messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -4, -11, 2],\n [-10, 1, -10, 0],\n [-5, 11, -1, -4],\n [3, 7, 11, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 291 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 8, 8, 2],\n [0, 2, 8, -5],\n [0, 0, 3, -6],\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"
}
] | 664 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 0, 3, -8],\n [0, -1, 3, -2],\n [3, 3, 8, 2],\n [-8, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -12, -10, -1],\n [0, -10, -1, -3],\n [0, 0, -6, 1],\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"
}
] | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 1, 7, 8],\n [1, -6, 2, -6],\n [7, 2, -8, -7],\n [8, -6, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 949 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, -8, 3],\n [0, 3, -2, 5],\n [0, 0, -8, -3],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 384 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 12, 6, 4],\n [0, -6, 1, -7],\n [0, 0, -7, 11],\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"
}
] | 496 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -6, -1, -5],\n [5, -9, 3, 7],\n [-8, 9, -11, -7],\n [8, -6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 373 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, -12, 6],\n [0, 8, 12, -10],\n [0, 0, -6, 9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 3, 8, -8],\n [3, -5, 8, 2],\n [8, 8, 11, 4],\n [-8, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 9, -3, -9],\n [0, -8, -2, 11],\n [0, 0, -5, -11],\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"
}
] | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -7, -11, 10],\n [-3, 12, -11, 4],\n [-8, -4, -5, -2],\n [-8, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 1, -6, -7],\n [0, -2, 9, -4],\n [0, 0, -6, 1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -1, 0, -2],\n [-1, 4, -2, -9],\n [-6, -12, 10, 11],\n [-9, 10, -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"
}
] | 120 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -5, 2, -1],\n [-3, -1, -2, -4],\n [8, -11, -7, -9],\n [-3, -4, -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"
}
] | 792 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 5, 11, 6],\n [0, -5, 0, -6],\n [0, 0, 4, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 0, 5, -2],\n [-7, 10, 7, 1],\n [3, -1, -3, 4],\n [7, -12, -12, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 882 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -6, 2, -5],\n [0, -3, 4, 5],\n [0, 0, -1, 10],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -8, -6, 7],\n [0, -4, 8, 7],\n [0, 0, 6, 7],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -5, -5, 7],\n [-2, -11, 5, 7],\n [8, 6, 4, 2],\n [-3, 8, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 364 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -11, 3, -1],\n [7, 8, 8, 11],\n [8, 11, 9, 10],\n [3, -9, 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"
}
] | 421 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 6, -12, -11],\n [0, 11, -4, -2],\n [0, 0, 11, -6],\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"
}
] | 911 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 2, 11, -8],\n [8, 11, -9, 7],\n [-7, -7, -10, -7],\n [-11, 2, -8, -11]]\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, 1],\n [-2, 8, 6, -4],\n [-4, 6, -2, -6],\n [1, -4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -12, 0, 11],\n [-9, 8, 12, -1],\n [-4, -11, -2, -3],\n [1, 6, -1, 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"
}
] | 82 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, -5, 6],\n [0, -4, 7, -5],\n [0, 0, 10, -1],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 4, 2, -4],\n [4, 9, -10, -8],\n [2, -10, 10, 4],\n [-4, -8, 4, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 778 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -5, -2, 2],\n [12, -8, -4, -5],\n [6, 2, -11, 6],\n [-8, 9, 7, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -4, 0],\n [0, 7, -5, 10],\n [0, 0, 6, 6],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 12, 9, 6],\n [0, 4, -12, -12],\n [0, 0, -8, -12],\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"
}
] | 920 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 2, 0, 6],\n [2, 6, 4, 7],\n [0, 4, 3, 0],\n [6, 7, 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"
}
] | 340 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -12, -9, -8],\n [-4, -3, 8, 11],\n [-10, 0, -7, -1],\n [8, -12, -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"
}
] | 511 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 5, -4, 8],\n [-4, 10, -5, -3],\n [-9, -11, 0, 9],\n [-11, -9, -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"
}
] | 844 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -4, 0, -12],\n [-4, -3, -6, 3],\n [0, -6, -10, 0],\n [-12, 3, 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"
}
] | 20 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 5, 11, 3],\n [0, -1, -4, 9],\n [0, 0, 1, 12],\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"
}
] | 955 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -1, -3, -12],\n [-11, 9, -10, 0],\n [-1, 1, -2, 2],\n [4, -8, -6, 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"
}
] | 822 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 3, 2, -4],\n [1, -9, 10, 2],\n [8, 6, 2, -9],\n [7, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 514 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 9, 12, 10],\n [0, -7, 5, -6],\n [0, 0, -10, 0],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 650 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -3, 8, 0],\n [-3, 7, 11, -9],\n [8, 11, 3, 2],\n [0, -9, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 654 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 6, 6, -10],\n [1, 3, 2, 11],\n [9, 1, 12, 3],\n [-2, -12, 7, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 452 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 4, 12, 6],\n [2, -4, 4, 3],\n [7, 10, 4, -1],\n [-9, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 6, -1, 3],\n [6, -12, -1, 2],\n [-1, -1, -11, -4],\n [3, 2, -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"
}
] | 589 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -1, 0, 4],\n [-2, 6, -3, 3],\n [3, -7, -1, 11],\n [11, 0, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 902 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -10, 6, 4],\n [2, -3, -2, 7],\n [12, 4, -9, -4],\n [-3, -6, 1, -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"
}
] | 775 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 0, 8, -12],\n [0, 9, 3, -2],\n [8, 3, -5, 4],\n [-12, -2, 4, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 844 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, -12, -6],\n [-2, 4, -2, 8],\n [-12, -2, -10, 0],\n [-6, 8, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 888 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, 6, 0],\n [8, 11, -6, 3],\n [0, 5, 3, -6],\n [7, -6, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 675 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, 2, 9, -7],\n [-4, -3, 8, -7],\n [-2, -3, 5, 11],\n [7, -7, -3, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 470 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 6, 0, 7],\n [0, 1, 3, 10],\n [0, 0, -9, -3],\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"
}
] | 136 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -9, 0, 7],\n [-5, -1, 11, -11],\n [4, -9, 12, -4],\n [11, 6, 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"
}
] | 449 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 11, -12, 5],\n [0, -12, 2, -10],\n [0, 0, -7, 2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 2, 2, 2],\n [2, 10, -2, 0],\n [2, -2, -10, -7],\n [2, 0, -7, 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"
}
] | 866 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, -3, 1],\n [4, -9, -3, 7],\n [-3, -3, -4, -2],\n [1, 7, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, 0, -4],\n [-12, 0, 4, 4],\n [11, 12, 3, 8],\n [9, 2, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 2, 0, 0],\n [2, -8, 0, 0],\n [0, 0, -8, -2],\n [0, 0, -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"
}
] | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -2, -3, -11],\n [-2, 8, -5, 6],\n [-3, -5, -2, 2],\n [-11, 6, 2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 427 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 0, 0, -10],\n [0, 1, 0, -8],\n [0, 0, 8, 5],\n [-10, -8, 5, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 583 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 5, 10, 5],\n [0, -3, -11, -7],\n [0, 0, 9, 10],\n [0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 136 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 6, -2, 2],\n [6, 10, -4, 0],\n [-2, -4, -3, 2],\n [2, 0, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -12, 6, 10],\n [0, 8, -12, 9],\n [0, 0, -6, 12],\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"
}
] | 952 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -6, -10, 7],\n [12, 12, -10, 4],\n [-5, 7, 3, 9],\n [-3, 0, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 522 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 3, -1, 8],\n [3, 7, -8, 8],\n [-1, -8, -11, 1],\n [8, 8, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 547 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -3, 2],\n [-2, -7, -2, 10],\n [-3, -2, -12, -4],\n [2, 10, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 372 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 5, 1, 4],\n [-2, -4, -12, 4],\n [5, 7, 2, 9],\n [12, 12, 11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 8, 4, -2],\n [5, -9, 1, 2],\n [5, 8, 11, 7],\n [3, -3, -6, 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"
}
] | 482 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 12, 4, -9],\n [10, -10, -1, -4],\n [1, -4, 4, 1],\n [5, -8, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 994 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -2, 6, -2],\n [-2, 12, -5, 9],\n [6, -5, 11, 0],\n [-2, 9, 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"
}
] | 500 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -4, -1, -6],\n [-4, 7, 3, -6],\n [-1, 3, -12, -10],\n [-6, -6, -10, 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"
}
] | 100 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 4, 1, 3],\n [4, 0, 3, -4],\n [1, 3, 11, -1],\n [3, -4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 963 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 4, -12, 0],\n [0, -6, -5, -11],\n [0, 0, -1, 12],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 820 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -9, 2, -2],\n [0, 7, 8, 3],\n [0, 0, -2, 6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 8, 1, 4],\n [0, -3, -9, 9],\n [0, 0, -10, -3],\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"
}
] | 690 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 4, 1, 0],\n [4, 6, 1, 6],\n [1, 1, -1, -4],\n [0, 6, -4, -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"
}
] | 52 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -10, 9, -12],\n [0, 12, -9, -8],\n [0, 0, -1, -4],\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"
}
] | 152 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, 2, -6],\n [0, -5, -6, 10],\n [2, -6, 4, 1],\n [-6, 10, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 12, 6, 1],\n [-3, 9, 3, -11],\n [-5, -12, 10, -7],\n [-4, -3, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, -11, 11],\n [-12, 6, 2, -2],\n [-11, 8, -9, -6],\n [-12, 6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -1, 0, 5],\n [2, 0, 3, 8],\n [4, -12, 8, 2],\n [2, -11, 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"
}
] | 382 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, -9, 5],\n [-5, 2, 4, 0],\n [-9, -7, 4, -1],\n [1, 4, 12, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 841 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -7, 0, -2],\n [7, 11, 5, -1],\n [6, -6, -4, 0],\n [-2, -12, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, 8, 0],\n [2, 9, -3, 2],\n [8, -3, -10, -5],\n [0, 2, -5, 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"
}
] | 616 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, 5, -2, -11],\n [0, 6, 12, -2],\n [0, 0, -8, -2],\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"
}
] | 168 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -6, 10, 6],\n [-6, -3, 10, -1],\n [10, 10, -6, 0],\n [6, -1, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 608 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -2, -2, -1],\n [-2, 12, -4, -10],\n [-2, -4, 3, -2],\n [-1, -10, -2, -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"
}
] | 784 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -5, 4, -7],\n [-5, 8, -4, -2],\n [4, -4, 4, 6],\n [-7, -2, 6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 876 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 4, 1, 10],\n [-4, -7, 3, -8],\n [-4, 5, 9, -11],\n [0, 1, 7, -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"
}
] | 964 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -8, 6, -2],\n [4, -1, 6, -7],\n [-7, 1, -8, 2],\n [7, 4, 1, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 3, -1, 4],\n [3, 11, 4, -3],\n [-1, 4, 11, -2],\n [4, -3, -2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 6, -5, 0],\n [6, 4, -8, 8],\n [-5, -8, -3, 0],\n [0, 8, 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"
}
] | 592 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -6, -9],\n [-5, 0, -7, -1],\n [-8, 6, 0, 8],\n [-8, -9, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 700 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 4, -6, 6],\n [4, -4, -2, 2],\n [-6, -2, 6, -10],\n [6, 2, -10, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 952 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 5, 10, 3],\n [1, 7, 2, 4],\n [3, -7, -4, -2],\n [7, -8, -12, -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"
}
] | 956 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 10, -9, -2],\n [10, 12, -6, -6],\n [-9, -6, 7, 4],\n [-2, -6, 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"
}
] | 376 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -5, -9, 12],\n [5, 9, 2, 0],\n [11, 6, 12, 1],\n [3, -1, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 921 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, 6, -8],\n [4, 7, -6, -6],\n [6, -6, 1, -10],\n [-8, -6, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 301 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -4, -2, 0],\n [-4, -6, -1, -6],\n [-2, -1, -5, 8],\n [0, -6, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 718 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 9, -8, -8],\n [-7, 6, -9, -10],\n [7, 9, -12, -4],\n [3, 9, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -3, 11, 5],\n [-8, -2, -1, 5],\n [-1, 11, 11, -3],\n [12, -10, -2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 740 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -2, -12, -2],\n [0, 2, -2, -5],\n [0, 0, -11, -9],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 5, -1, -6],\n [8, 11, -1, -11],\n [8, -8, 9, 10],\n [7, 11, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 125 | MATH |
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