messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -4, -11, 12],\n [0, 4, -10, 0],\n [0, 0, -12, 2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -6, 0, 8],\n [0, 3, 8, -11],\n [0, 0, 10, 9],\n [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": "user"
}
] | 700 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 1, -5, 8],\n [0, -9, -2, -4],\n [0, 0, 12, 11],\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"
}
] | 972 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, -1, -6],\n [0, -12, 10, 3],\n [0, 0, -6, 0],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 4, -6, 4],\n [4, 7, 4, -6],\n [-6, 4, 6, -2],\n [4, -6, -2, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 1, 1, -1],\n [0, 9, -7, -9],\n [0, 0, 1, 5],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 838 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 3, 1, 4],\n [3, 9, 8, -6],\n [1, 8, -10, 9],\n [4, -6, 9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 9, -11, 0],\n [-11, 2, 11, 12],\n [-7, -2, -9, -4],\n [7, 10, 10, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 916 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -1, 6, -1],\n [-1, 10, 6, -2],\n [6, 6, 6, -2],\n [-1, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 906 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -2, -8, 0],\n [-2, 1, -2, 0],\n [-8, -2, 1, -2],\n [0, 0, -2, 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"
}
] | 312 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 6, -1, -4],\n [6, -11, -6, 4],\n [-1, -6, 0, 8],\n [-4, 4, 8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 141 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 12, -5, -3],\n [11, 4, 9, 1],\n [-8, -3, 3, 6],\n [11, -12, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -4, 0, -2],\n [-4, -1, 0, 4],\n [0, 0, 8, -7],\n [-2, 4, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 617 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 3, -2, 2],\n [3, 1, -4, -1],\n [-2, -4, 8, 0],\n [2, -1, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 784 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -8, -7, -4],\n [-8, -4, -8, -2],\n [-7, -8, 12, 0],\n [-4, -2, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 656 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, 2, 0],\n [0, 3, -7, 6],\n [2, -7, -2, 0],\n [0, 6, 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"
}
] | 370 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 8, -8, 11],\n [7, -11, -11, -12],\n [-4, 11, 6, -6],\n [-5, 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"
}
] | 997 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -6, 12, 8],\n [0, -10, 11, 8],\n [0, 0, 6, -6],\n [0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 1, -9, 12],\n [8, -1, -9, 12],\n [3, 7, -10, 5],\n [-7, -2, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 236 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -7, 3, 2],\n [0, 7, 2, 2],\n [0, 0, 12, -1],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 12, 5, 0],\n [0, -2, 4, -3],\n [0, 0, -12, -2],\n [0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, -4, 0],\n [4, 6, -6, 3],\n [-4, -6, -4, 7],\n [0, 3, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 3, -10, -5],\n [3, 11, 6, 10],\n [-10, 6, 6, 1],\n [-5, 10, 1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, -1, -3],\n [2, -6, -2, -6],\n [-1, -2, 2, -6],\n [-3, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 110 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 5, -8, -4],\n [5, 4, 4, -7],\n [-8, 4, -8, -2],\n [-4, -7, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 788 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 6, 0, 6],\n [6, -3, -7, -4],\n [0, -7, -6, 4],\n [6, -4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 572 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 6, 0, 1],\n [6, 1, 1, 2],\n [0, 1, 9, 6],\n [1, 2, 6, -5]]\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": "What is the determinant of the matrix:\n[[-9, -6, -1, -6],\n [0, 5, 10, 8],\n [0, 0, 11, 5],\n [0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 950 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, -12, -4, -2],\n [-12, 0, -4, 8],\n [-4, -4, -8, -5],\n [-2, 8, -5, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 4, -9],\n [0, -11, 2, 8],\n [4, 2, -12, -4],\n [-9, 8, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, 2, 8],\n [-4, -6, -7, -4],\n [2, -7, -11, 2],\n [8, -4, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -12, 8, -11],\n [-2, 6, 10, -4],\n [7, -8, 1, 8],\n [11, -7, -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"
}
] | 910 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -6, -10, 2],\n [0, -2, 9, -4],\n [0, 0, 3, -9],\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"
}
] | 864 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 1, 4, 10],\n [1, -4, -8, -1],\n [4, -8, 8, 0],\n [10, -1, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -11, -10, 3],\n [0, 5, -9, 10],\n [0, 0, -7, 3],\n [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"
}
] | 40 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 12, 6, 4],\n [-6, -5, -9, -1],\n [-7, -9, -8, -7],\n [-9, 12, 9, 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"
}
] | 324 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -11, -5, -2],\n [5, 11, -11, -3],\n [-8, 4, -8, 7],\n [1, -10, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 372 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, -7, 0],\n [8, -4, -8, 12],\n [3, 8, 3, -9],\n [-5, -3, -8, 8]]\nRound to the nearest integer, then take the result modulo 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, 2, 3, 0],\n [-10, -6, -9, 5],\n [11, -6, 5, 8],\n [-9, 2, 6, 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"
}
] | 340 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 0, 9, 12],\n [6, 3, 0, -11],\n [8, -2, -5, -3],\n [11, 12, 5, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 817 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, 6, -2],\n [2, -8, -4, -10],\n [6, -4, -4, -8],\n [-2, -10, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -2, 11, -8],\n [-2, -11, -11, -6],\n [11, -11, -11, 8],\n [-8, -6, 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"
}
] | 688 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -9, -12, 6],\n [0, -5, -5, -4],\n [0, 0, -2, 11],\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"
}
] | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 6, -8, 2],\n [6, 0, -6, 9],\n [-8, -6, 0, 6],\n [2, 9, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 3, 0, -8],\n [7, -1, 8, -3],\n [0, 9, -5, 6],\n [-11, 2, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 506 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -12, 1, -12],\n [0, 4, 4, 11],\n [0, 0, -3, -1],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -8, 0, -9],\n [-8, 0, -5, 3],\n [0, -5, -9, -5],\n [-9, 3, -5, 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"
}
] | 620 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -6, 0, 3],\n [-6, -1, 2, 2],\n [0, 2, -5, 6],\n [3, 2, 6, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 998 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -12, 5, -7],\n [0, -10, 0, 8],\n [0, 0, 11, -3],\n [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"
}
] | 440 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -3, -9, -5],\n [0, 1, -4, 5],\n [0, 0, -3, -9],\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"
}
] | 970 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -12, -2, -4],\n [-2, 4, -1, -8],\n [10, 7, 4, 11],\n [-3, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 596 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -10, -12, -1],\n [0, -5, 9, -11],\n [0, 0, -4, 7],\n [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"
}
] | 320 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -4, 7, 2],\n [-4, 9, -2, -8],\n [7, -2, 8, 8],\n [2, -8, 8, 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"
}
] | 207 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 5, -7, 11],\n [0, -2, -12, -5],\n [0, 0, -5, 5],\n [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"
}
] | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -7, 2, 1],\n [1, 5, 7, -11],\n [-8, 4, -12, -1],\n [5, -5, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 870 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -1, -3, 6],\n [-10, -11, -7, -1],\n [-8, 2, -9, 7],\n [3, -12, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 303 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 8, -1, -6],\n [8, -6, 6, -9],\n [-1, 6, -8, -3],\n [-6, -9, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 333 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -7, 12, 8],\n [8, 7, 6, -5],\n [-3, 4, -6, 11],\n [9, 7, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 676 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 6, -5],\n [-5, -12, 6, -5],\n [10, 4, 7, 8],\n [-7, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, -2, 9],\n [-2, 5, 2, 8],\n [-2, 2, 8, -4],\n [9, 8, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -9, 8, 5],\n [6, -11, -12, -5],\n [8, 9, 11, 8],\n [9, -10, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -5, -9, -12],\n [6, -1, 1, -3],\n [3, -4, -11, -6],\n [6, 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"
}
] | 662 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -6, 0, 7],\n [-6, 8, 3, 5],\n [0, 3, -12, -6],\n [7, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 149 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 12, -1, -10],\n [0, 7, 0, -1],\n [0, 0, 5, -9],\n [0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 775 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -11, -6, 6],\n [0, -12, 2, -10],\n [0, 0, -6, -2],\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"
}
] | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, 2, 4],\n [4, 1, 2, -2],\n [2, 2, -9, -4],\n [4, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 5, 2, -3],\n [0, 7, -9, 12],\n [0, 0, -3, 10],\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"
}
] | 252 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 12, 7, -10],\n [0, 4, -6, 9],\n [0, 0, -12, 2],\n [0, 0, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 664 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -1, 10, 10],\n [2, -8, -5, 11],\n [5, 4, 12, 0],\n [10, -6, -12, -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"
}
] | 291 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -8, 2, 10],\n [0, 5, 1, -12],\n [0, 0, -5, 9],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 700 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 2, -6, 9],\n [0, 2, 3, -6],\n [0, 0, -11, -5],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 12, -6, -10],\n [0, 3, 8, -3],\n [0, 0, -4, 9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, 9, 6],\n [10, 11, -10, 10],\n [9, 3, 2, -12],\n [-3, -8, -1, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 923 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -4, -2, -4],\n [-4, 8, 2, 10],\n [-2, 2, -5, -2],\n [-4, 10, -2, -8]]? 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 |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -1, -6, 6],\n [-1, 4, 1, -3],\n [-6, 1, 2, 10],\n [6, -3, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 402 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 2, 12, -1],\n [0, -6, -7, -5],\n [0, 0, -2, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -12, 9, 8],\n [0, 2, -6, -5],\n [-8, 12, 10, -12],\n [0, 4, 11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -6, 7, -6],\n [0, 11, -2, 10],\n [0, 0, 12, -5],\n [0, 0, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 932 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -10, 6, 9],\n [-10, 5, -7, 8],\n [6, -7, -4, 8],\n [9, 8, 8, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, -2, 6],\n [-2, -8, 6, 4],\n [-2, 6, 6, 5],\n [6, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 996 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 11, -5, 12],\n [0, -3, 4, -10],\n [0, 0, 12, -8],\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"
}
] | 864 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, -4, -6],\n [6, 6, 5, 1],\n [-4, 5, -12, 2],\n [-6, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 596 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 0, -4, 8],\n [2, 2, 4, -1],\n [2, 1, 11, 2],\n [4, 9, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 547 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -8, -12, -2],\n [0, 7, -8, 3],\n [0, 0, -5, -7],\n [0, 0, 0, 7]]\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 |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -1, 11, 12],\n [0, 8, -6, -8],\n [0, 0, 11, 5],\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"
}
] | 584 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -3, -10, 0],\n [-3, -6, 4, -4],\n [-10, 4, 0, -8],\n [0, -4, -8, -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"
}
] | 112 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 1, -6],\n [-6, -3, 5, 12],\n [1, -12, -8, -4],\n [1, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 589 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 3, -1, -4],\n [3, 12, -6, 2],\n [-1, -6, -6, 2],\n [-4, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 798 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 3, 5, 8],\n [3, -9, 4, -7],\n [5, 4, 7, -2],\n [8, -7, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 783 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 12, -10, 3],\n [-2, -10, 0, 3],\n [5, -9, 2, 5],\n [12, -12, 3, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 553 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -10, -10, 0],\n [-10, 12, -1, -4],\n [-10, -1, 8, 7],\n [0, -4, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 375 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -10, 11, -7],\n [0, -2, -7, -11],\n [0, 0, 3, -3],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 790 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -8, -10, 3],\n [0, -4, -8, -6],\n [0, 0, 6, -5],\n [0, 0, 0, 7]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, -6, 0],\n [0, 6, -3, -8],\n [-6, -3, 6, 11],\n [0, -8, 11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, 0, 5],\n [4, 10, -2, 2],\n [0, -2, -12, 1],\n [5, 2, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 468 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -7, 8, 1],\n [-7, -11, -8, 0],\n [8, -8, 6, 2],\n [1, 0, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 11, 7, 2],\n [7, 8, 3, 10],\n [-5, 9, -2, 5],\n [-1, 2, 3, 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"
}
] | 986 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 8, -11, 6],\n [7, -9, -1, 5],\n [-9, 10, -11, -10],\n [12, 11, 11, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 997 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 1, 0, 12],\n [-10, 1, -11, -9],\n [1, -12, -7, 8],\n [7, 0, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 457 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -11, 10, 1],\n [1, 7, -6, 7],\n [-6, 9, -8, -12],\n [3, 6, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 566 | MATH |
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