messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -2, -2],\n [-2, -6, 4],\n [-2, 4, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 0, -8],\n [0, 4, 1],\n [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": "What is the determinant of the matrix:\n[[-2, -6, 3],\n [0, 10, -10],\n [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"
}
] | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -8, 4],\n [-8, 2, 0],\n [4, 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"
}
] | 672 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, 1],\n [0, 8, -10],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -6, 10],\n [0, -1, 8],\n [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"
}
] | 2 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, 2],\n [-2, 0, -4],\n [7, 6, -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"
}
] | 788 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 6, 2],\n [6, 0, 3],\n [2, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 748 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 2, 2],\n [1, -10, 0],\n [-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"
}
] | 782 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -4, 3],\n [0, -3, 7],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 2],\n [0, -3, 6],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 895 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 8, 4],\n [8, 1, 6],\n [4, 6, -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"
}
] | 626 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 8, 2],\n [8, -1, 6],\n [2, 6, -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"
}
] | 547 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -5, -2],\n [0, -10, -6],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 700 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -2, 4],\n [-2, 1, 10],\n [4, 10, 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"
}
] | 944 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -1, -2],\n [-5, 0, -8],\n [-2, -10, -4]]? 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": "Determine the value of det(A) where A =\n[[1, -10, 0],\n [-10, -4, 3],\n [0, 3, 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"
}
] | 263 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -3, 3],\n [0, 8, -7],\n [0, 0, 8]]\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, 8, 0],\n [0, -6, 7],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -6, -4],\n [0, 10, 4],\n [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"
}
] | 630 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, 0],\n [-2, 0, 1],\n [0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -2, -4],\n [6, 1, 4],\n [-8, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 924 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 3, 7],\n [0, 4, 6],\n [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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -4],\n [2, 8, -7],\n [-4, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 558 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -1, -4],\n [1, 5, -7],\n [2, 1, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 889 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -6, 2],\n [-6, 4, -6],\n [2, -6, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 900 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 1, -9],\n [0, -4, -5],\n [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"
}
] | 64 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -2, -9],\n [9, 8, -8],\n [7, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 341 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 0, 6],\n [0, -3, 8],\n [6, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 681 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 10, 9],\n [0, 1, -9],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -7, 3],\n [0, 5, 5],\n [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"
}
] | 210 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 1, -10],\n [6, 10, -7],\n [-5, -10, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 897 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -4, 1],\n [-7, 0, -10],\n [-4, -8, -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"
}
] | 244 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 0, -4],\n [0, 1, -2],\n [-4, -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"
}
] | 990 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -6, -6],\n [7, -8, -7],\n [2, -7, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 691 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 6, -2],\n [6, -8, 0],\n [-2, 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"
}
] | 272 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -1, -5],\n [-3, -1, 6],\n [-7, 7, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 762 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -5, -4],\n [-9, 1, 3],\n [-3, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 665 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, -3],\n [0, 7, -10],\n [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"
}
] | 965 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, -3],\n [5, -9, -10],\n [-7, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 888 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -4, 1],\n [7, 5, -8],\n [-1, 10, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 875 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -7, -9],\n [7, 4, 5],\n [-10, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 395 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 4, 0],\n [4, 8, 4],\n [0, 4, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -7, 0],\n [2, 10, -10],\n [-8, 3, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 926 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -4, -4],\n [-4, 4, 2],\n [-4, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -5, -10],\n [-1, 1, 4],\n [-7, -6, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, 2],\n [0, 5, 7],\n [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"
}
] | 820 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 7, -8],\n [0, 1, 6],\n [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"
}
] | 937 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 0, -2],\n [0, -7, -2],\n [-2, -2, -1]]? 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[[-9, 8, 1],\n [0, -5, -3],\n [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"
}
] | 450 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 6, -10],\n [6, -4, -8],\n [-10, -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"
}
] | 104 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 9, 8],\n [0, 1, 10],\n [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"
}
] | 990 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -10, 5],\n [0, -4, -1],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 252 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -3, 1],\n [2, -3, 10],\n [5, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 176 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 9, -4],\n [-3, -10, 4],\n [-1, 1, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 203 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 4, -8],\n [-7, -2, -8],\n [-6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 636 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, 5],\n [0, 10, 6],\n [5, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 158 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, 6],\n [-9, -7, 7],\n [2, 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"
}
] | 485 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -1, -8],\n [-7, -3, -9],\n [-7, -8, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 538 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 7, -5],\n [-3, 10, -1],\n [-1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 534 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, 8],\n [-4, -3, -8],\n [8, -8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 6, -2],\n [6, -2, 2],\n [-2, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 0, -2],\n [0, 6, -10],\n [0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 838 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -7, 2],\n [-1, 6, 10],\n [5, -3, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -2, -1],\n [-2, 4, -10],\n [-1, -10, -1]]? Round to the nearest integer, then express your answer 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[[7, 2, 4],\n [2, -5, -6],\n [4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 771 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 1, 5],\n [1, 1, 4],\n [5, 4, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 1, 6],\n [0, 0, 10],\n [1, -10, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -9, 7],\n [10, 10, -2],\n [-9, -3, -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[[9, 7, -3],\n [0, -6, -6],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 486 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 9, 9],\n [0, 4, 9],\n [-7, -4, 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"
}
] | 721 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 6, 8],\n [-1, -1, 2],\n [0, 9, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 884 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, 1],\n [-1, -7, 4],\n [-1, 7, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 628 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 2, -9],\n [-1, 2, -1],\n [3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -4, 0],\n [-4, -6, 2],\n [0, 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"
}
] | 944 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 7, -4],\n [0, 10, -6],\n [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"
}
] | 540 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -2, -6],\n [-2, -6, -9],\n [-6, -9, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 674 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, 9],\n [0, 5, 9],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 965 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -7, -7],\n [0, 3, -5],\n [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"
}
] | 865 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 6, -2],\n [6, 5, 4],\n [-2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 780 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 0, 10],\n [0, -8, 5],\n [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"
}
] | 808 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -7, 7],\n [0, 5, -9],\n [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"
}
] | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 3, -4],\n [10, 10, 6],\n [3, 9, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 590 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -6, 6],\n [-6, -2, 4],\n [6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -4, 4],\n [-4, -7, 2],\n [4, 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"
}
] | 935 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 5, -2],\n [0, 4, -6],\n [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"
}
] | 40 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 2, -4],\n [0, 8, -1],\n [0, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 6, -5],\n [6, 3, 7],\n [-4, 9, 5]]\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": "Compute |A| for the matrix A =\n[[2, 3, 2],\n [0, 8, -9],\n [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"
}
] | 840 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -4, -5],\n [-4, -5, -1],\n [-5, -1, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 857 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -3, -7],\n [0, 5, 3],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 1, 7],\n [0, -2, 1],\n [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"
}
] | 928 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 10, -2],\n [8, 8, -7],\n [-7, 8, 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"
}
] | 450 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -8, -8],\n [0, 10, -4],\n [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": "What is the determinant of the matrix:\n[[-7, 4, -8],\n [0, 8, -9],\n [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"
}
] | 280 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 8, 8],\n [-10, 8, -4],\n [-6, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 736 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -10, 2],\n [0, 2, 7],\n [0, 0, 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"
}
] | 14 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 7, -8],\n [0, 7, -8],\n [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"
}
] | 210 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 9, 10],\n [0, 3, -3],\n [0, 0, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 1, 4],\n [5, -5, -7],\n [0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 704 | MATH |
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