messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -5, -3, 5],\n [0, -10, 0, 12],\n [0, 0, 2, 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"
}
] | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, 7, 4],\n [0, -1, 0, 2],\n [0, 0, -11, -5],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, -7, -8],\n [0, -6, 1, 0],\n [-7, 1, -12, 7],\n [-8, 0, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 728 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -7, -2, 5],\n [-7, -1, 2, -2],\n [-2, 2, -2, 8],\n [5, -2, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 712 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 7, -11, -6],\n [12, 9, -4, 9],\n [11, 5, -7, 1],\n [-9, -3, -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"
}
] | 210 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 8, 2, -2],\n [8, 5, -2, -8],\n [2, -2, -3, -11],\n [-2, -8, -11, -9]]? 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": "What is the determinant of the matrix:\n[[4, 6, 1, 3],\n [0, -5, 11, -7],\n [0, 0, 12, 6],\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"
}
] | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 12, -8, 3],\n [0, -6, -11, -8],\n [0, 0, 7, -10],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 766 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, -4, 0],\n [0, -5, -1, -2],\n [-4, -1, 1, -7],\n [0, -2, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 674 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, 4, 9],\n [11, 10, 6, 10],\n [4, -2, -6, -3],\n [0, 0, -10, 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"
}
] | 116 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, 11, -9],\n [0, 7, -6, -6],\n [0, 0, 12, 0],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -1, -7, -1],\n [-1, 9, 0, 2],\n [-7, 0, 11, -6],\n [-1, 2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 446 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 9, -7, -6],\n [0, 1, -6, 5],\n [0, 0, 3, 11],\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"
}
] | 180 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 1, 5, 0],\n [2, 12, -5, 1],\n [-12, 12, 12, 11],\n [-4, 0, -12, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 524 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -2, 0, -6],\n [-2, 9, 8, 10],\n [0, 8, -12, -1],\n [-6, 10, -1, 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"
}
] | 307 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, 0, -10],\n [4, 4, 0, -4],\n [0, 0, -3, 2],\n [-10, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, 2, -4],\n [-2, -5, 4, 6],\n [2, 4, 6, 10],\n [-4, 6, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 116 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 4, 0, 5],\n [4, 3, 0, -6],\n [0, 0, 9, 2],\n [5, -6, 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"
}
] | 397 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 9, 4, 3],\n [-8, 4, 7, 9],\n [-12, -8, 0, -6],\n [-5, 6, -4, 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"
}
] | 906 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -4, 4, 0],\n [-4, -4, 6, -5],\n [4, 6, 5, 6],\n [0, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 428 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -10, 0, 8],\n [0, 11, 7, -2],\n [0, 0, 11, 1],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 641 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 1, 8, 7],\n [1, 9, 2, 10],\n [8, 2, -3, 2],\n [7, 10, 2, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 2, 0, -6],\n [2, 8, -8, -2],\n [0, -8, 11, 2],\n [-6, -2, 2, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 940 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -10, -10, 6],\n [7, 0, 2, -9],\n [11, -7, -6, 7],\n [7, 7, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 382 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 6, -12, -5],\n [0, -8, -5, 5],\n [0, 0, 1, -3],\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"
}
] | 120 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 9, 0, -12],\n [0, 12, -9, 10],\n [0, 0, -2, 12],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 704 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, -4, 5],\n [0, 8, 8, -7],\n [-4, 8, 8, 5],\n [5, -7, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 448 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 6, 4, 4],\n [6, 3, 7, -3],\n [4, 7, -8, -2],\n [4, -3, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -10, 3, -11],\n [0, 5, -7, 10],\n [0, 0, 3, 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"
}
] | 450 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -3, 1, 3],\n [0, 7, 11, 9],\n [0, 0, -8, -3],\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"
}
] | 344 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 10, -1, -9],\n [8, -11, -12, -1],\n [-4, -4, -10, 10],\n [-7, -10, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 788 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -2, -4, 0],\n [-2, -3, -2, 2],\n [-4, -2, -7, 8],\n [0, 2, 8, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 372 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 11, 6, -11],\n [0, -3, 5, 1],\n [0, 0, 5, 6],\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"
}
] | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -3, 2, 1],\n [0, 8, 0, -5],\n [0, 0, -1, -9],\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"
}
] | 280 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 0, -6, -4],\n [0, -12, -2, -2],\n [-6, -2, -5, -6],\n [-4, -2, -6, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 724 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -12, -9, -2],\n [0, -11, -5, 6],\n [0, 0, -8, 2],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 808 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, 3, -2],\n [-4, -4, 0, 6],\n [3, 0, -7, -2],\n [-2, 6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 776 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -12, 6, 9],\n [0, -11, 9, -1],\n [0, 0, 7, 4],\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"
}
] | 460 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 3, -10, 4],\n [0, 4, -6, 12],\n [0, 0, 10, -1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -5, -7, -1],\n [0, -11, -1, -3],\n [0, 0, -11, 10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 936 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 10, 10, -8],\n [0, 12, 9, 8],\n [9, -5, 6, 5],\n [11, -6, -7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 321 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 3, 7, 8],\n [-12, 4, 10, -3],\n [2, -12, -1, -4],\n [-8, 3, -9, 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"
}
] | 764 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -3, 11, -8],\n [5, -5, 10, -10],\n [3, -7, -7, -6],\n [9, 11, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -7, 1, 7],\n [0, -5, 1, -6],\n [0, 0, 7, 9],\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"
}
] | 845 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 10, -9, 6],\n [0, 2, -3, -11],\n [0, 0, -5, -4],\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"
}
] | 330 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 8, -10, -1],\n [8, -5, 4, 0],\n [-10, 4, -10, 0],\n [-1, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, -1, 7],\n [0, -6, 4, 10],\n [0, 0, 9, 5],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -3, 3, -1],\n [-11, -6, -4, 3],\n [-7, -9, 4, 7],\n [12, 4, 4, -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"
}
] | 55 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -4, -2, -8],\n [-4, 4, 4, 6],\n [-2, 4, -8, -10],\n [-8, 6, -10, -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"
}
] | 552 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -1, -1, 0],\n [12, 1, -9, 12],\n [0, 12, 10, 6],\n [3, -10, -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"
}
] | 556 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -8, -8, -6],\n [-8, 4, 2, 4],\n [-8, 2, 5, 3],\n [-6, 4, 3, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 984 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 2, 0, 3],\n [-10, 5, -5, 7],\n [1, -8, 0, -3],\n [5, -1, -2, -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": "Determine the value of det(A) where A =\n[[-2, -2, 0, 8],\n [5, -2, 7, 1],\n [12, 7, -7, 0],\n [-10, -11, -5, -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"
}
] | 164 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, 12, 6],\n [0, 3, 10, -1],\n [0, 0, 3, -1],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 514 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 11, 10, 0],\n [5, -3, 7, 7],\n [1, -6, 6, -6],\n [-10, 3, 5, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 630 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 6, -11, 6],\n [0, -1, 6, 9],\n [0, 0, 3, 4],\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"
}
] | 937 | 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, 4, 12, -9],\n [0, 0, -5, 9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 8, -2, -9],\n [0, -1, 5, 12],\n [0, 0, -12, -12],\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"
}
] | 756 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -6, 6, 4],\n [-6, 7, -3, 8],\n [6, -3, 1, -1],\n [4, 8, -1, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 220 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -3, -1, 1],\n [-1, -11, -1, 3],\n [-3, 7, 4, 11],\n [7, -2, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -5, -7, -10],\n [-5, -12, 10, 1],\n [-7, 10, 11, 1],\n [-10, 1, 1, 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"
}
] | 843 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 7, -12, 5],\n [8, -4, -4, 6],\n [-3, 0, 9, 5],\n [-5, 3, 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"
}
] | 624 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -1, -10, 9],\n [-3, 3, -3, -1],\n [9, -1, -8, 2],\n [3, 12, -12, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 995 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 4, -8, 5],\n [4, 4, 6, -2],\n [-8, 6, -12, 4],\n [5, -2, 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"
}
] | 476 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -10, -8, 7],\n [-6, 1, 6, -9],\n [-6, 9, 6, -4],\n [-12, 12, -10, 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"
}
] | 100 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, 10, -7],\n [0, 5, 11, -9],\n [0, 0, -10, 2],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, 12, -6],\n [6, -6, 9, 6],\n [10, 7, -10, -3],\n [-3, -6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -8, 0, 0],\n [-8, 11, 0, -2],\n [0, 0, 9, -8],\n [0, -2, -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"
}
] | 561 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 4, 0, 1],\n [4, 10, 3, -5],\n [0, 3, -8, -5],\n [1, -5, -5, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 167 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 6, 7, -4],\n [0, 1, 6, 3],\n [0, 0, -7, 2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 461 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -6, -4, -4],\n [-6, -6, 4, -10],\n [-4, 4, -3, 0],\n [-4, -10, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 1, 12, 4],\n [0, 5, 4, -3],\n [2, -5, 4, 3],\n [-11, 8, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 664 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -12, 9, 8],\n [5, -3, -9, -5],\n [-5, 6, 6, -6],\n [-11, 1, -7, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 153 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -5, 12, 12],\n [0, -2, -12, 8],\n [0, 0, 4, -10],\n [0, 0, 0, 5]]\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, 6, 4],\n [-2, 9, -1, 0],\n [6, -1, -6, 2],\n [4, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 738 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -1, 7, -11],\n [0, -4, 5, 6],\n [0, 0, -2, 2],\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"
}
] | 240 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 10, -4, 6],\n [0, -7, -4, -8],\n [0, 0, 9, 0],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 504 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 11, 10, 3],\n [3, -9, -7, 10],\n [-3, 1, 11, 2],\n [-4, 3, 12, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 10, 12, 12],\n [0, -6, 9, -12],\n [0, 0, 6, -2],\n [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"
}
] | 8 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -2, -10, -10],\n [-2, -3, 11, 7],\n [-10, 11, 11, -6],\n [-10, 7, -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"
}
] | 147 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -4, 10, 0],\n [-4, -10, 2, 8],\n [10, 2, -6, -2],\n [0, 8, -2, -12]]\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[[9, -3, -1, 0],\n [-3, -7, -8, -6],\n [-1, -8, -9, 2],\n [0, -6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 854 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -4, -9, 3],\n [0, -4, 4, -6],\n [0, 0, 5, 9],\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"
}
] | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 4, 6, -2],\n [6, -10, -6, 4],\n [6, 0, 6, -9],\n [-6, 0, -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"
}
] | 816 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 9, -9, -3],\n [0, -9, -10, 11],\n [0, 0, -1, -7],\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"
}
] | 514 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 1, -2, 0],\n [1, -7, -2, 2],\n [-2, -2, -10, -1],\n [0, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 12, -4, -2],\n [12, -3, 2, -4],\n [-4, 2, 12, 4],\n [-2, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -3, -4, -4],\n [-3, 3, -3, 4],\n [-4, -3, 12, 0],\n [-4, 4, 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"
}
] | 755 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -9, -2, 2],\n [-9, -3, 4, -6],\n [-2, 4, 4, 6],\n [2, -6, 6, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 852 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -3, -12, 4],\n [-8, -11, 4, 8],\n [3, -4, 3, 11],\n [2, -8, -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"
}
] | 766 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 8, -8, -8],\n [8, -12, 4, 3],\n [-8, 4, -1, -9],\n [-8, 3, -9, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 941 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -11, 12, -12],\n [0, 6, 12, 8],\n [0, 0, 3, -10],\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"
}
] | 756 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, -6, 4],\n [2, -9, -8, 0],\n [-6, -8, -3, 6],\n [4, 0, 6, -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"
}
] | 898 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -9, 4, 10],\n [0, 3, 0, -7],\n [0, 0, -6, -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"
}
] | 584 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -9, 6, 11],\n [0, -2, -4, -1],\n [0, 0, 7, -11],\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"
}
] | 328 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 7, 10, 10],\n [0, -1, -10, -4],\n [0, 0, -4, 6],\n [0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 604 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -2, 4, -3],\n [-2, 12, -4, -2],\n [4, -4, 10, 5],\n [-3, -2, 5, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 1, 1, 5],\n [1, 10, -3, 5],\n [1, -3, 10, -9],\n [5, 5, -9, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -5, 3, -8],\n [-3, 8, 2, 3],\n [3, -6, -3, 4],\n [0, 3, 2, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 6, -2, -6],\n [6, 2, 9, 8],\n [-2, 9, 2, 0],\n [-6, 8, 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"
}
] | 260 | MATH |
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