messages listlengths 1 1 | ground_truth stringclasses 992
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 10, 4, 0],\n [10, -1, 0, 0],\n [4, 0, 6, -5],\n [0, 0, -5, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 890 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -2, -11, -2],\n [-2, -3, -6, 0],\n [-11, -6, -8, 4],\n [-2, 0, 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"
}
] | 943 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -2, -9, 1],\n [-9, 0, 1, 1],\n [-10, 2, 10, 5],\n [-12, -4, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -1, 0],\n [-2, 9, 7, -9],\n [-1, 7, -11, 1],\n [0, -9, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 808 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 8, -3, -6],\n [-8, -9, 8, -2],\n [3, 7, -11, 5],\n [0, 6, -7, 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"
}
] | 751 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, 1, -2],\n [-4, 4, -1, 2],\n [1, -1, 10, -1],\n [-2, 2, -1, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 436 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -4, -12, 3],\n [-10, -5, 5, -8],\n [-1, -1, 12, 2],\n [0, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 115 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -10, -4, 0],\n [0, 12, 7, -1],\n [0, 0, -4, -12],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 296 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -2, 2, -7],\n [-6, 3, 5, 0],\n [-2, -2, -11, -12],\n [-6, -12, -8, -1]]? Round to the nearest integer, then express your answer 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[[-7, 3, 8, -2],\n [3, 12, 6, 8],\n [8, 6, 6, -4],\n [-2, 8, -4, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 272 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, -4, -4],\n [2, 8, -2, -1],\n [-4, -2, -10, -4],\n [-4, -1, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -7, 11, 6],\n [-9, 9, -10, 12],\n [-9, -1, -5, 2],\n [-8, -10, -8, -8]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -3, -1, 6],\n [10, 11, 4, 0],\n [-12, 2, -9, -2],\n [3, 11, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 895 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 5, 3, -10],\n [0, 11, 8, -4],\n [0, 0, -4, -8],\n [0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -8, -2, 0],\n [-8, -9, -1, 0],\n [-2, -1, -2, 12],\n [0, 0, 12, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 5, 12, 10],\n [0, -7, 11, -11],\n [0, 0, -3, 6],\n [0, 0, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 790 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -2, -3, 8],\n [7, 9, 11, 0],\n [0, -4, 5, -8],\n [3, 7, -11, 9]]\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": "Compute |A| for the matrix A =\n[[-5, 8, 4, 6],\n [8, 8, 5, 2],\n [4, 5, 5, -6],\n [6, 2, -6, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 777 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 2, 0, 2],\n [2, -7, -2, 8],\n [0, -2, -12, 4],\n [2, 8, 4, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 664 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -11, 1, -10],\n [0, -10, 3, -4],\n [0, 0, -3, -7],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 520 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 0, 8, -12],\n [0, -4, 7, 5],\n [-6, -5, -7, 3],\n [5, 11, -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"
}
] | 676 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -5, -8, 6],\n [-3, 9, -4, -6],\n [7, -3, 11, 10],\n [-11, 5, -11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -7, -12, 8],\n [9, 6, 6, 6],\n [9, 0, 0, 10],\n [-12, 0, 3, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 940 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -7, 6, 2],\n [0, -9, 7, -10],\n [0, 0, 5, -1],\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"
}
] | 700 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -7, -3, -8],\n [-8, 12, -5, 5],\n [10, -4, -12, -5],\n [-1, -8, -11, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 849 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -4, -10, -1],\n [-4, 7, -6, -6],\n [-10, -6, -11, -2],\n [-1, -6, -2, 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"
}
] | 654 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -1, -12, -2],\n [5, 1, 12, 0],\n [9, 7, 4, 5],\n [-6, -12, 6, 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"
}
] | 230 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -6, 3, 0],\n [-6, -1, 1, -2],\n [3, 1, -1, -2],\n [0, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 446 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 9, -9, -1],\n [0, 2, 9, -3],\n [0, 0, 12, -3],\n [0, 0, 0, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -7, -9, 10],\n [0, -3, -9, 5],\n [0, 0, 7, 2],\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"
}
] | 748 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 9, -12, 11],\n [12, -12, -9, -8],\n [-9, 5, 12, 10],\n [1, 0, 12, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 187 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, 6, -4],\n [-6, -9, -6, 11],\n [-4, -6, -11, 7],\n [-10, -1, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 736 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 10, 8, 9],\n [-4, -11, -11, -5],\n [10, -8, 2, -7],\n [-4, 4, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 964 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -3, -2, -11],\n [0, 6, 7, -9],\n [0, 0, 11, -12],\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"
}
] | 168 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -11, -1, 3],\n [-7, -7, -10, 11],\n [-9, 8, 8, -12],\n [7, 3, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -11, -10, -9],\n [0, 7, -12, 8],\n [0, 0, 10, -11],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -12, 2, 4],\n [0, 5, 8, 3],\n [0, 0, -3, 0],\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"
}
] | 825 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 5, -1, 12],\n [1, 6, -5, 4],\n [12, 12, -7, 12],\n [0, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 830 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 0, -4, 11],\n [0, -2, -10, -7],\n [-4, -10, -4, 0],\n [11, -7, 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"
}
] | 508 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, -11, -5],\n [0, 1, 0, 10],\n [-11, 0, -6, 2],\n [-5, 10, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -6, -4, 4],\n [-6, 11, -7, -1],\n [-4, -7, -4, -4],\n [4, -1, -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"
}
] | 882 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -10, 2, -4],\n [-10, 1, 2, 0],\n [2, 2, 12, -6],\n [-4, 0, -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"
}
] | 680 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -11, -9, -11],\n [12, 3, -1, 1],\n [10, 2, 7, 6],\n [11, -11, 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"
}
] | 771 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 3, 8, -6],\n [0, 2, 4, -3],\n [0, 0, -5, -12],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -3, 12, -9],\n [0, 2, -6, 10],\n [0, 0, 7, 8],\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"
}
] | 14 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -6, 6, 2],\n [-6, -12, 4, -3],\n [6, 4, 5, -2],\n [2, -3, -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"
}
] | 297 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -2, 4, 2],\n [-2, 9, 2, -2],\n [4, 2, -3, -6],\n [2, -2, -6, 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"
}
] | 252 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 11, -10, -5],\n [0, 4, 9, -12],\n [0, 0, -12, -4],\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"
}
] | 480 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -12, -2, 3],\n [1, 11, -2, -8],\n [0, 8, 9, 4],\n [-2, -1, -9, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 757 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 7, 3, 7],\n [0, -4, 4, -12],\n [0, 0, -5, -10],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 2, 6, 0],\n [-5, -4, 11, -10],\n [4, 6, 5, -9],\n [2, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 848 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 4, -1, 0],\n [4, -6, 2, 1],\n [-1, 2, -11, 0],\n [0, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, 2, 2],\n [-4, -1, 6, -2],\n [2, 6, 7, 0],\n [2, -2, 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"
}
] | 463 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -2, -10, -8],\n [-7, 3, 4, 5],\n [-3, 8, -11, 9],\n [6, 1, 12, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 456 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -8, -4, 2],\n [-8, -4, 1, -6],\n [-4, 1, 4, 0],\n [2, -6, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 648 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -12, -1, 5],\n [1, 11, -3, 6],\n [8, 10, 2, 1],\n [3, 7, 2, -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"
}
] | 394 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -9, -10, -6],\n [12, -1, -5, 1],\n [6, 10, 3, -7],\n [-4, -5, -4, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -2, 7, -1],\n [0, -3, -10, 5],\n [0, 0, -12, 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"
}
] | 208 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -4, 4, 3],\n [-4, 7, 0, -2],\n [4, 0, 6, 7],\n [3, -2, 7, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 702 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 2, 12, 9],\n [0, 6, 8, 8],\n [0, 0, -2, -9],\n [0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -7, -1, -7],\n [0, -7, 6, 3],\n [0, 0, -5, -8],\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"
}
] | 750 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 4, 9, 0],\n [1, -9, -9, 5],\n [12, 11, -12, -7],\n [6, 5, 7, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 896 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -6, 0, 2],\n [-6, -10, 4, -2],\n [0, 4, 1, -2],\n [2, -2, -2, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -2, -6, 11],\n [-9, -6, -6, 1],\n [-1, 7, 2, 10],\n [7, 7, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 616 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -2, 6, 0],\n [0, 12, -5, 2],\n [0, 0, -6, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -12, -10, -12],\n [-8, 6, 1, 5],\n [-8, 2, 11, 2],\n [2, -1, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 314 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -2, -6, 12],\n [10, 7, 9, 8],\n [-2, 9, -8, -6],\n [2, -3, -4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -2, -12, -2],\n [0, 1, 4, 11],\n [0, 0, 8, 4],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 336 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -3, 6, -7],\n [0, 10, -1, -1],\n [0, 0, 5, 8],\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"
}
] | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -1, -5, 8],\n [-1, -6, -5, -11],\n [-5, -5, 9, -6],\n [8, -11, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 952 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 5, 5, -5],\n [0, 3, -5, 6],\n [0, 0, -8, 3],\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"
}
] | 424 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -10, 0, 9],\n [7, 9, 6, -12],\n [4, 4, 3, -5],\n [-9, 0, 5, -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"
}
] | 443 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -11, 8, -4],\n [0, -9, -5, 5],\n [0, 0, -12, -3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 776 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 1, -2, -4],\n [1, 9, 2, -1],\n [-2, 2, -3, 1],\n [-4, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 555 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, 3, 2, 2],\n [3, -5, 0, 0],\n [2, 0, -1, -1],\n [2, 0, -1, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 710 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 12, 7, 12],\n [-1, 12, -4, 6],\n [-9, 10, 12, 0],\n [1, -10, 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"
}
] | 554 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 1, -10, 3],\n [1, 9, -8, -2],\n [-10, -8, -5, -2],\n [3, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 369 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -7, -4, -4],\n [2, 0, 1, -8],\n [2, 0, 2, -11],\n [-6, -1, 3, 5]]\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": "What is the determinant of the matrix:\n[[-2, 1, 0, -2],\n [0, -8, 12, 8],\n [0, 0, -10, -1],\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"
}
] | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 5, 1, 0],\n [-3, -8, -10, 6],\n [11, -11, -1, -1],\n [1, -7, -6, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 775 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 12, 6, -1],\n [0, -3, -8, 12],\n [0, 0, -8, -5],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -3, 0, 5],\n [0, -10, -11, 0],\n [0, 0, -4, -6],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -4, 6, 4],\n [0, 11, -12, 11],\n [0, 0, 9, 0],\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"
}
] | 584 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -10, -2, -5],\n [9, 10, -10, 12],\n [-5, 6, 5, -12],\n [12, 1, 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"
}
] | 37 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, -5, -2],\n [-12, 2, 5, 11],\n [-4, 2, 12, -3],\n [-12, 8, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 764 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -3, -11, -11],\n [0, 8, 5, 7],\n [0, 0, -12, 3],\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"
}
] | 880 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -2, 5, 10],\n [0, 1, 12, -1],\n [0, 0, -5, -9],\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"
}
] | 120 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 10, -8, 2],\n [0, -12, 0, -3],\n [0, 0, -3, 7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 252 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 2, 10, 2],\n [2, 8, 10, -8],\n [10, 10, 3, 6],\n [2, -8, 6, 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"
}
] | 260 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, 10, 0],\n [-1, 4, 4, -9],\n [10, 4, 7, 12],\n [0, -9, 12, 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"
}
] | 227 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, 7, 10],\n [6, 4, 1, 0],\n [12, 3, 8, -4],\n [-4, -4, -4, 0]]\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[[9, 0, -8, -4],\n [-8, 6, 3, 1],\n [6, -9, 4, -11],\n [-5, -4, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 899 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 11, 1, 10],\n [2, 6, 12, 12],\n [4, -1, 2, 10],\n [6, 4, -11, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 776 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 1, 9, 7],\n [0, -3, -7, 6],\n [0, 0, 10, -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"
}
] | 720 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -4, -8, 9],\n [0, 8, -7, 9],\n [0, 0, 7, 0],\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"
}
] | 104 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 3, 8, -1],\n [-5, 12, -8, -2],\n [-9, 4, 12, -11],\n [-9, -9, 1, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 751 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 9, 12, 7],\n [0, -1, -10, -9],\n [0, 0, -9, -3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -4, 2, -10],\n [0, -3, 9, -11],\n [0, 0, 3, 8],\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"
}
] | 648 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 4, 6, 12],\n [0, -2, -12, -3],\n [0, 0, -9, -9],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 3, -7, 2],\n [-7, 6, -2, -6],\n [2, 1, 5, -11],\n [12, -10, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | MATH |
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