messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 4, -6],\n [4, 9, 0],\n [-6, 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"
}
] | 911 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 1, 9],\n [8, -3, 10],\n [3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -3, -6],\n [-3, 2, 4],\n [-6, 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"
}
] | 119 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 9, -6],\n [0, 9, 7],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 5, 1],\n [5, -10, 0],\n [1, 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"
}
] | 850 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 6, 3],\n [6, 2, 0],\n [3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 886 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 4, -5],\n [-9, 4, -5],\n [-9, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 697 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 4, 6],\n [4, 3, 8],\n [6, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 321 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -7, 6],\n [0, -1, 6],\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"
}
] | 4 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -7, 4],\n [-10, 6, 6],\n [-10, 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"
}
] | 70 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -3, 1],\n [-8, 0, -9],\n [-10, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -1, -2],\n [2, -4, -4],\n [4, 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"
}
] | 974 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 3, 2],\n [0, 10, -9],\n [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"
}
] | 480 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 8, 4],\n [0, -4, -8],\n [0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -4, 6],\n [-4, 2, -8],\n [6, -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"
}
] | 80 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -9, 10],\n [0, 7, -3],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 706 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 0, -5],\n [-10, -9, 8],\n [-1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 3, -7],\n [-6, 2, -3],\n [9, 3, -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"
}
] | 139 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 2, -6],\n [2, 5, -5],\n [-6, -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"
}
] | 64 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, -10],\n [0, 4, -8],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 776 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, 4],\n [0, 6, -5],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, 4],\n [-10, -3, 1],\n [3, 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"
}
] | 911 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 5, 10],\n [9, -10, -5],\n [3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 235 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, 8],\n [-6, -4, -4],\n [8, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 784 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -1, 4],\n [-1, 9, 0],\n [4, 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"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -10, 10],\n [0, 1, 4],\n [0, 0, 5]]\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[[5, 2, 10],\n [0, 9, 3],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 730 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -9, 3],\n [0, -7, -7],\n [8, -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[[6, 4, 3],\n [-4, -4, 5],\n [6, -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"
}
] | 560 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 2, 2],\n [0, -3, -3],\n [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"
}
] | 144 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 4, -10],\n [0, 6, -1],\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"
}
] | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 5, -2],\n [5, 7, -1],\n [-2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 977 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -10, 9],\n [-1, 5, 2],\n [1, -8, -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"
}
] | 11 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -2, 4],\n [-2, -4, -1],\n [4, -1, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 5, -7],\n [0, -4, -4],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 808 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 6, -2],\n [0, -7, 3],\n [0, 0, 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"
}
] | 252 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 4, -7],\n [4, 2, -1],\n [-7, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 780 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -10, -6],\n [0, 2, 1],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 976 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -7, 8],\n [-8, -10, -8],\n [-8, -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"
}
] | 776 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, -8],\n [0, 6, -1],\n [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"
}
] | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 0, 2],\n [0, 3, -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"
}
] | 979 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -2, 6],\n [0, 7, 3],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 210 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 10, 0],\n [10, 1, -7],\n [0, -7, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 284 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 3, 3],\n [9, 4, 1],\n [7, 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"
}
] | 342 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, 10],\n [0, 5, 8],\n [0, 0, -8]]\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[[7, -8, -6],\n [0, -3, -6],\n [0, 0, 3]]\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, -3, -4],\n [-3, 6, 0],\n [-4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 6, 3],\n [3, 6, -1],\n [-1, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 860 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, -8],\n [1, 5, 10],\n [-4, -1, -2]]\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, 4, -2],\n [4, -6, 1],\n [-2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 924 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 1, -6],\n [1, -3, -2],\n [-6, -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"
}
] | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 10, 7],\n [0, -8, -9],\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"
}
] | 360 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 3, -4],\n [1, 7, -7],\n [-3, 4, 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"
}
] | 633 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -6, -9],\n [-6, -5, -4],\n [-9, -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"
}
] | 953 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 0, 1],\n [0, 10, -2],\n [1, -2, 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"
}
] | 2 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -9, 10],\n [0, -6, -9],\n [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"
}
] | 946 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, -9],\n [0, 4, 2],\n [0, 0, 3]]\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[[-1, 0, -6],\n [0, 4, 9],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 6, -8],\n [0, -8, -8],\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"
}
] | 288 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 6, -1],\n [0, 8, -8],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 872 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 4, -8],\n [-8, -9, 10],\n [-8, 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"
}
] | 165 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -6, 10],\n [-6, -2, -10],\n [5, 1, 5]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, 4],\n [-6, -3, 7],\n [4, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 892 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 1, 6],\n [0, -6, 5],\n [0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 808 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 2, -10],\n [0, -2, -6],\n [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"
}
] | 64 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -3, 2],\n [-3, 8, 6],\n [2, 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"
}
] | 682 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -8, 1],\n [-8, 1, 1],\n [1, 1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 143 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -5, 3],\n [0, -9, -9],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -2, -4],\n [-2, 2, 5],\n [-4, 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"
}
] | 133 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -4, -4],\n [-4, 7, 2],\n [-4, 2, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, 4],\n [6, -6, -4],\n [4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 968 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -6, -3],\n [0, 4, 4],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 0, -6],\n [0, 10, 4],\n [-6, 4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 780 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 1, -2],\n [1, -2, -7],\n [-2, -7, 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"
}
] | 223 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -8, 2],\n [-8, 4, -3],\n [2, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 565 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 5, -3],\n [0, -4, -8],\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"
}
] | 996 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -3, 7],\n [3, -1, 1],\n [9, 4, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 6, 4],\n [6, -5, 8],\n [4, 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"
}
] | 20 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 1, 1],\n [-9, 4, -10],\n [10, -9, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 881 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -3, -5],\n [1, -2, -6],\n [-6, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 879 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -6, -10],\n [0, 10, -3],\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"
}
] | 50 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -5, 0],\n [0, -1, 0],\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"
}
] | 970 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 0, 0],\n [0, 6, -2],\n [0, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -3, -2],\n [-9, -3, -9],\n [-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"
}
] | 952 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -1, 5],\n [0, -3, 7],\n [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"
}
] | 36 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 9, 9],\n [0, -5, 0],\n [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"
}
] | 930 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, -2],\n [0, -9, -6],\n [-2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 820 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 4, 0],\n [0, 4, -9],\n [0, 0, -6]]\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[[-6, 1, -6],\n [1, -3, 6],\n [-6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 286 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 0, 5],\n [0, -8, 2],\n [5, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 996 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -5, -7],\n [0, -4, 10],\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"
}
] | 940 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -5, 8],\n [0, -10, 10],\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"
}
] | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -4, 2],\n [-4, -4, -4],\n [2, -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"
}
] | 108 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -3, 3],\n [0, 6, -2],\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"
}
] | 520 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 9, -2],\n [0, 9, 0],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 973 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -4, 10],\n [-4, -8, 0],\n [10, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 912 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 9, -4],\n [9, 1, 0],\n [-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"
}
] | 648 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -2, -2],\n [-2, 2, 0],\n [-2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 6, -7],\n [6, 9, 1],\n [-7, 1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 611 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -6, -5],\n [0, 1, -6],\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"
}
] | 964 | MATH |
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