messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 3, -6],\n [3, -7, -3],\n [-6, -3, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 955 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 10, -4],\n [-3, -2, 4],\n [-4, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 5, -10],\n [0, 8, -9],\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"
}
] | 16 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 9, 7],\n [6, -9, 6],\n [4, -1, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 0, 8],\n [0, -7, 9],\n [8, 9, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 520 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -8, -1],\n [-8, 8, -8],\n [-1, -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"
}
] | 712 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 8, 5],\n [8, 1, -1],\n [-10, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 362 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 9, -5],\n [-6, -7, -9],\n [10, -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"
}
] | 758 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 2, 3],\n [2, -6, 2],\n [3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 2, 8],\n [2, -7, -2],\n [8, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 243 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -5, 9],\n [0, 6, -9],\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"
}
] | 940 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 10, 6],\n [0, -2, 2],\n [-1, -9, 0]]\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[[9, 1, 3],\n [1, 4, 4],\n [3, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 494 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 1, 0],\n [1, 5, -4],\n [0, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -8, 6],\n [0, 8, -10],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 10, -9],\n [0, 2, -5],\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"
}
] | 872 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -1, 8],\n [-1, -9, 3],\n [8, 3, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 529 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, 8],\n [-9, 2, -3],\n [8, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 258 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 9, 3],\n [0, -5, 7],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 955 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 6, -6],\n [0, 2, -10],\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"
}
] | 6 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 2, 8],\n [2, 10, -2],\n [8, -2, 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"
}
] | 184 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 8, 4],\n [-7, -3, -8],\n [5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 622 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 1, -4],\n [0, 5, -5],\n [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"
}
] | 930 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 2, 0],\n [-4, -2, -9],\n [3, -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"
}
] | 914 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, 4],\n [-4, 4, 8],\n [4, 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"
}
] | 984 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 2, -6],\n [2, 8, 0],\n [-6, 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"
}
] | 820 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -5, 6],\n [0, -8, 5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 4, -8],\n [0, -6, 5],\n [-5, -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"
}
] | 240 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 5, 1],\n [-3, -1, 0],\n [0, 7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 749 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -5, -2],\n [0, -10, 9],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 5, 8],\n [0, 9, -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"
}
] | 892 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -8, 6],\n [7, 1, 3],\n [1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 610 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -1, -5],\n [3, 3, -1],\n [-8, -9, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 968 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -1, -9],\n [-8, 6, -8],\n [-5, -10, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 790 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, 2],\n [0, 4, -4],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 216 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 6, -6],\n [1, 1, 6],\n [3, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 985 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -9, -6],\n [0, 6, 3],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -7, -9],\n [2, 7, -2],\n [9, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 703 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 2, 2],\n [2, 5, 1],\n [2, 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"
}
] | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 2, 0],\n [2, -2, 5],\n [0, 5, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 158 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -6, 4],\n [0, -8, -7],\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"
}
] | 784 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 0, -2],\n [0, 1, -3],\n [-2, -3, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 969 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 5, 1],\n [0, -2, -4],\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[[1, -10, -3],\n [4, 7, -10],\n [5, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 871 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 6, -1],\n [0, 0, 10],\n [3, 7, -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"
}
] | 900 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -7, 5],\n [-7, -2, -5],\n [5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -2, 6],\n [-2, 3, 0],\n [6, 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"
}
] | 887 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 4, 2],\n [4, 9, 1],\n [2, 1, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 621 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -8, -2],\n [0, -2, 8],\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"
}
] | 920 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -1, -8],\n [-7, 9, -3],\n [9, -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"
}
] | 528 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, 4],\n [-2, -1, 0],\n [4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, 0],\n [-4, 9, -5],\n [0, -5, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 807 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 5, -6],\n [-2, 6, -6],\n [-5, -5, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -7, 9],\n [0, -5, 7],\n [0, 0, 3]]\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, -2, -2],\n [-2, -5, -4],\n [-2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -6, -8],\n [0, -5, 10],\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[[5, -7, -7],\n [0, -8, -9],\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"
}
] | 840 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -4, -3],\n [0, -1, -6],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, -2],\n [0, 10, 2],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 10, 9],\n [0, -1, 5],\n [0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 2, -4],\n [0, 2, 1],\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"
}
] | 840 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -3, -3],\n [5, 10, 3],\n [8, 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"
}
] | 193 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 5, -2],\n [5, -9, 2],\n [-2, 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"
}
] | 264 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 3, -5],\n [3, 7, 4],\n [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"
}
] | 265 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -2, 3],\n [0, 4, -10],\n [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"
}
] | 976 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -9, -9],\n [1, -2, -7],\n [-3, -8, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 658 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 4, 6],\n [0, -9, -9],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 567 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, 0],\n [4, 3, 2],\n [0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 956 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 2, -4],\n [2, 5, -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"
}
] | 116 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, -8],\n [3, -8, -6],\n [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"
}
] | 536 | 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, -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[[4, 1, -6],\n [1, 5, -2],\n [-6, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 657 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 3, 2],\n [3, 9, -4],\n [2, -4, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 902 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -7, 4],\n [0, 5, -10],\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"
}
] | 25 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 7, 6],\n [0, 5, 5],\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"
}
] | 135 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 4, 0],\n [4, -1, -2],\n [0, -2, -4]]\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[[2, 8, 9],\n [-4, -2, 10],\n [-8, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -3, -9],\n [0, -3, 4],\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"
}
] | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -6, -3],\n [9, 9, 2],\n [4, 10, 10]]\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, -6, 4],\n [-6, 2, 8],\n [4, 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"
}
] | 552 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 0, 5],\n [6, -10, -10],\n [0, -5, -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"
}
] | 910 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 2, -7],\n [-1, 9, 1],\n [6, -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"
}
] | 385 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -7, -4],\n [-7, -4, -1],\n [-4, -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"
}
] | 764 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -3, 0],\n [0, 2, -1],\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"
}
] | 960 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -1, -7],\n [-8, 5, -10],\n [-3, -10, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, -10],\n [0, -6, 6],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 622 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 7, 6],\n [7, 7, 0],\n [6, 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"
}
] | 196 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -4, -8],\n [-4, -8, 2],\n [-8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 0, 10],\n [0, 7, -4],\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"
}
] | 63 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -4, -10],\n [0, 3, -10],\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"
}
] | 946 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -4, -6],\n [-4, 7, -2],\n [-6, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -4, 3],\n [-4, 5, -4],\n [3, -4, -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"
}
] | 619 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -4, -8],\n [0, -5, 1],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 650 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, -6],\n [-4, 3, -1],\n [-6, -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"
}
] | 552 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 9, -8],\n [10, 2, -2],\n [-8, 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"
}
] | 88 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 2, 2],\n [2, 0, 1],\n [2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, 4],\n [0, 2, 6],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 992 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 3, 5],\n [0, -3, 5],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -1, 8],\n [0, -4, 3],\n [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"
}
] | 48 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, 6],\n [0, 8, -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"
}
] | 808 | MATH |
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