, 7, 10],\n [0, -1, 11, -9],\n [0, 0, -3, 6],\n [0, 0, 0, -7]]\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"
}
] | 168 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -8, -10, -11],\n [0, -7, -12, 5],\n [12, 9, 5, 3],\n [5, 11, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 335 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -7, 8, 0],\n [0, 6, 7, -3],\n [0, 0, -9, -10],\n [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"
}
] | 544 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 12, -7, -1],\n [0, 2, 12, -10],\n [0, 0, -9, 5],\n [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"
}
] | 216 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -9, -7, 9],\n [0, -12, 4, 12],\n [0, 0, 7, 5],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 504 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 10, 3, 0],\n [10, 0, -8, 1],\n [3, -8, 7, -3],\n [0, 1, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 803 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 6, 2, 4],\n [6, -7, 5, 0],\n [2, 5, -4, -7],\n [4, 0, -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 |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -9, 2, -8],\n [2, -7, 5, -10],\n [5, 1, 5, 5],\n [-8, 8, -7, 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"
}
] | 197 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 12, 4, 1],\n [0, 2, 7, -10],\n [0, 0, 12, -4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 3, -3, -12],\n [9, 8, 11, 9],\n [-7, 2, -6, -10],\n [-3, 2, 10, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 902 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -4, 0, 0],\n [-4, -2, 2, -2],\n [0, 2, -1, -7],\n [0, -2, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 736 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 1, -5, 12],\n [0, -6, -6, -11],\n [0, 0, 9, 0],\n [0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 812 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -5, -2, -3],\n [0, 12, 2, -6],\n [0, 0, 9, -12],\n [0, 0, 0, -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"
}
] | 940 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, -2, -7],\n [0, -3, -6, 10],\n [0, 0, -3, -1],\n [0, 0, 0, -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"
}
] | 730 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -3, 12, 8],\n [-8, 11, -2, -7],\n [2, -2, -5, -11],\n [11, 4, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -1, -12, 0],\n [11, 9, -2, -8],\n [-1, 0, 7, -8],\n [0, -11, 4, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -9, 2, -3],\n [-9, -11, 2, -4],\n [2, 2, -2, 2],\n [-3, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 394 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 3, 7, -10],\n [5, -4, -9, 0],\n [-3, 3, -9, -7],\n [-6, -1, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, -6, -4],\n [4, -6, 2, -4],\n [-6, 2, 3, 0],\n [-4, -4, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -12, 5, -11],\n [3, -3, 3, 10],\n [-9, 11, 11, 5],\n [-3, -11, -9, -11]]? 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 |
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, -9, 10],\n [0, 6, -4, 1],\n [0, 0, -8, -1],\n [0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 672 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, 7, 2],\n [8, 12, 11, -9],\n [-10, 7, -6, 12],\n [-12, 4, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -1, -5, 12],\n [2, 9, 1, -2],\n [-2, 5, 5, -9],\n [12, -11, -4, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 827 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -2, 0, -10],\n [-2, -7, 9, 0],\n [0, 9, 11, -11],\n [-10, 0, -11, 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": "user"
}
] | 703 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, -4, 4],\n [6, -9, 6, -6],\n [-4, 6, -4, 3],\n [4, -6, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 1, 12, 9],\n [-7, 11, -7, 7],\n [-1, 4, 0, -9],\n [0, -1, 9, -7]]\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"
}
] | 57 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 4, -3, 2],\n [5, 2, 8, 0],\n [-10, -9, -2, 7],\n [-12, -4, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 572 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 10, -10, 4],\n [10, 7, -2, -4],\n [-10, -2, 6, -8],\n [4, -4, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 990 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 1, -10, -5],\n [0, -3, -3, 2],\n [0, 0, 12, 8],\n [0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 756 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -7, -6, 2],\n [-7, -1, 0, 0],\n [-6, 0, -1, 0],\n [2, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 902 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 2, -8, 12],\n [0, 4, 4, -7],\n [0, 0, -4, 1],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 11, -8, 1],\n [7, -4, -4, 12],\n [-10, -6, 6, 5],\n [2, -6, 4, -7]]\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"
}
] | 186 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 11, 7, 8],\n [2, -12, 11, -8],\n [4, 6, 7, -7],\n [-2, -6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 338 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 10, -10, 12],\n [10, 10, 6, 2],\n [-10, 6, -8, 8],\n [12, 2, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 716 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -5, 8, 12],\n [-10, 8, 11, -10],\n [3, -11, 9, 3],\n [5, 5, -12, -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"
}
] | 396 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -2, -11, 8],\n [-2, 12, -7, 2],\n [-11, -7, -11, 2],\n [8, 2, 2, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 230 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 6, 0, -4],\n [0, 2, -3, 11],\n [0, 0, -11, -12],\n [0, 0, 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": "user"
}
] | 198 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -8, -5, -7],\n [-8, 11, -7, 4],\n [3, 5, 11, 6],\n [-2, -2, 7, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -12, 2, 3],\n [0, 7, 7, 11],\n [0, 0, 1, 4],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 630 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -9, -7, -6],\n [0, 9, -7, -8],\n [0, 0, 6, -9],\n [0, 0, 0, 4]]\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"
}
] | 376 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 7, -4, 0],\n [0, 6, -5, -10],\n [0, 0, 1, -10],\n [0, 0, 0, 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"
}
] | 462 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -4, 1, 8],\n [0, 1, 11, -11],\n [0, 0, 6, 5],\n [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"
}
] | 676 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 11, 4, 10],\n [0, -2, -10, -5],\n [0, 0, -5, -7],\n [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"
}
] | 640 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 10, 0, 4],\n [10, -8, -6, -2],\n [0, -6, 10, 2],\n [4, -2, 2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 3, 8, 10],\n [-10, 8, 0, 7],\n [-10, -5, -12, -2],\n [5, 5, 3, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 426 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -7, -3, -7],\n [-8, -12, 0, 8],\n [0, -8, 1, -4],\n [-9, 10, -12, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 644 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -10, 8, -8],\n [11, -7, -2, 0],\n [5, 5, -6, 3],\n [11, -12, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 10, -2, 4],\n [10, 7, 8, 5],\n [-2, 8, -6, -8],\n [4, 5, -8, -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"
}
] | 488 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 4, -10, 8],\n [0, 5, 12, -6],\n [0, 0, -10, 6],\n [0, 0, 0, -12]]\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 |
[
{
"content": "What is the determinant of the matrix:\n[[0, 4, -6, 0],\n [4, -12, -1, 1],\n [-6, -1, -3, 0],\n [0, 1, 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"
}
] | 148 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 2, 1, -2],\n [2, -2, 4, 6],\n [1, 4, 1, -1],\n [-2, 6, -1, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 9, 11, 3],\n [0, 3, -1, -10],\n [0, 0, 3, -6],\n [0, 0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -12, 7, -12],\n [0, 9, -1, -1],\n [0, 0, 6, 11],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 840 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 11, 8],\n [12, 10, 11, 3],\n [5, 2, -4, -9],\n [-5, 4, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 470 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -2, 5, 2],\n [-2, 2, -7, 2],\n [5, -7, 1, 2],\n [2, 2, 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": "user"
}
] | 17 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 7, -11, -4],\n [0, -3, 7, 7],\n [0, 0, 2, -8],\n [0, 0, 0, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 336 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -4, -2, 9],\n [4, -4, 9, -1],\n [8, 4, 4, -4],\n [4, 3, 12, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -5, 6, 12],\n [0, -3, 4, 4],\n [0, 0, 1, -1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -6, 0, -4],\n [-6, 8, -1, -4],\n [0, -1, 4, 8],\n [-4, -4, 8, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, 4, -3],\n [2, -2, 3, -8],\n [4, 3, 7, -8],\n [-3, -8, -8, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 463 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -4, -9, -11],\n [4, -12, 11, -4],\n [-12, 9, -12, 3],\n [0, 0, 8, -4]]\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"
}
] | 576 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -10, 4, -10],\n [-10, -1, 2, 1],\n [4, 2, -7, -6],\n [-10, 1, -6, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 903 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -7, 8, -9],\n [0, -10, 5, 12],\n [0, 0, 4, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 9, -4, 7],\n [0, -1, 12, 11],\n [0, 0, -8, 10],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, 5, 8],\n [-4, -1, 4, -9],\n [5, 4, 12, 8],\n [8, -9, 8, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 858 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, -10, 12],\n [4, 4, 9, 12],\n [5, -6, 7, -3],\n [4, 4, 11, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 710 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 11, -3, 4],\n [-3, -5, -7, 2],\n [-11, 6, -12, 3],\n [-1, 12, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -4, 4],\n [2, -9, -2, 6],\n [-4, -2, 2, -12],\n [4, 6, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 570 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, 1, 4],\n [-4, -11, -7, -6],\n [1, -7, -3, 1],\n [4, -6, 1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 747 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -5, 7, 11],\n [0, 12, -10, -11],\n [0, 0, 7, -12],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 8, 4, 1],\n [8, 9, -4, -7],\n [4, -4, -9, -8],\n [1, -7, -8, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 729 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -7, 4, 1],\n [-7, -4, -10, 2],\n [4, -10, -5, -4],\n [1, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 956 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 6, 8, 1],\n [6, -10, -2, -11],\n [8, -2, 9, -1],\n [1, -11, -1, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 762 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -11, -12, 8],\n [5, 5, -9, -3],\n [-12, 8, -11, -6],\n [4, 6, 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"
}
] | 776 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -4, -8, 4],\n [0, 2, 2, -6],\n [0, 0, -6, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 568 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 11, -6, 2],\n [12, -9, -3, 8],\n [-12, 5, -12, -4],\n [-10, -11, -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"
}
] | 866 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, -3, -8],\n [-10, 5, 5, 3],\n [-11, -8, 3, 1],\n [-12, -6, -7, 7]]\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"
}
] | 871 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, -11, -1],\n [6, 5, -10, 11],\n [1, 7, 5, 10],\n [-6, 1, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 133 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -3, -6, 6],\n [-5, 11, -2, -7],\n [-6, -3, 7, -1],\n [3, -12, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 7, 2, 6],\n [7, 1, 1, -4],\n [2, 1, -2, -6],\n [6, -4, -6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, 5, 11],\n [0, 12, 0, -2],\n [0, 0, -7, 4],\n [0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 260 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -12, 9, -12],\n [0, -8, 2, 5],\n [0, 0, 4, 0],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 10, -9, -3],\n [0, -1, 0, 6],\n [0, 0, 7, -5],\n [0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 685 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -8, -7],\n [0, 1, 11, -3],\n [0, 0, 6, -5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -12, 7, -9],\n [0, -12, -8, -8],\n [0, 0, 7, -5],\n [0, 0, 0, 10]]\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": "Compute |A| for the matrix A =\n[[-4, 3, 1, -1],\n [0, 7, -10, -8],\n [0, 0, 7, 5],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 608 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -5, 2, -3],\n [-8, 2, -9, -12],\n [-9, 6, 9, -9],\n [7, -4, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, 4, 0],\n [0, 6, 2, 2],\n [4, 2, 6, -7],\n [0, 2, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 198 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 1, 1, 0],\n [-7, 4, -11, -5],\n [4, -9, -9, 0],\n [3, 8, 11, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 650 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -5, -2, 2],\n [-6, 4, 11, -6],\n [-9, -5, 9, -8],\n [8, -8, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 912 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -6, -4, -10],\n [0, 9, -8, 9],\n [0, 0, 8, 9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 4, 9, -9],\n [-4, -9, 3, -12],\n [7, -4, -5, -10],\n [6, -6, -11, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 284 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.