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[[-3, 0, -2, -7],\n [0, -5, 8, 9],\n [0, 0, 2, 0],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 850 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 8, 6, -4],\n [8, 12, 12, -11],\n [4, 0, 1, -6],\n [-4, -9, 9, 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"
}
] | 817 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 4, -7, -7],\n [-12, 8, 1, 6],\n [-2, -8, -6, -10],\n [-2, -5, -3, 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": "What is the determinant of the matrix:\n[[-10, 0, 5, 11],\n [5, 7, 7, -11],\n [-12, 2, 12, -9],\n [9, 7, -12, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -3, -6, 5],\n [-7, 6, -10, 3],\n [11, -10, -7, 9],\n [-8, 9, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -12, -4, -4],\n [0, -8, -7, -12],\n [0, 0, 10, -10],\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"
}
] | 160 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 3, -4, 0],\n [0, -8, 5, -5],\n [0, 0, 6, 5],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -9, 4, 5],\n [6, -12, 2, -4],\n [3, 7, 10, 7],\n [-6, -12, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -4, -5, -8],\n [-4, 1, 2, -1],\n [-5, 2, -4, -1],\n [-8, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 768 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -12, 12, -8],\n [0, -1, -4, -6],\n [0, 0, 2, -6],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 0, 4, -1],\n [0, 12, 1, -2],\n [4, 1, -7, -8],\n [-1, -2, -8, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 0, 9, -6],\n [0, -4, -2, -11],\n [0, 0, -3, -3],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 5, -8, 2],\n [5, -4, 6, -4],\n [-8, 6, 10, 3],\n [2, -4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 729 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -6, 1, -3],\n [-2, -10, 3, 1],\n [-2, -1, 2, 5],\n [8, -6, -11, 5]]\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": "Determine the value of det(A) where A =\n[[-11, -11, -7, -4],\n [-7, 1, -12, -12],\n [1, -9, 2, 6],\n [-4, 7, 4, 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"
}
] | 578 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 6, -10, 8],\n [-4, -7, -4, 12],\n [-3, 12, -3, 6],\n [-1, 3, -6, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 468 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 2, 6],\n [0, -11, -2, 2],\n [2, -2, -6, -9],\n [6, 2, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 886 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 1, 5, 11],\n [0, 8, 4, -9],\n [0, 0, -4, 12],\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"
}
] | 240 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -7, -1, -9],\n [-7, -1, -12, -7],\n [-1, -12, 12, 6],\n [-9, -7, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -9, -4, 7],\n [0, 5, -8, -7],\n [0, 0, -1, 3],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 0, -4],\n [0, 10, 9, 1],\n [0, 0, 12, 4],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -12, -5, -3],\n [0, 8, -9, 8],\n [0, 0, 12, 4],\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"
}
] | 608 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -7, 8, -6],\n [-11, -6, 7, -5],\n [-5, -12, -5, -7],\n [6, 0, 8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -4, 5, 5],\n [-4, 7, -2, -4],\n [5, -2, -6, 5],\n [5, -4, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 3, -8, -1],\n [-2, -10, 0, -4],\n [-12, 11, 2, 11],\n [-6, -6, 1, -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"
}
] | 90 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 7, 2, -4],\n [8, 10, -1, 12],\n [10, 1, 4, -10],\n [0, 3, 7, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -1, -6, -10],\n [0, 11, -9, 10],\n [0, 0, -5, 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"
}
] | 990 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 3, 4, -8],\n [3, -12, -2, -8],\n [4, -2, -10, 8],\n [-8, -8, 8, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 2, -2, 2],\n [2, 11, 4, 6],\n [-2, 4, -9, 2],\n [2, 6, 2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 186 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 11, 6, 6],\n [0, 1, 1, -3],\n [0, 0, 4, -8],\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"
}
] | 96 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 11, -7, -5],\n [1, -11, -11, 8],\n [7, 5, 11, -7],\n [-1, 2, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 410 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -1, -7, -9],\n [-10, 8, -4, -6],\n [-8, 0, -6, -1],\n [-1, 5, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 576 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, -5, 6],\n [-5, -6, 10, -7],\n [7, 7, 0, 5],\n [-8, 6, 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"
}
] | 134 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, 1, -12],\n [0, -10, 3, -12],\n [0, 0, -11, -9],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 520 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, 8, -4],\n [-5, -3, -7, -9],\n [8, -7, -2, -1],\n [-4, -9, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -4, 0, 5],\n [0, -6, -4, 0],\n [0, 0, 9, 0],\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"
}
] | 944 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 10, 6, -8],\n [11, -11, -4, -7],\n [1, 7, 5, -10],\n [8, 0, 3, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 392 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -12, -10, -1],\n [2, -4, -4, -2],\n [-1, 5, -1, 12],\n [-3, -5, 9, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 2, -4, -4],\n [2, -8, 0, -3],\n [-4, 0, 3, -1],\n [-4, -3, -1, 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"
}
] | 995 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -12, 9, -11],\n [0, -6, -8, 12],\n [0, 0, -2, 12],\n [0, 0, 0, -12]]\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, 1, 8, 1],\n [-4, 2, -12, 4],\n [6, -7, -5, 6],\n [-3, -12, -5, -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"
}
] | 516 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, -4, 11],\n [0, 5, 7, -12],\n [0, 0, 4, 3],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 3, -8, -9],\n [0, -9, -9, -5],\n [0, 0, 3, -3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, 2, 0],\n [6, -10, 1, -2],\n [2, 1, -7, -2],\n [0, -2, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -1, 0, -2],\n [-1, 1, 5, -6],\n [0, 5, 2, 0],\n [-2, -6, 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"
}
] | 588 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -2, 10, -11],\n [-2, 3, 10, -8],\n [10, 10, -3, 2],\n [-11, -8, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 301 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, 9, -9],\n [0, 5, 2, 4],\n [0, 0, 8, -2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -2, 0, 0],\n [-2, -8, 6, 2],\n [0, 6, 8, -3],\n [0, 2, -3, 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"
}
] | 116 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, -5, 5],\n [0, 5, 6, 0],\n [0, 0, -1, 8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 330 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -5, 5, -2],\n [-5, 0, 1, 8],\n [5, 1, 8, -9],\n [-2, 8, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 485 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -1, -2, -6],\n [0, 11, -7, -12],\n [0, 0, -10, 10],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 900 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 2, -9, -2],\n [2, 10, 8, 2],\n [-9, 8, 1, 0],\n [-2, 2, 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"
}
] | 228 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -10, 2, -9],\n [-10, -3, 2, 8],\n [2, 2, -11, 8],\n [-9, 8, 8, 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"
}
] | 471 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -2, 3, -3],\n [0, 12, -9, 0],\n [0, 0, 5, -12],\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"
}
] | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 0, 0, 0],\n [0, 4, -4, 0],\n [0, -4, -9, 0],\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"
}
] | 816 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 0, -5, -2],\n [0, -1, 0, 3],\n [-5, 0, 7, 4],\n [-2, 3, 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"
}
] | 873 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -12, 3, -1],\n [0, -10, -9, 10],\n [0, 0, -6, 1],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 0, 4, 9],\n [0, 11, -3, -4],\n [0, 0, -12, 4],\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"
}
] | 112 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 7, -8, -8],\n [7, -6, 1, -8],\n [-8, 1, 0, -2],\n [-8, -8, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 616 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 5, 0, -6],\n [6, 4, -4, -9],\n [0, -3, -9, 12],\n [-1, -6, 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"
}
] | 512 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 7, -1, -8],\n [0, 10, 9, 0],\n [0, 0, 2, -6],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -1, -11, -2],\n [0, 4, 6, 11],\n [0, 0, -10, -2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 4, -2, -4],\n [4, -2, 5, -4],\n [-2, 5, 8, -5],\n [-4, -4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 322 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, 10, 4],\n [0, -3, -4, -3],\n [0, 0, 6, -10],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 11, 5, -7],\n [12, 12, -11, -5],\n [-1, 2, 12, 0],\n [10, -5, 3, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 251 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 6, 7, -7],\n [0, 1, 9, -12],\n [0, 0, -7, -9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -2, 2],\n [0, -2, -2, -3],\n [-2, -2, 9, 0],\n [2, -3, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 481 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 9, -6, -2],\n [9, -8, 3, -7],\n [-6, 3, 9, 10],\n [-2, -7, 10, 7]]? Round to the nearest integer, then express your answer 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[[9, -2, -1, -5],\n [-2, -2, -4, 0],\n [-1, -4, 12, 4],\n [-5, 0, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 950 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 4, -10],\n [-2, -12, 2, 5],\n [4, 2, -1, 1],\n [-10, 5, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 868 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 0, 3, -6],\n [0, -4, -8, 12],\n [0, 0, -11, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 7, 2, 0],\n [7, 9, 2, -4],\n [2, 2, -3, 5],\n [0, -4, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 8, 4, 7],\n [8, -11, 2, -10],\n [4, 2, 6, 4],\n [7, -10, 4, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 772 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, -12, -5],\n [0, -6, 8, -5],\n [0, 0, 7, -12],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 8, -3, -10],\n [-9, -5, 9, -6],\n [8, -12, -8, 6],\n [-9, 0, 11, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 206 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 4, 2, -6],\n [4, -10, 2, 2],\n [2, 2, 5, -6],\n [-6, 2, -6, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 736 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, 7, -9],\n [0, 4, 12, 11],\n [0, 0, -8, -12],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 1, 0, 0],\n [1, 6, 2, 6],\n [0, 2, -11, 2],\n [0, 6, 2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 956 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -10, 0, 0],\n [-10, 11, -2, 2],\n [0, -2, -12, 1],\n [0, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 565 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 1, -1, -12],\n [0, 9, 2, 5],\n [0, 0, 8, 12],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 504 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -5, -4, -7],\n [0, 4, 11, -5],\n [0, 0, 8, 6],\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"
}
] | 408 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 4, 10, 9],\n [8, -10, 4, 1],\n [2, -4, -11, 11],\n [9, -4, 7, 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"
}
] | 958 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 0, -6, 8],\n [0, -8, 0, -2],\n [-6, 0, -1, 2],\n [8, -2, 2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -7, -8, 11],\n [12, 11, -3, -7],\n [8, 1, 8, 4],\n [-11, -2, -5, 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"
}
] | 187 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -2, 11, 5],\n [0, -10, 8, 5],\n [0, 0, -6, 10],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 500 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -7, 11, -2],\n [0, 12, -3, -11],\n [0, 0, -4, 10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 560 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 1, 4, -3],\n [1, 9, 2, -4],\n [4, 2, -12, 0],\n [-3, -4, 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"
}
] | 456 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, -4, 4],\n [0, 0, -1, 7],\n [-4, -1, -8, 2],\n [4, 7, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 236 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -4, 5, 2],\n [-4, -9, -2, 2],\n [5, -2, -6, 1],\n [2, 2, 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"
}
] | 25 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -11, -8, -2],\n [2, 11, 5, -3],\n [3, 7, 8, 4],\n [8, 12, -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"
}
] | 560 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -7, -5, 2],\n [-4, -11, 1, 8],\n [9, -4, -6, 11],\n [10, 10, 6, 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"
}
] | 942 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 4, 6, 2],\n [4, -11, 6, -2],\n [6, 6, 2, -10],\n [2, -2, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 1, -7, 0],\n [1, -5, 0, 8],\n [-7, 0, -7, -5],\n [0, 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"
}
] | 781 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -10, -12, 0],\n [0, 5, -8, 10],\n [0, 0, 3, -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"
}
] | 90 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, -2, 1],\n [4, 6, -2, -6],\n [-2, -2, 1, -12],\n [1, -6, -12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 802 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 11, -2, 4],\n [0, 9, -3, -5],\n [0, 0, -7, 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"
}
] | 795 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 8, 7, -2],\n [-3, -4, 5, 6],\n [-11, 4, -1, -8],\n [5, 1, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 582 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 6, 5, 0],\n [6, -12, -2, -5],\n [5, -2, 0, 1],\n [0, -5, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 681 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -2, 12, 3],\n [-9, -2, -1, 1],\n [-5, 4, -1, 9],\n [6, -8, -6, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 2, -2, 2],\n [2, -12, 3, 6],\n [-2, 3, -8, 4],\n [2, 6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
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