messages listlengths 1 1 | ground_truth stringclasses 989
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 4, -1],\n [4, 6, 6],\n [-1, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 6, -1],\n [0, 4, -6],\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"
}
] | 856 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -7, 10],\n [0, -5, 6],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | 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, 3, -6],\n [6, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 252 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -6, 0],\n [0, 1, -8],\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"
}
] | 964 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 10, -8],\n [0, 4, -4],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -3, 1],\n [7, -10, 5],\n [-5, -1, 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": "What is the determinant of the matrix:\n[[-9, 1, 2],\n [7, 1, -4],\n [10, -8, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 260 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -2, 0],\n [-2, 3, -4],\n [0, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 337 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -9, -6],\n [-3, -1, -9],\n [-10, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 613 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 2, -2],\n [-3, -1, 5],\n [3, 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"
}
] | 120 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -2, 8],\n [0, -3, 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"
}
] | 892 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -7, -8],\n [-6, -1, 9],\n [-10, 2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 752 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -8, 8],\n [7, 2, -10],\n [-4, -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"
}
] | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -6, 6],\n [0, -4, -7],\n [8, 6, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 428 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 2, -8],\n [0, 2, 0],\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": "What is the determinant of the matrix:\n[[3, 6, 5],\n [-6, 10, 1],\n [3, 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"
}
] | 241 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 0, -8],\n [0, 9, 4],\n [-8, 4, 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"
}
] | 452 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 4, -10],\n [-3, -6, -5],\n [-2, 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"
}
] | 220 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, -4],\n [10, -3, -8],\n [-5, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 442 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 4, 4],\n [4, 3, -2],\n [4, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 8, -2],\n [0, -8, 9],\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"
}
] | 680 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -9, 5],\n [0, 10, -1],\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"
}
] | 300 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 3, 7],\n [4, 9, 0],\n [-3, 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"
}
] | 341 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -9, -5],\n [-9, 1, 4],\n [-5, 4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 331 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 3, 3],\n [3, -7, 4],\n [3, 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"
}
] | 192 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 10, 1],\n [-4, -4, -5],\n [3, 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"
}
] | 654 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 0, -2],\n [6, 0, -1],\n [-2, -5, 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"
}
] | 110 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 4, -2],\n [4, -10, 2],\n [-2, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 8, 4],\n [8, 10, 3],\n [4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 621 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -5, 6],\n [0, 6, 0],\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"
}
] | 90 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, 2],\n [-2, 2, 1],\n [2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 982 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, 0],\n [0, -5, 2],\n [0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -7, -7],\n [-1, 1, -9],\n [-2, 7, -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"
}
] | 864 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, 2],\n [-4, -5, 2],\n [2, 2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -8, 7],\n [0, -7, 0],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 993 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -8, 9],\n [0, 5, 0],\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"
}
] | 950 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -6, 6],\n [0, -4, -5],\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"
}
] | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 4, 0],\n [0, 2, -9],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 988 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -2, 0],\n [-2, -7, 6],\n [0, 6, -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"
}
] | 989 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 7, 6],\n [-9, -7, -9],\n [-5, 7, 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"
}
] | 98 | 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, 1],\n [-2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 1, 6],\n [0, -7, 9],\n [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"
}
] | 441 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 1, -4],\n [1, -7, 0],\n [-4, 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"
}
] | 152 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -5, 0],\n [-5, -3, 4],\n [0, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -3, -8],\n [-3, -2, 1],\n [-8, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -1, -8],\n [2, 8, -5],\n [-3, -5, 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"
}
] | 798 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -9, 6],\n [-7, 5, 4],\n [5, 3, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 563 | 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 [0, 6, 7],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -4, 1],\n [-4, 2, -4],\n [1, -4, -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"
}
] | 292 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -10, 4],\n [0, -4, 0],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 8, -7],\n [0, 1, -3],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 0, -4],\n [0, -6, -2],\n [-4, -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"
}
] | 316 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 0, 0],\n [0, -4, 1],\n [-7, -5, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 703 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, 8],\n [7, 2, -1],\n [-10, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 612 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -5, 6],\n [-5, -1, 8],\n [6, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 331 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -8, -1],\n [0, -7, -7],\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"
}
] | 252 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -7, -8],\n [0, 8, -8],\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"
}
] | 80 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 5, -7],\n [0, -6, 6],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -7, -5],\n [0, 10, 6],\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"
}
] | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 9, 0],\n [0, 1, -3],\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"
}
] | 988 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 10, -9],\n [5, 4, -6],\n [-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"
}
] | 285 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 2, 8],\n [2, -2, -6],\n [8, -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"
}
] | 888 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -1, 7],\n [0, 5, -7],\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"
}
] | 30 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -8, 0],\n [-8, 2, -4],\n [0, -4, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, -6],\n [0, 4, -9],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 1, 3],\n [0, -10, 7],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -9, 6],\n [0, 4, 1],\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"
}
] | 964 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 0, -1],\n [0, 10, -6],\n [-1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 318 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -7, -6],\n [3, -1, 6],\n [-8, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 276 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 1, -2],\n [0, -1, -5],\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"
}
] | 45 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 9, 5],\n [0, -5, -4],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 0, 0],\n [0, 5, -4],\n [0, -4, -8]]\nRound to the nearest integer, then take the result 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[[-10, 4, 5],\n [0, 5, -2],\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"
}
] | 550 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -9, 4],\n [-4, -3, -1],\n [6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -8, -7],\n [0, -9, 0],\n [0, 0, 3]]\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[[-1, -9, -6],\n [0, -6, 10],\n [0, 0, -5]]\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[[3, -8, 0],\n [-8, -8, -4],\n [0, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 0, -3],\n [0, -10, 10],\n [-3, 10, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 650 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -10, -3],\n [0, -5, 4],\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"
}
] | 880 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -1, -2],\n [-1, -2, 4],\n [-2, 4, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 5, 0],\n [2, 0, 3],\n [9, -6, 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"
}
] | 971 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 8, 1],\n [-3, 0, -5],\n [-8, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 6, 8],\n [6, -8, 10],\n [8, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 332 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 8, -6],\n [0, -4, 1],\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"
}
] | 168 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -3, 2],\n [-1, -9, -8],\n [3, 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"
}
] | 895 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -6, -9],\n [0, -8, 2],\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"
}
] | 24 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -5, 5],\n [0, 4, -6],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 0, 3],\n [3, 0, -10],\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"
}
] | 352 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, -4],\n [-2, 7, 8],\n [-4, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -4, -3],\n [-5, -1, -9],\n [-3, -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"
}
] | 641 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, -5],\n [-6, 7, 6],\n [3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -7, -10],\n [3, 4, -6],\n [-7, 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"
}
] | 590 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -3, 5],\n [-3, 6, -3],\n [5, 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"
}
] | 874 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, 8],\n [0, 1, -8],\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"
}
] | 950 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, -7],\n [0, 9, 7],\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"
}
] | 820 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 0, -2],\n [0, -3, -5],\n [-10, 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"
}
] | 66 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, 3],\n [-4, -3, -4],\n [3, -4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 595 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, 3],\n [0, -3, 9],\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"
}
] | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, -2],\n [0, -3, 5],\n [-2, 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"
}
] | 92 | MATH |
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