messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[5, -1, 0, 4],\n [9, 5, 6, 5],\n [-3, 9, -8, -6],\n [-12, -5, 4, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 684 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 12, -8, 2],\n [0, 6, 2, 1],\n [0, 0, -9, 7],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -12, -4, -6],\n [-12, -6, -4, 6],\n [-4, -4, -3, 6],\n [-6, 6, 6, -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"
}
] | 328 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, -1, 12],\n [5, -11, -2, 8],\n [-2, 6, -4, 1],\n [-8, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -9, -1, -4],\n [0, -1, 10, -3],\n [0, 0, -4, 0],\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"
}
] | 64 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -2, 11, -11],\n [0, -9, -10, -11],\n [0, 0, 9, 3],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 7, -5, 3],\n [0, -10, -12, 8],\n [0, 0, 2, -11],\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"
}
] | 660 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, -8, -6, -6],\n [0, 1, 1, 4],\n [0, 0, -1, -9],\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"
}
] | 24 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 5, -11, 8],\n [-10, 5, -12, -2],\n [9, 4, -4, -12],\n [1, 11, -4, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 0, 5, -12],\n [3, -9, 7, -3],\n [9, 3, -8, -1],\n [-2, -11, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 0, 6, 0],\n [0, -7, 2, 11],\n [0, 0, -10, 3],\n [0, 0, 0, 8]]\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[[5, -7, 8, 3],\n [-7, 9, 9, -6],\n [8, 9, -10, 1],\n [3, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 266 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 4, 0, 9],\n [0, 5, 1, -7],\n [0, 0, -5, 7],\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"
}
] | 475 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -3, -5, 12],\n [0, -3, -5, -3],\n [0, 0, -1, 5],\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"
}
] | 396 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -11, -4, -9],\n [-5, 2, -5, -11],\n [-4, -4, 11, 12],\n [-2, 4, -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"
}
] | 541 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 12, 2, -4],\n [12, -9, 0, -3],\n [2, 0, -6, 4],\n [-4, -3, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 850 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -2, 9, 9],\n [0, -9, 1, 10],\n [10, 10, 9, 1],\n [10, -7, 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"
}
] | 962 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -12, -4, 8],\n [0, -1, -12, 5],\n [0, 0, -6, 9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 3, -3, 1],\n [0, -9, 9, 12],\n [0, 0, -12, 2],\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"
}
] | 760 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 7, 1, 3],\n [-8, -1, -8, 11],\n [5, -4, -12, 11],\n [1, -11, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 754 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 10, -5, -8],\n [-11, 11, 12, 2],\n [5, -9, -10, 0],\n [-11, -9, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 856 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -2, -4, 4],\n [-2, -10, 8, 0],\n [-4, 8, 0, 3],\n [4, 0, 3, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -3, -8, 7],\n [-3, 9, -2, 4],\n [-8, -2, -8, -2],\n [7, 4, -2, 9]]? 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 |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 0, -6, 6],\n [8, 0, -3, -6],\n [-6, 11, 1, 7],\n [-10, 8, 10, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -10, 6, 10],\n [0, 10, -8, -3],\n [0, 0, -6, -10],\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"
}
] | 620 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -1, -4, -3],\n [0, 3, -3, -5],\n [0, 0, 1, 5],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, -10, -6],\n [2, -5, 3, 6],\n [-10, 3, -4, 4],\n [-6, 6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -2, 0, -6],\n [-2, -10, -6, 2],\n [0, -6, 2, 9],\n [-6, 2, 9, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 546 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 3, 2, -3],\n [3, 7, -4, -8],\n [2, -4, -12, -3],\n [-3, -8, -3, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -9, 12, -9],\n [0, 5, 1, -8],\n [0, 0, 7, -12],\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"
}
] | 350 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, -2, 10],\n [-6, 11, 0, 0],\n [-2, 0, -2, 5],\n [10, 0, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 619 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 4, -1, -6],\n [4, 5, 4, 4],\n [-1, 4, 0, -4],\n [-6, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 927 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -10, 7, -1],\n [0, -10, -12, -10],\n [0, 0, 6, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 840 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 1, -3, 1],\n [0, 7, 10, 5],\n [0, 0, -3, -6],\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"
}
] | 210 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 7, 12, 12],\n [-11, 2, -12, -7],\n [3, -11, 4, 9],\n [9, -10, -4, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 552 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 2, -8, 3],\n [0, 5, -5, -8],\n [0, 0, 1, -2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -12, 0, 1],\n [0, -4, 7, 10],\n [0, 0, 10, -3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -9, 2, -4],\n [-1, 0, -7, 2],\n [-10, 7, -4, -3],\n [2, 3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 502 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 11, 4, 0],\n [0, 7, -11, -6],\n [0, 0, -12, -11],\n [0, 0, 0, 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"
}
] | 580 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, -9, 3],\n [1, 11, 2, 1],\n [5, 0, -12, -9],\n [3, 3, -1, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 890 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 8, 12, 9],\n [10, 1, 6, 0],\n [-12, 11, 1, 0],\n [-3, -6, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 124 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -7, -5, 5],\n [-1, -4, 12, 12],\n [-2, 3, 12, 5],\n [-9, -6, 12, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 6, -1, -5],\n [0, -2, 12, 3],\n [0, 0, -2, -5],\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"
}
] | 56 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 3, 4, -4],\n [3, -3, -6, -1],\n [4, -6, -7, -6],\n [-4, -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"
}
] | 33 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 2, 10, 0],\n [2, -4, -4, 10],\n [10, -4, 4, 6],\n [0, 10, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 536 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 10, 5, -7],\n [-1, 7, 2, 12],\n [0, 1, -11, 10],\n [4, 10, 9, -9]]\nRound to the nearest integer, then take the result modulo 1000.\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[[7, 0, -2, -4],\n [0, -4, -4, 0],\n [-2, -4, -6, -7],\n [-4, 0, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, -12, 10],\n [0, -5, 8, 3],\n [0, 0, 6, 4],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -5, 2, -8],\n [-3, -3, -1, -5],\n [-3, -3, -10, -2],\n [9, 11, -11, 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"
}
] | 960 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, -12, -4],\n [-12, -5, -1, 4],\n [2, -2, -8, 9],\n [-10, -3, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 2, -10, 4],\n [-7, -7, -2, 1],\n [12, -3, -10, 9],\n [-7, 12, 8, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, 8, 3],\n [0, -11, -1, 9],\n [0, 0, 8, 4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 4, 2, -8],\n [4, 7, 0, 2],\n [2, 0, -4, -1],\n [-8, 2, -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"
}
] | 660 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -4, 2, 6],\n [0, 12, -11, 2],\n [0, 0, 6, 9],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 0, -2, 6],\n [0, 8, 8, -3],\n [-2, 8, -10, -2],\n [6, -3, -2, -3]]\nRound to the nearest integer, then take the result 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[[-11, 8, 7, -4],\n [8, 10, -2, 6],\n [7, -2, 5, -2],\n [-4, 6, -2, -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"
}
] | 244 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 7, -1, -12],\n [0, -5, 5, 3],\n [0, 0, 1, -2],\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"
}
] | 60 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 12, 11, 4],\n [0, 8, 3, -7],\n [0, 0, -1, 7],\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"
}
] | 784 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 0, 11, 4],\n [11, 7, -5, -5],\n [2, -12, -6, -1],\n [8, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 573 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -11, 1, 1],\n [0, -10, -10, 3],\n [0, 0, 12, -6],\n [0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -9, -9, 8],\n [-1, -10, 6, 2],\n [2, -1, -3, 6],\n [-6, 12, -7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 748 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 0, -12, -2],\n [0, -5, 11, -1],\n [-12, 11, -10, -2],\n [-2, -1, -2, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 672 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 6, 0, -6],\n [6, 10, -4, 6],\n [0, -4, -4, 7],\n [-6, 6, 7, -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"
}
] | 908 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, -4, 5],\n [0, 4, -9, 10],\n [0, 0, 10, -10],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -9, -1, -6],\n [0, -9, 11, 1],\n [0, 0, -12, 7],\n [0, 0, 0, -4]]\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[[6, 7, -6, 4],\n [0, 4, -12, -4],\n [0, 0, -1, 2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 976 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 10, 2, -7],\n [0, -9, -10, 8],\n [0, 0, 1, -8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, -1, -10],\n [-8, 3, 0, -1],\n [-1, 0, -3, 0],\n [-10, -1, 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"
}
] | 654 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, -6, 9],\n [0, -10, -4, -5],\n [0, 0, 10, 7],\n [0, 0, 0, 1]]\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[[8, 8, 0, -2],\n [0, -12, 4, 6],\n [0, 0, 1, 9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 864 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 0, -8, 3],\n [0, -8, 2, 4],\n [-8, 2, -6, -9],\n [3, 4, -9, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 620 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -6, -4, -4],\n [0, -2, -5, -1],\n [0, 0, -8, -12],\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"
}
] | 768 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, 0, -6],\n [2, 8, 0, 0],\n [0, 0, -5, 4],\n [-6, 0, 4, 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"
}
] | 24 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -8, 0, 11],\n [-8, -10, -2, -3],\n [0, -2, 0, 6],\n [11, -3, 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"
}
] | 792 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 6, 7, -8],\n [0, 1, 9, -11],\n [0, 0, 9, -12],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 3, -4, 0],\n [3, 3, -4, 2],\n [-4, -4, -9, -1],\n [0, 2, -1, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 530 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, 4, 8],\n [-2, 0, 0, 5],\n [4, 0, -4, 2],\n [8, 5, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -6, 2, -4],\n [-6, -4, -6, 0],\n [2, -6, 12, -4],\n [-4, 0, -4, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 636 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 3, -5, -9],\n [12, -7, -7, -12],\n [3, -7, 7, 8],\n [4, -11, -12, -6]]\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": "Compute |A| for the matrix A =\n[[-12, 2, -4, -1],\n [2, -4, 8, 4],\n [-4, 8, -7, 0],\n [-1, 4, 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"
}
] | 972 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, -10, 1],\n [0, -2, 10, -12],\n [0, 0, -4, 1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 0, 9, 4],\n [0, -10, -4, 3],\n [0, 0, 4, 11],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 0, 2, 10],\n [0, -11, -6, 2],\n [2, -6, 1, -1],\n [10, 2, -1, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 544 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, 4, 7],\n [0, 4, -9, -3],\n [0, 0, -7, 0],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -9, 0, -6],\n [0, 8, -1, 12],\n [0, 0, 5, -8],\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"
}
] | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 5, 0, 4],\n [5, -4, -5, -8],\n [0, -5, 5, -4],\n [4, -8, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 941 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -6, -4, -2],\n [-6, 8, 0, -1],\n [-4, 0, 3, -8],\n [-2, -1, -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"
}
] | 909 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, 5, 5, 2],\n [0, 4, 10, 6],\n [0, 0, -2, -11],\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"
}
] | 192 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 11, -11, -4],\n [-12, 0, 5, -11],\n [-1, 7, 3, 8],\n [-2, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -1, 0, -2],\n [-1, -10, 4, 1],\n [0, 4, -10, -8],\n [-2, 1, -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"
}
] | 232 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -5, 0, 6],\n [0, -1, -2, 4],\n [0, 0, -6, 12],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 12, 12, -6],\n [0, -6, -12, -3],\n [0, 0, -10, -12],\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"
}
] | 600 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 11, 9, 1],\n [0, 12, -9, -11],\n [0, 0, -2, 7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -5, 0, 6],\n [-5, 6, 12, -6],\n [0, 12, 11, -9],\n [6, -6, -9, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 734 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -7, 8, -12],\n [11, 3, -12, 10],\n [-3, -9, -10, -2],\n [-5, -11, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 998 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -8, -6, -8],\n [-8, 6, 4, -2],\n [-6, 4, -8, -10],\n [-8, -2, -10, 10]]\nRound to the nearest integer, then take the result modulo 1000.\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[[-4, -6, 4, 6],\n [-6, 6, 8, -8],\n [4, 8, 4, 6],\n [6, -8, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 408 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 3, -4, 7],\n [11, -3, 6, 12],\n [11, 12, 9, -6],\n [-4, 2, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -6, -10, 4],\n [4, -10, -9, -7],\n [2, 9, -10, -1],\n [2, -9, 9, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 274 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -3, -4, -2],\n [0, 5, 7, 2],\n [0, 0, 11, 6],\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"
}
] | 495 | MATH |
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