messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, -4, -4],\n [0, 0, -3, -10],\n [-4, -3, -11, 4],\n [-4, -10, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 354 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -10, 6, -4],\n [-10, 6, -6, 4],\n [6, -6, -11, 4],\n [-4, 4, 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"
}
] | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -7, -3, 1],\n [7, -1, -4, -9],\n [-5, 8, 6, 6],\n [6, 7, -2, 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"
}
] | 925 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 8, -7, -2],\n [0, -2, -7, -4],\n [0, 0, -12, -3],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 728 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -3, -8, 2],\n [-3, -8, 12, -9],\n [-8, 12, -11, -8],\n [2, -9, -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"
}
] | 980 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 8, -11, 3],\n [8, -12, -3, 10],\n [3, 1, 0, 3],\n [0, 7, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 0, -5, 2],\n [0, -8, 10, -2],\n [-5, 10, -8, 2],\n [2, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 900 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -9, 4, 9],\n [-9, -4, 8, -2],\n [4, 8, -12, 0],\n [9, -2, 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"
}
] | 148 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -1, -4, 5],\n [0, -11, 7, -3],\n [0, 0, -5, 1],\n [0, 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"
}
] | 505 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -11, -12, 5],\n [0, 11, 3, -6],\n [0, 0, -1, -2],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, 0, -6],\n [2, 0, -5, 4],\n [0, -5, 7, 5],\n [-6, 4, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 290 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 11, -1, 3],\n [0, 4, 12, -9],\n [0, 0, 8, 11],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 552 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -11, 6, 0],\n [0, 5, 6, -5],\n [0, 0, 3, 7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -6, -5, 0],\n [-6, 7, 6, -7],\n [-5, 6, -9, -3],\n [0, -7, -3, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 847 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -3, 8, -12],\n [0, 11, 8, 0],\n [0, 0, 8, -2],\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"
}
] | 496 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 11, -9, -2],\n [0, -11, 0, -3],\n [0, 0, 7, -9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 153 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 12, -2, 11],\n [0, -7, -6, -8],\n [0, 0, -12, 10],\n [0, 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"
}
] | 880 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -1, -3, 4],\n [11, 11, -12, -3],\n [8, 1, 7, 2],\n [1, 11, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 738 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -1, -12, 6],\n [0, -3, -8, -7],\n [0, 0, -10, -1],\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"
}
] | 440 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -8, 10, -10],\n [9, 0, 2, 10],\n [-7, -4, 7, -7],\n [12, 4, -3, 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"
}
] | 736 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -10, -9, 4],\n [6, 7, 10, -11],\n [-1, 11, 10, -4],\n [-12, -1, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -9, -7, -12],\n [0, 7, -1, -6],\n [0, 0, -5, -9],\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"
}
] | 280 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 9, 6, -12],\n [-6, -4, 8, -1],\n [6, 2, -5, 4],\n [9, -7, 5, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 273 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 10, -9, -8],\n [0, 6, 7, 9],\n [0, 0, 7, -4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 5, -9, 1],\n [0, -3, -9, 8],\n [0, 0, 2, -9],\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"
}
] | 934 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 10, 4, 6],\n [-1, -12, -12, 11],\n [-2, -2, -10, 12],\n [-11, -7, 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"
}
] | 222 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -8, 11, -8],\n [0, -10, 0, -5],\n [0, 0, 4, 10],\n [0, 0, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -4, -5, 10],\n [0, 7, -3, 10],\n [0, 0, 1, 10],\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"
}
] | 168 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 2, -7, -8],\n [2, 6, -11, -1],\n [-7, -11, 2, -1],\n [-8, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -6, -4, -1],\n [-7, -9, 6, 9],\n [0, -6, 2, 2],\n [-8, -6, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -8, -4, 8],\n [0, 3, 3, -10],\n [0, 0, -3, -3],\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"
}
] | 99 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -12, 5, 6],\n [-10, -11, -2, 1],\n [-12, 11, 1, 10],\n [0, -6, 12, 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"
}
] | 559 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, -10, -7],\n [0, 12, 3, -7],\n [0, 0, 10, 2],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, 7, 4],\n [0, -4, -9, 1],\n [0, 0, 5, 3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -2, 2, 12],\n [5, 1, 3, -7],\n [12, 11, -1, -5],\n [-8, 7, 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"
}
] | 270 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 0, -4, 0],\n [0, 1, -1, -4],\n [-4, -1, -5, 2],\n [0, -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"
}
] | 648 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 7, 0, -6],\n [7, -9, 2, 0],\n [0, 2, 0, -5],\n [-6, 0, -5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 633 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -12, 6, 12],\n [2, 4, -6, -10],\n [-4, 2, 8, 12],\n [-3, 9, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 772 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -3, 7, 6],\n [0, 6, 0, -8],\n [0, 0, -1, -1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 406 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 4, -11, -1],\n [0, -3, -10, -3],\n [0, 0, -1, -1],\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"
}
] | 66 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -2, 2, 0],\n [-2, -4, 2, 2],\n [2, 2, -4, 8],\n [0, 2, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -11, -6, -7],\n [0, -5, -11, 6],\n [0, 0, -6, 1],\n [0, 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"
}
] | 900 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -5, -2, 2],\n [12, -4, 9, 6],\n [-2, -8, 11, 8],\n [5, -10, -3, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 3, 8, 12],\n [10, 10, -5, -11],\n [-6, -10, -11, -10],\n [3, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 848 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, -12, -5],\n [0, 4, -10, 6],\n [0, 0, -1, -9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 0, 6, 6],\n [0, -1, -2, -6],\n [6, -2, 5, 0],\n [6, -6, 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"
}
] | 236 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 12, 4, 12],\n [0, -1, -10, 2],\n [0, 0, 4, -11],\n [0, 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"
}
] | 264 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -5, -12, -3],\n [-1, 5, -9, -12],\n [-7, -11, -7, 11],\n [-10, -11, -6, 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"
}
] | 716 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -5, 9, -6],\n [-10, -2, 9, 1],\n [0, 10, -11, 4],\n [12, 7, 2, 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"
}
] | 707 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 8, -11, -1],\n [0, 9, 0, -9],\n [0, 0, -11, 6],\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"
}
] | 584 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 9, -6, 11],\n [2, 3, 5, 6],\n [10, -7, -1, -6],\n [8, 11, -10, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 712 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 6, 11, -6],\n [-12, 0, -3, 10],\n [-11, -10, -2, 9],\n [0, 9, 5, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 282 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -11, 3, -3],\n [0, -10, 6, -7],\n [0, 0, -5, -10],\n [0, 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"
}
] | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -1, 4, -4],\n [-1, 10, 10, 7],\n [4, 10, -3, 2],\n [-4, 7, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 272 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 4, 1, 2],\n [4, 4, -10, -6],\n [1, -10, -6, 7],\n [2, -6, 7, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 12, 10, 7],\n [12, 2, -2, 12],\n [-2, 9, 0, 5],\n [7, -8, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 986 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -12, -12, 9],\n [0, 12, 3, -7],\n [0, 0, 8, 6],\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"
}
] | 608 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 6, -3, 0],\n [-1, 0, -9, -12],\n [0, 12, -12, -10],\n [12, 5, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 318 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 4, -9, -11],\n [0, 2, -4, 8],\n [0, 0, 10, -4],\n [0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -7, -11, 0],\n [0, -4, 7, 12],\n [0, 0, -9, -8],\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"
}
] | 20 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -8, 0, -6],\n [-8, 2, -4, 6],\n [0, -4, -12, 0],\n [-6, 6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 296 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 2, 3, -5],\n [2, 6, 5, 1],\n [3, 5, -4, -4],\n [-5, 1, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 802 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -9, -1, 6],\n [8, -5, -4, -8],\n [2, 1, 10, -4],\n [-9, 9, 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"
}
] | 920 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 10, 0, -3],\n [10, 4, 8, -4],\n [-7, -6, -2, 1],\n [1, -6, 7, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, -8, 11],\n [-12, 10, 1, -12],\n [10, 0, 6, -11],\n [1, -2, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 594 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, 5, 9],\n [0, 8, 1, 8],\n [0, 0, -4, -5],\n [0, 0, 0, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 328 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, -3, 7],\n [-3, 4, 1, -12],\n [8, 9, 8, 8],\n [-5, -11, 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"
}
] | 321 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -6, 8, 1],\n [7, 6, 10, 6],\n [6, -8, 6, -1],\n [11, 1, 10, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 850 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -4, 5, 9],\n [-7, -12, 1, -7],\n [-6, 9, -12, -1],\n [4, -5, 10, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 505 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -7, 12, 8],\n [0, -7, 6, 1],\n [2, 11, 3, -9],\n [-4, 2, -11, 8]]? 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[[0, -4, 9, -4],\n [10, 11, 11, 6],\n [-1, 2, -1, 4],\n [-8, 1, 11, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 942 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -7, 1, 0],\n [0, -11, 3, -3],\n [0, 0, -8, 5],\n [0, 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"
}
] | 120 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -9, -2, 2],\n [-9, 3, -2, -4],\n [-2, -2, 8, 4],\n [2, -4, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 312 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -6, 5, 10],\n [-6, 0, -4, -8],\n [5, -4, 10, 6],\n [10, -8, 6, 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"
}
] | 648 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -8, -1, 8],\n [0, -6, 5, 1],\n [0, 0, -6, -1],\n [0, 0, 0, 1]]\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, -8, -2, -5],\n [0, 8, -5, -7],\n [0, 0, -5, 11],\n [0, 0, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -3, -5, -12],\n [-3, -6, 4, -8],\n [-5, 4, -12, 5],\n [-12, -8, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 329 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 3, -2, -4],\n [3, 0, 2, 6],\n [-2, 2, -2, 3],\n [-4, 6, 3, -10]]\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": "Compute |A| for the matrix A =\n[[6, -2, 6, 1],\n [-2, 2, -1, -10],\n [6, -1, 5, -3],\n [1, -10, -3, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -8, 0, -11],\n [-8, 5, -6, 0],\n [0, -6, -5, 0],\n [-11, 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"
}
] | 741 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -9, -11, -11],\n [0, -6, -1, 5],\n [0, 0, 9, -10],\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"
}
] | 436 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 4, 4, -8],\n [4, 0, 8, 2],\n [4, 8, -7, 0],\n [-8, 2, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -8, 8, -4],\n [0, 6, 11, 6],\n [0, 0, -4, -4],\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"
}
] | 624 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -7, -4, -7],\n [7, 11, -4, 6],\n [-2, 4, 7, 3],\n [-6, -1, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 6, 12, 5],\n [0, 9, 10, -7],\n [0, 0, -1, 3],\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"
}
] | 972 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, -10, -8],\n [0, -6, 9, 6],\n [-10, 9, 8, -4],\n [-8, 6, -4, -9]]\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[[-6, 4, 5, -2],\n [0, -8, -12, -5],\n [0, 0, 12, 4],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 10, -9, 9],\n [0, -8, -1, -12],\n [0, 0, -2, 3],\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"
}
] | 120 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 10, -5, -6],\n [0, 6, -12, -4],\n [0, 0, -1, 0],\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"
}
] | 538 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 6, 0, 6],\n [6, 0, -6, 6],\n [0, -6, -1, 10],\n [6, 6, 10, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 620 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, -10, 0],\n [-7, -12, 0, -4],\n [-10, 0, 5, -2],\n [0, -4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 871 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -4, -3, -8],\n [-4, 0, 6, -8],\n [-3, 6, -1, 6],\n [-8, -8, 6, 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"
}
] | 80 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -3, -2, 0],\n [2, 3, 7, 5],\n [11, -6, -8, -8],\n [-5, -10, 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"
}
] | 931 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 2, 4, -10],\n [2, -3, -7, 1],\n [4, -7, 10, 5],\n [-10, 1, 5, -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"
}
] | 132 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 8, 4, 4],\n [8, -11, 2, -7],\n [4, 2, -4, 2],\n [4, -7, 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"
}
] | 160 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 6, 2, 1],\n [0, 7, 9, -5],\n [0, 0, -11, -5],\n [0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 616 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -2, -3, 4],\n [-2, -12, 6, -6],\n [-3, 6, 8, -2],\n [4, -6, -2, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -7, 9, -12],\n [-6, 2, -7, 8],\n [8, -6, -11, -7],\n [-1, -12, -6, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 469 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 7, -10, 11],\n [-1, -5, -12, -5],\n [-1, 4, -4, 7],\n [9, 7, -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"
}
] | 84 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -2, 10, -10],\n [3, -6, -10, 11],\n [-10, 10, 0, 12],\n [-5, -6, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 380 | MATH |
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