messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 3, -2, -5],\n [0, 5, -4, 4],\n [0, 0, -1, -1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 495 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 0, -3, 7],\n [-7, 10, 1, -8],\n [-11, 0, -1, 5],\n [-10, 11, -9, 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"
}
] | 612 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 8, -10, -6],\n [4, -6, -4, 1],\n [-11, 7, 2, 10],\n [-3, -8, -5, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 573 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, 3, -4, -5],\n [-11, 7, 5, 1],\n [7, -1, 2, 2],\n [12, 10, -4, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 874 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 11, -11, -5],\n [-4, 5, -8, -9],\n [-3, 3, 3, 7],\n [8, 12, 10, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 579 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -3, 1, 9],\n [0, -8, -7, 4],\n [0, 0, 6, 9],\n [0, 0, 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"
}
] | 960 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -12, -11, 12],\n [0, 11, 9, -3],\n [0, 0, -1, 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"
}
] | 847 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 5, 9, -8],\n [-5, -3, 6, 9],\n [5, -12, -11, -8],\n [-7, 1, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 869 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -4, -1, 6],\n [-4, 5, -2, -6],\n [-1, -2, -11, 4],\n [6, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 7, 6, -9],\n [0, 7, -11, 8],\n [0, 0, -3, -1],\n [0, 0, 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"
}
] | 580 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, 0, -10, -6],\n [-5, -2, 7, -1],\n [1, -2, -10, 11],\n [-3, -4, 12, 4]]? 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": "Compute |A| for the matrix A =\n[[-12, 8, -11, -5],\n [8, 10, 4, 5],\n [-11, 4, -1, 2],\n [-5, 5, 2, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 495 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 7, -6, 6],\n [7, -3, 2, 6],\n [-6, 2, 3, 12],\n [6, 6, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 402 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 8, -1, 4],\n [0, 11, 7, -6],\n [0, 0, 11, -12],\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"
}
] | 459 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, 9, -11],\n [0, 2, -12, 11],\n [0, 0, 5, 1],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -8, -11, 2],\n [0, -10, 7, -12],\n [0, 0, -7, -8],\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"
}
] | 600 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 6, 11, 0],\n [5, 3, 2, -3],\n [-2, 7, 2, 10],\n [6, -6, -2, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 962 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -8, -5, 3],\n [0, 3, -2, -2],\n [0, 0, 4, 3],\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"
}
] | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 5, -1, 12],\n [0, -5, 3, 12],\n [0, 0, 7, -11],\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[[4, -5, -6, 5],\n [0, 12, -5, 12],\n [0, 0, -11, 12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 336 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -6, 2, 2],\n [-6, -10, 4, -6],\n [2, 4, 12, -2],\n [2, -6, -2, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 328 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 3, 8, 7],\n [7, -2, -12, -1],\n [1, 8, 4, 10],\n [0, -1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 970 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -9, -9, 12],\n [0, 2, 9, 0],\n [0, 0, -6, -1],\n [0, 0, 0, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 812 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, -4, -4],\n [0, -6, 3, -5],\n [-4, 3, -5, -4],\n [-4, -5, -4, 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"
}
] | 721 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 8, -5, -4],\n [8, 12, -6, -4],\n [-5, -6, -6, 2],\n [-4, -4, 2, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 896 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -8, -7, -10],\n [0, 1, -12, -10],\n [0, 0, -3, 10],\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"
}
] | 324 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 2, 11, -9],\n [2, 10, -3, -1],\n [11, -3, -11, 4],\n [-9, -1, 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"
}
] | 826 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -6, 1, 0],\n [-6, -2, 3, -11],\n [1, 3, 6, -6],\n [0, -11, -6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 459 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, -1, -7],\n [-5, 5, -3, -11],\n [-12, -5, 8, -3],\n [-2, 5, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 731 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 2, 12, -1],\n [2, -4, -2, -1],\n [12, -2, 0, -1],\n [-1, -1, -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"
}
] | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 8, -11, 11],\n [0, 10, 6, 11],\n [0, 0, -3, -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"
}
] | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 5, -6, -2],\n [6, -4, 6, 4],\n [-3, 8, -4, 7],\n [-7, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -4, 11, 10],\n [2, 1, -9, 8],\n [-6, 12, 1, 11],\n [6, -9, -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"
}
] | 781 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 6, 10, 9],\n [0, -4, -5, 2],\n [0, 0, 2, 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"
}
] | 888 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 10, -10, -11],\n [0, 11, -5, -8],\n [0, 0, -1, 1],\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"
}
] | 967 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -9, 6, 2],\n [0, 12, 9, -6],\n [0, 0, -2, 10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 568 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 6, -12, -4],\n [0, -5, -1, -3],\n [0, 0, -3, -3],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 2, -12, 11],\n [0, 1, -1, -2],\n [0, 0, 3, 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"
}
] | 48 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -4, 5, 3],\n [0, 10, -10, -10],\n [0, 0, -6, 12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 11, 4, -7],\n [0, -7, 1, -6],\n [0, 0, 9, 10],\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"
}
] | 149 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -4, 9, 6],\n [2, -10, 10, 6],\n [6, -5, 8, 9],\n [9, -12, -8, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 566 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, -9, -10, 6],\n [0, 6, -11, -9],\n [0, 0, -8, 8],\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"
}
] | 240 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -3, -4, 3],\n [-3, 2, 2, 1],\n [-4, 2, 1, 2],\n [3, 1, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 6, 2, -4],\n [6, 5, -2, 2],\n [2, -2, 2, -2],\n [-4, 2, -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"
}
] | 860 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -6, 3, 0],\n [0, -6, -6, 0],\n [0, 0, 2, -11],\n [0, 0, 0, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 3, 0, -2],\n [3, 8, -4, 8],\n [0, -4, -2, 1],\n [-2, 8, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -4, -8, 12],\n [0, -7, 3, 2],\n [0, 0, -3, 8],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 228 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 1, 9, -12],\n [7, 2, 11, -3],\n [11, 11, 0, -12],\n [3, -4, 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"
}
] | 178 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -6, 1, 5],\n [0, 10, -1, 4],\n [9, -1, -1, 8],\n [-4, -4, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 503 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, -2, -9],\n [0, -7, 6, -7],\n [0, 0, 9, 8],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 780 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 4, -6, 5],\n [4, -5, -2, 2],\n [-6, -2, 7, -10],\n [5, 2, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 671 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -10, -1, -2],\n [-3, 4, -10, 4],\n [-4, -9, 7, 4],\n [-2, 6, 6, 8]]\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[[6, -4, 0, -8],\n [-12, -6, 1, -7],\n [-8, -5, -12, 8],\n [5, 8, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, 4, -3],\n [2, -5, -2, -5],\n [4, -2, -10, -11],\n [-3, -5, -11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 497 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 1, -3, 11],\n [-7, 0, -3, -3],\n [4, 5, -4, -10],\n [-12, 10, -1, -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"
}
] | 44 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -8, 3, 0],\n [-8, -9, -2, -6],\n [3, -2, -1, -6],\n [0, -6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 196 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 11, -9, -12],\n [8, -7, -12, -8],\n [-5, 11, 6, -1],\n [11, -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"
}
] | 623 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, -11, 10],\n [-11, 3, 9, 10],\n [7, -4, 12, -4],\n [1, -3, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 911 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -1, 11, 1],\n [-1, 0, 3, 0],\n [11, 3, -7, -6],\n [1, 0, -6, 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"
}
] | 593 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 10, 9, -1],\n [0, -3, -11, -5],\n [0, 0, 5, -8],\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"
}
] | 520 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -8, 5, -9],\n [6, 4, -7, -12],\n [9, 9, 0, 11],\n [-10, 3, 7, -11]]? 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[[3, -2, -5, 0],\n [-2, -11, 0, 6],\n [-5, 0, -8, -3],\n [0, 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"
}
] | 747 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 4, 10, 2],\n [4, 2, -2, -7],\n [10, -2, 9, 5],\n [2, -7, 5, -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"
}
] | 76 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -4, -8, -7],\n [-4, 5, -2, 0],\n [-8, -2, 4, 6],\n [-7, 0, 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"
}
] | 372 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -4, 2, 0],\n [-4, -9, 10, -2],\n [2, 10, 8, 0],\n [0, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 580 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -9, -7, 6],\n [-4, 10, 9, 8],\n [5, 5, -6, 5],\n [8, 10, 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"
}
] | 224 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -6, 10, 4],\n [-6, 3, 0, 2],\n [10, 0, 7, -4],\n [4, 2, -4, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 284 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -5, -5, -1],\n [5, -5, -1, -6],\n [-5, 6, -8, 1],\n [2, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 668 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -12, -11, -2],\n [0, 7, -2, 9],\n [0, 0, -2, -5],\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"
}
] | 300 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -8, 7, -1],\n [3, -4, 1, -6],\n [12, -8, 2, 9],\n [4, -8, 5, 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"
}
] | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 3, 11, 5],\n [5, 6, -3, 2],\n [-8, -10, 1, 2],\n [6, 5, -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"
}
] | 199 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 6, 4, 9],\n [6, 9, 4, -5],\n [4, 4, -9, -4],\n [9, -5, -4, -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"
}
] | 391 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, 6, 0, -5],\n [6, 1, 0, 0],\n [0, 0, -2, -3],\n [-5, 0, -3, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 410 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -4, 0, 10],\n [-2, 1, 11, -3],\n [5, -9, -12, 12],\n [-7, 12, 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"
}
] | 710 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -8, 0, 11],\n [0, -2, 8, 1],\n [0, 0, 12, 4],\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"
}
] | 360 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -6, -12, -10],\n [-10, -6, 7, -7],\n [-9, 0, -12, -3],\n [-6, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 210 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 4, -5, 4],\n [0, -4, 5, 12],\n [0, 0, 11, 9],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, -1, -9, 11],\n [9, 2, 5, 10],\n [5, 9, 10, -2],\n [-7, 3, 5, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 6, 11, 3],\n [7, -12, -8, 9],\n [10, -1, -5, -6],\n [-12, 4, 3, 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"
}
] | 464 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 5, 3, -7],\n [10, 8, 7, 12],\n [-4, 4, 2, 7],\n [4, 9, 12, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 995 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -4, -2, 0],\n [-4, 9, 4, -8],\n [-2, 4, 3, 4],\n [0, -8, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -8, 5, 10],\n [-8, 5, 4, -2],\n [5, 4, 6, -2],\n [10, -2, -2, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 209 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 4, 12, -8],\n [0, 4, 4, 5],\n [-9, 6, -4, -3],\n [-2, -7, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 332 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 10, 1, 7],\n [0, 10, 8, 10],\n [0, 0, -6, -10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -8, 2, -4],\n [-8, -7, -5, -7],\n [2, -5, -5, 4],\n [-4, -7, 4, 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"
}
] | 248 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -9, 1, 2],\n [0, -7, -12, -6],\n [0, 0, 2, -8],\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"
}
] | 860 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -9, -4, -1],\n [6, -7, 6, -12],\n [9, 8, 10, -6],\n [-7, 9, 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"
}
] | 556 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 6, -2, -5],\n [0, 1, 7, -4],\n [0, 0, 2, 8],\n [0, 0, 0, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 0, 0, 8],\n [0, 2, 4, 8],\n [0, 4, 7, 6],\n [8, 8, 6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 756 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -4, -7, 4],\n [0, -1, 7, -1],\n [-7, 4, -11, 11],\n [-12, -11, 8, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 729 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -9, -4, -4],\n [-7, 0, 3, 11],\n [2, 6, 4, -6],\n [-7, 5, 9, -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"
}
] | 452 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 12, -1, 3],\n [11, 8, 5, 7],\n [9, -12, -9, -7],\n [9, 12, 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"
}
] | 8 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 4, -3, -5],\n [9, 4, 3, -4],\n [-4, 6, -3, -10],\n [11, -8, 9, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 134 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -12, 10, 3],\n [-7, 1, -5, 12],\n [10, 5, 5, -5],\n [4, -9, 12, 2]]? 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": "Compute |A| for the matrix A =\n[[3, -2, 12, 12],\n [0, -10, 6, -9],\n [0, 0, -8, 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"
}
] | 360 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, -2, 8],\n [0, 11, 6, 10],\n [-2, 6, 10, -3],\n [8, 10, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 436 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -1, -4, -9],\n [5, 8, 8, 4],\n [-5, -7, 1, 3],\n [11, -8, 7, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 333 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 2, -5, -1],\n [2, 4, 10, -1],\n [-5, 10, 2, 10],\n [-1, -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"
}
] | 127 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -8, -10, -4],\n [0, 11, -1, -2],\n [0, 0, 4, 0],\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"
}
] | 968 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -4, -10, -3],\n [9, 3, -11, -4],\n [12, -8, 4, -12],\n [-10, 4, 12, 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"
}
] | 176 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.