messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 11, -9, 10],\n [0, -5, -6, 8],\n [0, 0, 2, -1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
50
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 2, -4, 3],\n [-2, 11, -8, -4],\n [7, 2, 6, -7],\n [-3, -7, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
506
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 3, 6, 11],\n [7, 0, 4, -9],\n [-7, -7, 11, 12],\n [11, -12, -9, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
856
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 0, -2, -8],\n [0, -7, 2, -1],\n [-2, 2, 10, -2],\n [-8, -1, -2, -3]]? 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": "What is the determinant of the matrix:\n[[-1, 0, 7, -10],\n [0, -3, 3, -6],\n [0, 0, 2, 7],\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"
}
] |
988
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -7, 2, -5],\n [-7, 4, -4, 0],\n [2, -4, -10, -5],\n [-5, 0, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
311
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 0, 7, 2],\n [0, 11, -3, 2],\n [7, -3, -12, 1],\n [2, 2, 1, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
151
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 8, -10, 4],\n [0, 3, 2, -6],\n [0, 0, 6, -6],\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"
}
] |
458
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 6, -1, 4],\n [-10, -8, -11, -9],\n [9, -12, 10, -7],\n [-5, 6, -5, -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"
}
] |
888
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, 0, 8],\n [2, -1, -7, 2],\n [0, -7, 10, -10],\n [8, 2, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
931
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 2, -3, 8],\n [2, 2, 1, 0],\n [-3, 1, 11, 4],\n [8, 0, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
815
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 2, 9],\n [6, 10, -11, 8],\n [-3, 8, -9, 9],\n [-11, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
676
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 5, -6, -11],\n [5, -1, 4, -7],\n [-6, 4, -2, 4],\n [-11, -7, 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"
}
] |
494
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 5, 0, 12],\n [0, 2, 6, 3],\n [0, 0, 9, 10],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
712
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -11, -4, -11],\n [3, 7, 0, -1],\n [1, 11, -4, 7],\n [-1, 11, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
304
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -2, -7, -11],\n [4, -9, -3, 8],\n [1, -10, -3, -2],\n [9, -7, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
219
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 2, 5, 12],\n [7, 11, -10, -11],\n [0, -1, -12, 6],\n [-5, 0, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
418
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 0, -3, -4],\n [0, -10, -2, 3],\n [-3, -2, 0, -8],\n [-4, 3, -8, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
945
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -3, 3, -5],\n [3, 6, 4, -9],\n [6, 12, 12, -1],\n [-10, -5, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
702
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -7, 4, 8],\n [-7, 11, 7, -6],\n [4, 7, -11, 2],\n [8, -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"
}
] |
443
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -4, -9, 0],\n [-4, -11, 10, 2],\n [-9, 10, 2, 1],\n [0, 2, 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"
}
] |
857
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -10, 11, -9],\n [0, 6, 10, -10],\n [0, 0, 2, 10],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
892
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 5, -9, 4],\n [0, -2, -4, 5],\n [0, 0, 5, -12],\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"
}
] |
520
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -10, 6, -9],\n [-10, 11, 4, 0],\n [6, 4, 11, -2],\n [-9, 0, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 2, 10, -2],\n [2, 2, -8, 6],\n [10, -8, -3, 0],\n [-2, 6, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, -3, -12],\n [0, -10, 4, -8],\n [0, 0, 2, -6],\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"
}
] |
760
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 12, 7, -1],\n [12, -5, -6, -4],\n [7, -6, 12, -1],\n [-1, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
974
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 11, -3, -5],\n [4, -6, 7, -10],\n [-8, -2, -6, 9],\n [-3, 6, -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"
}
] |
111
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -9, -6, 5],\n [12, 11, -10, 6],\n [1, 10, 6, -5],\n [-3, 4, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 9, 2, 2],\n [0, -11, 11, -5],\n [0, 0, 6, -7],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
924
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 11, -2, 1],\n [0, 7, -5, 1],\n [0, 0, -10, 7],\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"
}
] |
0
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 10, 3, -2],\n [10, -10, -5, 1],\n [3, -5, 11, 6],\n [-2, 1, 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"
}
] |
329
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 0, 6, -5],\n [0, 8, -1, 6],\n [0, 0, -11, -2],\n [0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 9, -4, 9],\n [9, 11, -4, -8],\n [-4, -4, -5, -4],\n [9, -8, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
986
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, 2, 3],\n [-12, -2, 9, -9],\n [10, -5, -8, 7],\n [6, 1, 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"
}
] |
470
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -5, -2, 3],\n [-5, 3, -4, -4],\n [-2, -4, 6, 1],\n [3, -4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, -12, 0],\n [0, 5, -10, 12],\n [0, 0, -8, -12],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 10, -7, 4],\n [10, 6, -4, 2],\n [-7, -4, 3, 10],\n [4, 2, 10, -3]]? 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": "What is the determinant of the matrix:\n[[3, 0, -1, 1],\n [0, 5, 5, -7],\n [0, 0, -10, -10],\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"
}
] |
650
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -6, 4, -7],\n [-6, -7, -6, -2],\n [4, -6, 6, -6],\n [-7, -2, -6, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 6, 4, 8],\n [6, 0, 2, -6],\n [4, 2, 0, 6],\n [8, -6, 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"
}
] |
40
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -10, -10, -2],\n [0, -5, 9, 6],\n [0, 0, -1, 2],\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"
}
] |
910
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 0, -9, 10],\n [10, 1, 3, 4],\n [-2, 10, -12, -9],\n [5, -4, 8, -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"
}
] |
925
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -11, 10, -11],\n [5, 1, 11, -8],\n [11, 4, 6, -4],\n [9, 3, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
871
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 12, 0, 4],\n [0, -6, -9, -2],\n [0, 0, -5, 9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 11, -8, 8],\n [11, -8, 2, 3],\n [-8, 2, -11, 2],\n [8, 3, 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"
}
] |
249
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 10, 0, 8],\n [0, 8, -4, 1],\n [0, 0, -6, -3],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
312
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, -10, 6],\n [0, 5, -4, 10],\n [0, 0, 8, 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"
}
] |
360
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -8, -6, -4],\n [-8, -9, 0, 8],\n [-6, 0, -2, -4],\n [-4, 8, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
620
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -9, 8, -6],\n [0, 7, 1, 2],\n [0, 0, 9, 9],\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"
}
] |
149
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, 6, -1],\n [2, -12, 2, -2],\n [6, 2, -5, 6],\n [-1, -2, 6, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -11, -8, 1],\n [0, 10, -7, -8],\n [0, 0, -4, -11],\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"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -4, 4, 3],\n [0, 2, -7, -9],\n [0, 0, 11, -10],\n [0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
924
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -3, 11, -5],\n [-7, 5, 9, 3],\n [-1, 4, 5, 8],\n [-8, -11, -5, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
257
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -2, -7, 2],\n [0, -12, -5, 10],\n [0, 0, 1, -11],\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"
}
] |
8
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -1, -9, -7],\n [1, 8, -8, -10],\n [-3, -8, -12, 0],\n [-4, -12, 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"
}
] |
98
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -6, 2, 4],\n [1, 4, 0, 2],\n [-12, 6, 9, 9],\n [-6, -7, 4, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
978
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 11, 9, -4],\n [1, 4, 0, -6],\n [-10, 3, -3, -12],\n [11, 6, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
348
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -1, -10, 10],\n [4, -12, 10, 2],\n [0, 12, 4, -6],\n [-3, -5, 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"
}
] |
800
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -7, 2, 12],\n [-1, 6, 12, 7],\n [2, 11, 3, -9],\n [8, -7, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
499
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 4, 5, 8],\n [0, 11, -1, -5],\n [0, 0, -7, -6],\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"
}
] |
152
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 7, -1, -11],\n [0, 2, 8, 0],\n [0, 0, 6, 5],\n [0, 0, 0, -7]]? 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": "Determine the value of det(A) where A =\n[[2, -4, 7, 6],\n [-3, 8, -9, 10],\n [1, -11, -10, -1],\n [5, -4, -9, 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"
}
] |
996
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -2, 8, 4],\n [-2, 6, 0, 1],\n [8, 0, 3, 1],\n [4, 1, 1, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
429
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -10, -9, -7],\n [9, 5, 10, 1],\n [4, -10, 9, 11],\n [0, -5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -8, -4, 6],\n [-6, 11, 10, 5],\n [1, -1, 3, -3],\n [2, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
442
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -9, -11, 5],\n [0, -9, -11, -6],\n [0, 0, 5, 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"
}
] |
600
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, 4, -1],\n [0, -12, 0, 0],\n [4, 0, 0, -8],\n [-1, 0, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
504
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, -4, -1],\n [0, -2, -3, -2],\n [0, 0, -6, -6],\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"
}
] |
664
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -11, 0, -9],\n [5, 4, 3, 6],\n [-1, -4, -8, 4],\n [5, 3, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
535
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, -2, -4],\n [0, 3, -2, -2],\n [-2, -2, 2, 0],\n [-4, -2, 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"
}
] |
914
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 6, -7, -4],\n [6, -7, -4, 4],\n [-7, -4, -5, 0],\n [-4, 4, 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"
}
] |
306
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 0, -6, -5],\n [0, -12, -6, -4],\n [-6, -6, 12, -8],\n [-5, -4, -8, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
708
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -2, -10, 0],\n [0, -4, -6, 11],\n [0, 0, -10, 7],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 2, -2, -9],\n [0, -2, -11, 11],\n [0, 0, -8, -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"
}
] |
768
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 5, 12, 7],\n [0, -8, -2, 10],\n [0, 0, -4, -5],\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"
}
] |
744
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -10, 5, 1],\n [-10, -9, -2, 9],\n [5, -2, -11, -4],\n [1, 9, -4, -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"
}
] |
907
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -12, 3, -11],\n [-3, -11, 2, -5],\n [-12, -1, 8, -12],\n [8, 1, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
631
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -6, 0, -4],\n [-6, -5, 0, 8],\n [0, 0, -2, 4],\n [-4, 8, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
474
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 1, 4, 9],\n [0, 10, 3, 11],\n [0, 0, 8, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -7, -10, -5],\n [-4, 1, 7, 7],\n [-6, -4, 11, -5],\n [11, 10, 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"
}
] |
417
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -10, 0, -2],\n [-10, -8, 2, -2],\n [0, 2, -10, -1],\n [-2, -2, -1, -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"
}
] |
564
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 12, -12, -3],\n [5, -12, -6, 3],\n [1, 8, 8, 11],\n [3, -9, 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"
}
] |
118
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 3, -9, -7],\n [-5, 4, -10, 10],\n [9, 12, 1, 2],\n [12, 0, 3, -10]]? Round to the nearest integer, then express your answer modulo 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, 3, 4],\n [-8, -1, 7, -5],\n [10, -2, 8, -5],\n [-11, -8, 9, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
804
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -1, 5, -5],\n [0, 12, 3, -12],\n [0, 0, -11, -10],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
812
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -1, -11, 4],\n [0, -2, 5, 1],\n [0, 0, 5, -11],\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"
}
] |
220
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, -4, -2],\n [0, -7, 0, 2],\n [-4, 0, 6, -3],\n [-2, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
397
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -11, 12, 8],\n [0, 1, 10, 6],\n [0, 0, -8, 10],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 10, 2, 8],\n [0, 6, -2, -1],\n [0, 0, -10, 4],\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"
}
] |
520
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -12, -9, -12],\n [-1, -5, -11, 6],\n [-9, -8, 6, -7],\n [7, 11, -3, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
63
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 4, -7, -3],\n [0, -2, -5, -2],\n [0, 0, 7, -1],\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"
}
] |
538
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -1, -6, -4],\n [-1, 7, 1, -6],\n [-6, 1, 1, 2],\n [-4, -6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
124
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 4, 8, 2],\n [4, -12, -5, -5],\n [8, -5, 8, 0],\n [2, -5, 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"
}
] |
544
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 0, -4, 2],\n [0, -7, 6, 4],\n [-4, 6, 2, 4],\n [2, 4, 4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
624
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -5, 9, 9],\n [0, 3, 12, 12],\n [0, 0, -8, -5],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -2, 5, -3],\n [-2, 1, 5, -8],\n [5, 5, -9, 0],\n [-3, -8, 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"
}
] |
624
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -4, 2, -4],\n [-4, -4, 1, -2],\n [2, 1, -12, 0],\n [-4, -2, 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"
}
] |
807
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -1, 10, 3],\n [0, 8, -12, 7],\n [0, 0, 4, -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"
}
] |
280
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -2, -2, 6],\n [-2, -3, 0, -11],\n [-2, 0, -7, -4],\n [6, -11, -4, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
634
|
MATH
|
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