messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, 5, 11],\n [-6, -10, 6, 4],\n [7, 12, -8, 4],\n [9, 5, -1, -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"
}
] | 216 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -5, 9, -3],\n [0, 8, -11, -1],\n [0, 0, -12, -11],\n [0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 968 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 6, 5, 1],\n [6, -3, 10, 11],\n [5, 10, 8, 0],\n [1, 11, 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"
}
] | 596 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 10, 12, -8],\n [0, -8, -3, -5],\n [0, 0, -7, -1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 952 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 9, 4, 8],\n [0, -8, 9, 6],\n [0, 0, -11, 6],\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"
}
] | 112 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 12, 8, 12],\n [0, 11, -8, 10],\n [10, -4, 7, -10],\n [-9, 8, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 405 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, -10, -8],\n [0, -3, 5, 5],\n [0, 0, 3, -1],\n [0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -11, 0, 6],\n [-10, 6, 9, 11],\n [7, 8, 4, -12],\n [-4, 3, -4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 177 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -5, 10, -5],\n [0, 7, -7, -8],\n [0, 0, -5, -11],\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"
}
] | 50 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, 3, 9],\n [0, -2, -6, -10],\n [0, 0, -9, 0],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, 8, -12],\n [0, -12, -11, 9],\n [0, 0, -12, -1],\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"
}
] | 760 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -9, -10, -9],\n [0, 4, -7, -9],\n [0, 0, -1, 7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -2, -1, 5],\n [-4, -12, -6, -10],\n [9, -12, -8, 7],\n [1, 12, 4, -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"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 5, -7, 0],\n [-6, 8, 7, 5],\n [6, -9, 1, -9],\n [1, 3, 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"
}
] | 495 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -11, -2, -7],\n [0, -11, -12, -8],\n [0, 0, -9, 1],\n [0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 535 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -11, 9, -6],\n [-11, -3, 6, -4],\n [9, 6, 7, 4],\n [-6, -4, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 6, 8, -6],\n [6, 4, 4, -6],\n [8, 4, 9, -8],\n [-6, -6, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 188 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, -6, -7],\n [0, -3, -11, -4],\n [0, 0, -5, 2],\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"
}
] | 895 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, 2, 6],\n [-2, 6, -9, 3],\n [2, -9, 1, -1],\n [6, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 11, 12, -12],\n [0, 7, -8, -2],\n [0, 0, 3, 7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -3, -12, -1],\n [-1, -6, 8, 0],\n [6, 9, 10, 1],\n [6, -11, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 278 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -11, 2, 0],\n [0, -7, 2, 12],\n [0, 0, 6, 7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 984 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -12, 2, 8],\n [9, 1, 10, -4],\n [-12, -12, 4, -9],\n [-4, 5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 602 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 8, -9, -12],\n [-11, -3, 5, 3],\n [-7, -8, -5, 11],\n [6, -5, -4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 508 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 5, -11, -3],\n [0, -2, 11, -8],\n [0, 0, -11, 5],\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"
}
] | 100 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -5, 12, 8],\n [2, -7, 5, 10],\n [9, -11, 0, 9],\n [8, -5, 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"
}
] | 706 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -4, -2, 0],\n [-4, 3, -2, -4],\n [-2, -2, 4, -8],\n [0, -4, -8, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 2, 3, -9],\n [0, -7, 2, 7],\n [0, 0, -4, -4],\n [0, 0, 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"
}
] | 920 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, -9, -2],\n [7, -3, 4, -9],\n [-9, 3, 1, -11],\n [-4, -5, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 972 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -11, -3, 0],\n [0, -2, 10, 7],\n [0, 0, 3, -6],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, 11, 12],\n [0, -2, 1, -7],\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"
}
] | 822 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -7, -6, 7],\n [0, 5, 3, 5],\n [0, 0, -8, 6],\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"
}
] | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, 6, -3],\n [0, 11, -10, 7],\n [0, 0, 11, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 338 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 12, 9, 9],\n [0, 3, -8, 11],\n [0, 0, 9, 5],\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"
}
] | 271 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -4, 4, -5],\n [-4, 0, -2, 4],\n [4, -2, 8, -4],\n [-5, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 556 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -9, -4, -3],\n [6, -8, -12, -10],\n [-9, 3, -6, 3],\n [2, 8, -4, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 3, -6, 2],\n [0, 5, -8, -11],\n [0, 0, 9, -10],\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"
}
] | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 7, 8, 11],\n [-11, -3, 3, 3],\n [-10, 8, -12, -5],\n [6, 3, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 787 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 8, 4, 1],\n [8, -9, 2, 6],\n [4, 2, -8, 2],\n [1, 6, 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"
}
] | 308 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 2, -1, -9],\n [0, -2, -3, 11],\n [0, 0, -6, -8],\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"
}
] | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -4, 6, -3],\n [-4, -1, 11, 8],\n [6, 11, 10, 3],\n [-3, 8, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -10, -8, -8],\n [12, 7, -1, 11],\n [-3, -4, -9, 0],\n [7, -2, 1, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 970 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -1, 1],\n [0, -3, -3, -7],\n [-1, -3, -1, -2],\n [1, -7, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 147 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -8, -6, 9],\n [-5, -8, -4, 9],\n [-4, -8, 10, -1],\n [4, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 4, 2, 6],\n [4, -6, -1, -2],\n [2, -1, 2, 4],\n [6, -2, 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"
}
] | 253 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, 11, 5, 6],\n [0, 5, 10, -3],\n [0, 0, 3, 11],\n [0, 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"
}
] | 900 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, -7, 12],\n [0, -2, 0, -12],\n [0, 0, 1, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, -8, -6],\n [0, 12, 0, 2],\n [0, 0, -6, 0],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 5, -8, -3],\n [6, 11, -4, 2],\n [-10, -11, -2, -10],\n [3, -1, -10, 6]]\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, -2, 9],\n [0, -6, -10, 1],\n [0, 0, 6, -4],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 592 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 1, 3, 1],\n [-12, 6, 10, 9],\n [-6, -11, 6, 11],\n [-12, 4, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 492 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -2, -5, 3],\n [-10, -11, 4, 1],\n [1, -11, 3, 2],\n [-11, -6, 7, -7]]\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": "Compute |A| for the matrix A =\n[[8, 8, -7, 3],\n [-4, 9, 3, 10],\n [-11, 8, -12, 1],\n [9, 9, 5, -6]]\nRound to the nearest integer, then take the result modulo 1000.\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, 12, 2],\n [2, -5, 4, -1],\n [-2, 12, -1, 8],\n [-7, 2, 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"
}
] | 520 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -6, -6, 2],\n [-6, -5, 0, -4],\n [-6, 0, 5, 5],\n [2, -4, 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"
}
] | 96 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 8, 0, 12],\n [-1, -2, -2, 0],\n [10, -12, 2, -7],\n [5, 9, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -4, 9, 7],\n [-4, -2, 4, 0],\n [9, 4, -11, -8],\n [7, 0, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 282 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, 6, -10],\n [12, 6, 2, 3],\n [-4, -1, 0, -8],\n [5, 11, -4, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 458 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 6, 9, 12],\n [-1, -2, 11, -3],\n [-6, -12, -2, -3],\n [11, 1, 9, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 656 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 0, 0, -1],\n [0, -10, -6, -2],\n [0, -6, 5, 4],\n [-1, -2, 4, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 926 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 4, 7, 12],\n [8, -2, -2, -6],\n [-8, 0, 2, 7],\n [-11, -4, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 992 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -6, 10, -2],\n [0, 7, 0, 0],\n [0, 0, -1, 6],\n [0, 0, 0, -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"
}
] | 916 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 2, 0, -9],\n [2, 0, 10, 6],\n [0, 10, -7, 5],\n [-9, 6, 5, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -10, -2, -1],\n [-10, -7, 2, -9],\n [-2, 2, -4, 3],\n [-1, -9, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, 0, 0],\n [1, 7, -8, 0],\n [0, -8, 0, -1],\n [0, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 807 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -2, -4],\n [4, 5, 3, -6],\n [-2, 3, 12, -10],\n [-4, -6, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 314 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -11, 6, -8],\n [6, 6, 11, 4],\n [-9, -8, -3, -1],\n [-6, -10, 2, 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"
}
] | 52 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, -2, 11],\n [2, -7, 1, 0],\n [-2, 1, 1, 6],\n [11, 0, 6, -11]]\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": "Determine the value of det(A) where A =\n[[-3, 11, 4, 2],\n [11, 2, 4, 6],\n [4, 4, -1, 0],\n [2, 6, 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"
}
] | 902 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -3, 9, -12],\n [1, -1, -1, -4],\n [10, 10, 5, -9],\n [-1, -7, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 2, 0, 9],\n [2, -8, -6, -8],\n [0, -6, 7, 6],\n [9, -8, 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"
}
] | 852 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 12, -5],\n [0, 10, -12, 11],\n [0, 0, -1, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 520 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 7, -4, -4],\n [7, 10, 0, -2],\n [-4, 0, 4, 1],\n [-4, -2, 1, -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"
}
] | 553 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, 2, 6],\n [-4, -9, 8, -3],\n [2, 8, -6, 2],\n [6, -3, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 7, 6, -12],\n [-6, -4, -3, 3],\n [9, 4, -12, 12],\n [-6, 6, -7, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -10, -4, -9],\n [6, -11, 7, -10],\n [-2, 4, -11, -12],\n [3, -11, 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"
}
] | 639 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 10, -10, -4],\n [0, 3, -7, -4],\n [0, 0, -8, 4],\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"
}
] | 864 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 12, -4, -10],\n [0, 6, 2, -8],\n [0, 0, 9, -6],\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"
}
] | 56 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -11, -7, -1],\n [0, -10, -7, 5],\n [0, 0, 9, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -10, 10, -11],\n [3, 12, 5, -1],\n [12, 3, 8, -9],\n [11, 9, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 211 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 6, 2, -2],\n [6, 9, 2, 0],\n [2, 2, -2, -8],\n [-2, 0, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -4, 2, -7],\n [0, -4, 2, 6],\n [0, 0, 9, -6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 376 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -4, -8, -6],\n [-4, -5, 5, 4],\n [-8, 5, 12, 6],\n [-6, 4, 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"
}
] | 252 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -2, -6, -12],\n [0, -6, 0, -6],\n [0, 0, 1, 10],\n [0, 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"
}
] | 784 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 12, -4, -2],\n [3, -7, 3, -10],\n [-10, -12, -12, 4],\n [-9, 11, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 428 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 0, -6, 2],\n [0, -6, 2, 4],\n [-6, 2, -6, 4],\n [2, 4, 4, 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"
}
] | 888 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -5, 7],\n [4, 11, -1, 2],\n [-5, -1, -1, 2],\n [7, 2, 2, 12]]? Round to the nearest integer, then express your answer modulo 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[[-2, -10, 12, 2],\n [4, -6, -6, -5],\n [-8, -11, -2, -5],\n [9, 1, -11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 678 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -4, 7],\n [0, -11, -2, 0],\n [-4, -2, 9, -2],\n [7, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 374 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -6, -2, -9],\n [-5, -2, 7, 8],\n [7, -8, 7, 9],\n [-10, 5, -12, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 453 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, 5, -4],\n [0, 6, 0, 9],\n [5, 0, 10, 1],\n [-4, 9, 1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 243 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 10, -12, 8],\n [0, -8, -2, -1],\n [2, -7, 4, 4],\n [12, -4, -11, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 657 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -12, -1, 3],\n [0, 3, -2, 1],\n [-8, -9, 0, 12],\n [0, -9, -8, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 596 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, -7, -1],\n [9, 8, -12, 11],\n [6, -6, 0, -9],\n [-8, 2, 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"
}
] | 182 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -6, -4],\n [2, 9, -4, 4],\n [-6, -4, -7, -1],\n [-4, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 379 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 7, 12, -4],\n [-9, 6, 6, 3],\n [-4, 8, -6, 4],\n [1, 8, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 826 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, -2, 12],\n [0, -10, 7, -3],\n [-2, 7, -8, 1],\n [12, -3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 614 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, 12, -4],\n [0, -4, 2, -7],\n [0, 0, 8, -6],\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"
}
] | 352 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -4, -3, -11],\n [-2, 11, -7, 2],\n [6, 9, 7, 3],\n [0, -4, -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"
}
] | 802 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, 0, -4],\n [8, 3, 2, -1],\n [0, 2, -11, 0],\n [-4, -1, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
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