messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -10, 6, 4],\n [-1, 10, -7, 9],\n [-7, -9, -5, -12],\n [-5, -9, -6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 236 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 0, 2, 6],\n [0, -5, 6, 3],\n [2, 6, 1, 7],\n [6, 3, 7, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 111 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 3, 7, -8],\n [0, 8, 0, 7],\n [0, 0, -10, 4],\n [0, 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"
}
] | 40 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -7, 0, -6],\n [-7, 2, 2, -6],\n [0, 2, 0, 4],\n [-6, -6, 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"
}
] | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 11, 12, 3],\n [-12, 3, 3, 6],\n [0, -4, -11, -3],\n [-2, -4, -2, 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"
}
] | 912 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -1, 10, -3],\n [-1, 2, 0, -4],\n [10, 0, -1, 5],\n [-3, -4, 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"
}
] | 186 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -3, -7, 12],\n [0, 6, -10, -1],\n [0, 0, 11, -9],\n [0, 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"
}
] | 472 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 8, 12, 1],\n [8, 2, 6, 0],\n [12, 6, 11, 9],\n [1, 0, 9, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 986 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, 4, -2],\n [2, -11, -4, 6],\n [4, -4, 4, -2],\n [-2, 6, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 936 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 2, -1, -2],\n [2, -11, -4, -11],\n [-1, -4, 3, -2],\n [-2, -11, -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"
}
] | 395 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -1, -7, 9],\n [-10, -9, -3, 6],\n [11, -12, -6, -8],\n [-8, -10, -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"
}
] | 102 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, -11, 6],\n [8, -8, -11, -3],\n [-11, 8, 9, -7],\n [2, 10, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 494 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 7, 0, -6],\n [7, -4, -1, -11],\n [0, -1, 10, 6],\n [-6, -11, 6, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 948 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, 8, -12],\n [0, -12, 3, -9],\n [0, 0, -4, 4],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 336 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -6, -9, 9],\n [-2, 7, -4, -2],\n [-7, 0, 12, 11],\n [-4, -1, -11, -6]]\nRound to the nearest integer, then take the result 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[[4, -6, -11, 0],\n [-6, -10, 3, -1],\n [-11, 3, 4, 0],\n [0, -1, 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"
}
] | 233 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -7, 1, 4],\n [-7, -6, 0, -2],\n [1, 0, 1, 5],\n [4, -2, 5, -12]]\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"
}
] | 663 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, 0, -2],\n [-2, -6, -2, -2],\n [0, -2, 4, 6],\n [-2, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 448 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -5, 11, 3],\n [0, -10, -3, 6],\n [-11, -4, -6, -6],\n [-12, 6, -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"
}
] | 532 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 2, -6, 4],\n [2, -2, 0, -7],\n [-6, 0, -7, -9],\n [4, -7, -9, 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"
}
] | 67 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 5, 7, -5],\n [0, -3, -3, 2],\n [0, 0, 6, 1],\n [0, 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, -8, -6],\n [6, -10, 0, 2],\n [-1, 1, -5, 11],\n [8, 11, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 380 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -10, 8, 1],\n [6, 10, -2, 0],\n [-3, -4, -3, 9],\n [-8, 5, 1, 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"
}
] | 170 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 3, 5, 10],\n [0, 7, -7, -10],\n [0, 0, -2, 8],\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"
}
] | 496 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -6, 12, -3],\n [-6, 12, -8, -4],\n [12, -8, 11, 2],\n [-3, -4, 2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 688 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -4, 2, -11],\n [0, -2, -11, -9],\n [0, 0, -7, -9],\n [0, 0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 3, 8, 8],\n [0, -2, 9, -1],\n [0, 0, 12, 6],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 12, 8, -4],\n [0, 2, 5, 8],\n [0, 0, -11, 3],\n [0, 0, 0, 8]]\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[[-7, 9, -9, -7],\n [0, 10, -1, 10],\n [0, 0, -5, 8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 850 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -10, 11, -4],\n [-3, -10, -6, -5],\n [-8, 5, 1, -12],\n [7, -7, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 668 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, 7, 10],\n [4, 4, 3, -1],\n [7, -9, 5, 9],\n [-7, 0, -11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -4, 7, 6],\n [0, 4, 0, 11],\n [0, 0, 7, 4],\n [0, 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"
}
] | 840 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -2, 0],\n [2, 4, 2, -1],\n [-2, 2, 6, 4],\n [0, -1, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 848 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 7, -9, 5],\n [-10, 6, -7, -5],\n [-2, 3, 10, -4],\n [12, -8, -5, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 6, 11, 0],\n [-11, -8, 10, 11],\n [8, 6, -12, 2],\n [10, -5, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 314 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -12, 11, 8],\n [11, -3, 2, 2],\n [5, 5, -4, 12],\n [10, 4, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 580 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -12, 6, -4],\n [0, -2, 3, 4],\n [0, 0, -11, -5],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 2, -8, 4],\n [-8, -3, 1, -9],\n [0, 7, -8, 10],\n [3, -7, -5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 888 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -8, -9, 2],\n [-8, -7, -4, 2],\n [-9, -4, 3, 2],\n [2, 2, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -12, 5, -4],\n [0, 12, 12, 8],\n [0, 0, -3, -9],\n [0, 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"
}
] | 16 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -11, -9, -9],\n [-2, 1, -5, -8],\n [-4, 12, 11, 8],\n [6, -4, 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"
}
] | 582 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 6, 3, -11],\n [6, -3, 4, 2],\n [3, 4, 5, -8],\n [-11, 2, -8, -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"
}
] | 166 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 4, -3, 4],\n [0, 1, -2, -2],\n [0, 0, -11, 10],\n [0, 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"
}
] | 944 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -8, -1, -12],\n [0, 4, -11, 5],\n [0, 0, 12, 1],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 1, 2, 4],\n [11, 3, -5, -6],\n [-7, 7, -11, 8],\n [-10, 11, 8, -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"
}
] | 654 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 3, -1, 10],\n [0, -9, 3, -6],\n [0, 0, 7, -8],\n [0, 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"
}
] | 984 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 3, 1, 8],\n [0, -8, 7, 3],\n [0, 0, 1, 8],\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"
}
] | 784 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -3, -10, 12],\n [-5, -5, 10, 5],\n [-11, -12, 12, 3],\n [-7, -1, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -9, 7, 5],\n [0, 4, 0, 10],\n [0, 0, -5, -5],\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"
}
] | 780 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, -7, 9],\n [-9, 0, -2, -10],\n [1, -3, -2, 8],\n [0, -1, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -10, -3, 11],\n [-10, 7, -7, -6],\n [-5, 0, 10, -6],\n [-6, 2, 5, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 463 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 1, -1, 9],\n [0, 5, 8, 11],\n [0, 0, 8, 1],\n [0, 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"
}
] | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, -9, 9],\n [0, -3, 2, -8],\n [0, 0, -5, 7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -5, -2, -7],\n [-5, 9, 1, 1],\n [-2, 1, 1, -6],\n [-7, 1, -6, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 0, -9, 2],\n [0, 11, -4, 0],\n [-9, -4, -12, 4],\n [2, 0, 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"
}
] | 910 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 4, -5, 8],\n [-6, 3, -8, 3],\n [-12, -2, -5, -11],\n [-11, 3, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 10, 0, 4],\n [10, -2, -6, 2],\n [0, -6, 10, 10],\n [4, 2, 10, 0]]? 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": "Compute |A| for the matrix A =\n[[-4, 4, -8, 9],\n [7, 10, -11, -6],\n [12, 3, 8, -2],\n [-3, -2, 11, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -10, -6, 4],\n [-10, -4, -10, 0],\n [-6, -10, -4, 4],\n [4, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -11, -2, 4],\n [0, 5, -9, -6],\n [0, 0, -2, -9],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 630 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -3, -3, -10],\n [-7, 12, 0, -2],\n [-4, 0, 7, 2],\n [-4, -2, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -3, 6, 8],\n [-3, 9, 4, 6],\n [6, 4, 10, 8],\n [8, 6, 8, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 8, -3, 8],\n [-7, -2, 1, 8],\n [-2, -10, 8, 8],\n [-7, -7, 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"
}
] | 644 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, 0, -3],\n [6, 6, 2, 4],\n [0, 2, -2, 2],\n [-3, 4, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 728 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 6, -12, -2],\n [-11, 6, 6, -12],\n [10, -4, 3, -12],\n [-4, 12, -3, 4]]\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[[5, 7, 6, 8],\n [-2, 6, 10, -3],\n [-9, -11, -1, 11],\n [-3, 9, 2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 326 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, 2, -3],\n [-12, -1, 3, 12],\n [-10, -9, 7, -10],\n [7, 9, -12, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 550 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 3, 4, 5],\n [0, -10, 3, 12],\n [0, 0, 3, -2],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -7, 3, 10],\n [7, 3, -8, -9],\n [-10, 3, -10, -6],\n [-10, 9, -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"
}
] | 582 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, -12, -10],\n [-7, -11, 7, -3],\n [-7, 2, -9, 4],\n [-10, 4, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 363 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 6, 1, -7],\n [0, 6, -7, -2],\n [0, 0, -12, -3],\n [0, 0, 0, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -12, 11, 9],\n [2, 6, 4, -6],\n [3, 5, 1, 6],\n [-7, -8, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 676 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 2, 2, -4],\n [2, 10, 10, 4],\n [2, 10, -4, 2],\n [-4, 4, 2, -10]]? 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": "What is the determinant of the matrix:\n[[9, -2, -3, 1],\n [-2, 7, 0, 6],\n [-3, 0, -2, -7],\n [1, 6, -7, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 484 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 9, -2, 4],\n [1, 1, -12, 0],\n [-1, 10, 1, 4],\n [9, 5, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, 1, 0],\n [-2, -5, 6, -4],\n [1, 6, 8, -6],\n [0, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 872 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -1, 7, 9],\n [12, -9, 11, -10],\n [-8, -9, 8, -4],\n [6, 3, 6, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 936 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, -1, -2],\n [-1, 4, -6, 6],\n [-1, -6, 9, 1],\n [-2, 6, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 850 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -4, 9, 10],\n [0, -1, -8, -2],\n [0, 0, 7, -2],\n [0, 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"
}
] | 748 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -9, -9, -6],\n [7, -9, -4, -6],\n [10, 4, -1, -8],\n [2, 7, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 718 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 9, 9, -8],\n [0, -7, 2, 12],\n [0, 0, -2, -11],\n [0, 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"
}
] | 378 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 6, -3, 10],\n [-6, -3, -9, -9],\n [5, -10, -1, -10],\n [-4, -7, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 1, -12, 8],\n [6, -11, 0, -5],\n [6, -8, 9, 10],\n [-10, -2, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 858 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 2, 5, 0],\n [2, -1, -2, 5],\n [5, -2, -5, -1],\n [0, 5, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -6, -5, -4],\n [-6, -9, 0, 4],\n [-5, 0, -12, 0],\n [-4, 4, 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"
}
] | 133 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 0, -4, 4],\n [0, 10, -2, -6],\n [-4, -2, -8, 6],\n [4, -6, 6, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -2, -3, -11],\n [0, 11, -10, -10],\n [0, 0, 10, -2],\n [0, 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"
}
] | 680 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 12, -1, 0],\n [12, -12, 2, 12],\n [-1, 0, 8, 10],\n [7, 4, 11, 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"
}
] | 236 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 5, -8, 4],\n [5, -10, -3, -4],\n [-8, -3, 11, -1],\n [4, -4, -1, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 261 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, 11, 9],\n [0, 10, -4, 8],\n [0, 0, -11, 4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 8, -6, -6],\n [8, 9, 2, 4],\n [-6, 2, -11, 6],\n [-6, 4, 6, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 917 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 5, -3, 6],\n [0, 7, -9, -4],\n [0, 0, 9, 6],\n [0, 0, 0, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 165 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 2, -7, 12],\n [0, 7, -8, 5],\n [0, 0, -11, -11],\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"
}
] | 924 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 7, -6, 4],\n [0, -5, -10, -11],\n [0, 0, -1, 10],\n [0, 0, 0, 2]]\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[[-5, 5, -9, -3],\n [0, 8, 4, -2],\n [0, 0, 3, 0],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 12, 10, -7],\n [0, 1, 8, -9],\n [0, 0, 3, 5],\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"
}
] | 958 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, 11, -9],\n [12, 1, -11, -2],\n [-7, 10, 6, -4],\n [-2, -7, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 401 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -6, 1, -1],\n [-6, -9, 1, -9],\n [1, 1, 3, 4],\n [-1, -9, 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"
}
] | 26 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 5, -6, -3],\n [0, 2, -6, 5],\n [0, 0, -5, 2],\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"
}
] | 960 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 12, -12, -10],\n [0, -3, -12, 7],\n [0, 0, 12, 5],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
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