messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 3, 9],\n [-9, 6, -10],\n [1, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, 5],\n [0, 6, 7],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -5, 0],\n [5, 7, 8],\n [-9, -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"
}
] | 991 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -7, -5],\n [0, -3, -7],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0],\n [-2, 3, -7],\n [0, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 838 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -4, 5],\n [0, 5, 1],\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"
}
] | 995 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 2, 4],\n [0, 9, -2],\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"
}
] | 640 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 1, 4],\n [1, 1, -2],\n [4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, -1],\n [-1, -8, 7],\n [-3, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 541 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -5, -6],\n [0, 3, -6],\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"
}
] | 919 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -4, 6],\n [0, 8, 0],\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"
}
] | 336 | 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, -2, -1],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 1, -4],\n [-4, -8, 1],\n [-5, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 975 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -7, -9],\n [7, -9, 1],\n [4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -8, -3],\n [-8, 2, -6],\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"
}
] | 928 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -3, -9],\n [0, 1, -3],\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"
}
] | 30 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 7, -2],\n [3, 9, -10],\n [-7, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 4, -7],\n [4, -2, 3],\n [-7, 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"
}
] | 32 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 0, 4],\n [0, 1, 2],\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"
}
] | 9 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 1, 4],\n [-1, -10, -10],\n [-8, 8, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 618 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -9, -7],\n [-10, 7, 10],\n [8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 8, -6],\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"
}
] | 965 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 10, -8],\n [-1, 10, 10],\n [-2, 9, -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"
}
] | 402 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 5, -8],\n [0, 4, 2],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -9, 6],\n [-9, 3, -2],\n [6, -2, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 586 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 10, -6],\n [0, -3, 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"
}
] | 910 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -2, -8],\n [0, 2, 9],\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"
}
] | 984 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -9, 9],\n [-4, 3, 4],\n [-4, 2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 9, -8],\n [0, 10, 10],\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"
}
] | 720 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 2, 1],\n [-9, -2, -10],\n [-6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 351 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 1, -10],\n [0, 4, 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"
}
] | 920 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -9, -2],\n [0, -6, 7],\n [10, 10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -2, -10],\n [0, -5, -1],\n [-7, 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"
}
] | 26 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 8, 5],\n [0, -9, 3],\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"
}
] | 433 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 3, 0],\n [3, -5, -6],\n [0, -6, -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": "What is the determinant of the matrix:\n[[-9, 0, -4],\n [0, 10, -5],\n [-4, -5, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 615 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -6, 5],\n [-6, 0, 0],\n [5, 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"
}
] | 748 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -3, 6],\n [0, -6, 10],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -7, -3],\n [0, 1, -2],\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"
}
] | 36 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, -5],\n [-4, -2, -8],\n [-5, -8, -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"
}
] | 540 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -12, -3, -12],\n [0, -8, 5, 1],\n [0, 0, 8, 10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 10, 2, -9],\n [10, -6, 8, 4],\n [2, 8, 0, 7],\n [-9, 4, 7, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 9, 8, 9],\n [-7, -11, 1, 8],\n [11, 9, -1, 11],\n [-10, -4, -1, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 449 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 1, 8, 1],\n [7, 7, 6, -1],\n [12, 11, -11, 0],\n [-6, 11, -1, -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"
}
] | 784 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -12, 4, 7],\n [6, -11, -2, -1],\n [8, -2, 2, 2],\n [-7, -7, 8, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 12, -8, 3],\n [0, 11, 7, -7],\n [0, 0, -9, 5],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -11, 10, 8],\n [0, -4, 3, 5],\n [0, 0, 6, -11],\n [0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 624 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -6, -2, 5],\n [-6, 6, 10, 2],\n [-2, 10, 11, 9],\n [5, 2, 9, -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"
}
] | 490 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -4, 0, 6],\n [-4, -9, 2, -2],\n [0, 2, -11, 0],\n [6, -2, 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[[-11, 2, 12, 3],\n [0, 6, -5, 9],\n [0, 0, 5, -7],\n [0, 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"
}
] | 300 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -12, 6, 5],\n [-12, 12, -2, 8],\n [6, -2, -1, -7],\n [5, 8, -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"
}
] | 660 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -2, -11, -11],\n [-11, -11, 4, -12],\n [-7, 8, 12, -8],\n [12, -12, -2, 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"
}
] | 250 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -8, -4, -4],\n [12, 1, 5, 5],\n [-4, 12, 2, 6],\n [-9, -5, 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"
}
] | 688 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 0, -10, 10],\n [-11, 2, -12, -6],\n [-8, -12, 11, -4],\n [12, -8, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -6, -10, 8],\n [-6, -7, 4, -2],\n [-10, 4, -11, 5],\n [8, -2, 5, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 92 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 12, 7, -4],\n [8, -1, -6, -8],\n [7, 9, 6, 4],\n [7, -12, -7, 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"
}
] | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, 11, 4],\n [12, -12, -1, 1],\n [-12, -8, 10, 1],\n [4, 0, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 656 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 8, 0, 3],\n [8, 11, -2, -4],\n [0, -2, 7, 2],\n [3, -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"
}
] | 552 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -2, 4, -1],\n [-4, 2, 4, 4],\n [-6, 3, 12, -4],\n [10, 5, 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"
}
] | 880 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 4, -6, 6],\n [0, -9, -4, -9],\n [0, 0, 8, 8],\n [0, 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"
}
] | 288 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -5, 1, -9],\n [0, -9, 12, -6],\n [0, 0, 7, 12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 969 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 10, -7, 1],\n [10, -11, 3, -2],\n [-7, 3, -10, -4],\n [1, -2, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 961 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 12, 7, 0],\n [5, 1, 10, -6],\n [-9, 6, -2, 4],\n [1, 6, -1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 2, 8, 0],\n [2, -9, 0, 6],\n [8, 0, 12, -4],\n [0, 6, -4, -11]]? 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": "Determine the value of det(A) where A =\n[[9, 4, 10, 12],\n [4, -4, 6, 2],\n [10, 6, -7, -4],\n [12, 2, -4, 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"
}
] | 92 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 6, 10, -6],\n [6, 0, 8, 4],\n [10, 8, 6, -6],\n [-6, 4, -6, 3]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 11, -8, -7],\n [11, 7, -8, -3],\n [-8, -8, -4, -3],\n [-7, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 568 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -10, -10, 12],\n [-9, -3, -2, -7],\n [-5, 5, 4, -11],\n [5, 5, 12, -3]]\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[[7, -8, 7, 1],\n [-7, -9, 10, -6],\n [-1, -9, 5, -8],\n [-12, -10, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 517 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -8, -2, -2],\n [-8, 8, -6, 5],\n [-2, -6, 2, -1],\n [-2, 5, -1, -1]]\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[[-12, -5, -11, 5],\n [-7, -6, -11, -8],\n [-12, 4, -10, -3],\n [3, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 598 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 12, 4, -9],\n [-11, 0, -3, -1],\n [-10, 4, 11, 5],\n [12, 2, -6, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 0, -6, 8],\n [0, -1, 8, -2],\n [-6, 8, 5, -4],\n [8, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 456 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -2, 4, 4],\n [-2, 6, -4, -1],\n [4, -4, 8, 8],\n [4, -1, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -7, -5, 8],\n [-7, -6, 5, -2],\n [-5, 5, 10, 1],\n [8, -2, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -5, -4, -2],\n [-5, 8, 0, 6],\n [-4, 0, -10, -4],\n [-2, 6, -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"
}
] | 996 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 10, -11, 1],\n [0, -7, 3, -4],\n [0, 0, -7, -9],\n [0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 559 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, -9, -5],\n [6, 10, 0, 4],\n [-9, 0, -1, 4],\n [-5, 4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 596 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -6, -6, -3],\n [0, 6, 8, -6],\n [0, 0, -6, -4],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 272 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 1, 0, 2],\n [2, -6, 9, -1],\n [-7, -6, 7, -9],\n [-11, 9, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 999 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 4, 10, 9],\n [4, -6, 8, -9],\n [10, 8, 3, 3],\n [9, -9, 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"
}
] | 39 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 12, -9, 10],\n [0, -4, 2, -7],\n [0, 0, -2, -8],\n [0, 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"
}
] | 80 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 11, 3, 5],\n [0, -3, 9, -12],\n [0, 0, 5, -4],\n [0, 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"
}
] | 505 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 10, -12, -9],\n [-1, -11, 9, 11],\n [0, -12, 10, 4],\n [-8, 12, 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"
}
] | 862 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -7, 1, 5],\n [0, -7, -12, 2],\n [0, 0, -6, 0],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -2, 0, 0],\n [0, -3, 12, -3],\n [0, 0, 5, 2],\n [0, 0, 0, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 185 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -4, -10, -6],\n [-4, -5, 0, 4],\n [-10, 0, -12, 4],\n [-6, 4, 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"
}
] | 480 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 0, 4, 0],\n [0, -2, 0, 0],\n [4, 0, 6, 0],\n [0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 352 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -12, -11, 8],\n [11, 11, -1, 4],\n [-1, 9, -12, 0],\n [-6, 1, -11, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 923 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 1, -6, 4],\n [1, -8, 4, -6],\n [-6, 4, -3, -2],\n [4, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 766 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -11, -7, -4],\n [-10, 4, 2, 8],\n [-2, -8, -6, 6],\n [9, 4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, -11, 1],\n [0, 3, 2, 7],\n [0, 0, -7, 1],\n [0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 622 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 5, 6, 0],\n [5, -12, -4, -6],\n [6, -4, -1, 0],\n [0, -6, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 707 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -12, -5, 4],\n [-10, -7, -3, 9],\n [6, 11, 9, 12],\n [10, -5, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 714 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -7, 5, -9],\n [0, -6, -8, 10],\n [0, 0, 11, 6],\n [0, 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"
}
] | 654 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 11, 0, 7],\n [0, 5, -8, 8],\n [8, 6, -12, 12],\n [-7, -7, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 516 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -1, -1, 7],\n [10, -1, -2, -1],\n [-11, -2, -9, -4],\n [-9, -2, -1, -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": "Determine the value of det(A) where A =\n[[12, -9, 0, 0],\n [-8, 9, -2, 0],\n [4, -4, 0, 10],\n [4, 6, 9, 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"
}
] | 408 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 7, 6, 0],\n [7, -4, 6, 0],\n [6, 6, -2, 2],\n [0, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, -12, 3],\n [0, -3, -10, -5],\n [0, 0, 1, -2],\n [0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
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