messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, -4, -6],\n [-4, 8, -4, -6],\n [-4, -4, -1, 1],\n [-6, -6, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -4, 7, 1],\n [-4, -5, 1, -2],\n [7, 1, -4, 0],\n [1, -2, 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"
}
] |
861
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, -2, 6],\n [10, -3, -2, -2],\n [-2, -2, 9, -8],\n [6, -2, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
875
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -1, 0, -8],\n [-1, 4, 8, -4],\n [0, 8, 12, 8],\n [-8, -4, 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"
}
] |
916
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -1, -1, 10],\n [-6, -5, 0, -12],\n [-1, -11, 4, 2],\n [9, -9, 11, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
590
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -6, 12, 6],\n [9, 12, -10, -9],\n [-2, 6, 7, -9],\n [-10, -6, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
776
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -7, 6, 8],\n [0, 6, 2, -1],\n [0, 0, -1, -1],\n [0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
940
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, 4, 11],\n [-8, -10, 9, 0],\n [5, -10, -7, 12],\n [2, 2, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -11, -4, -5],\n [1, -9, 1, 6],\n [-4, 0, -10, 9],\n [11, 10, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
961
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 1, 5, -4],\n [1, -6, 2, -4],\n [5, 2, -6, -2],\n [-4, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
276
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -9, 0, 10],\n [-2, -1, -12, 9],\n [6, 3, 2, 1],\n [-4, -6, 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"
}
] |
144
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 1, 8, -11],\n [0, -4, -2, 10],\n [0, 0, -7, -1],\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"
}
] |
648
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 0, -4, 6],\n [0, -11, 0, -6],\n [-4, 0, -6, 2],\n [6, -6, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
998
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 5, -11, 8],\n [-4, 11, -9, 7],\n [-5, -4, 3, 1],\n [6, 8, -10, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 2, 2, -7],\n [2, 1, 6, -8],\n [2, 6, 12, -7],\n [-7, -8, -7, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
183
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 1, 5, 12],\n [0, 10, 0, -1],\n [0, 0, -8, -5],\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"
}
] |
360
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -4, -8, 7],\n [-4, 9, -8, -2],\n [-8, -8, -9, -2],\n [7, -2, -2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
548
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -5, 3, -3],\n [-5, 4, 11, -11],\n [-9, -6, -10, 12],\n [12, 3, -2, 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"
}
] |
942
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 11, 7, -4],\n [-8, -2, -2, -12],\n [9, 11, -9, -10],\n [-4, 4, -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"
}
] |
132
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, -6, 6],\n [0, 6, -6, -4],\n [0, 0, -1, -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"
}
] |
700
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 7, -9, 1],\n [0, 9, 10, 9],\n [0, 0, 9, -3],\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"
}
] |
710
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -5, 1, -7],\n [12, 10, 6, 2],\n [-2, 3, -8, 7],\n [-9, -8, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
54
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -5, -10, 12],\n [-1, -7, 8, 7],\n [-7, -10, -12, -4],\n [10, 2, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -5, 12, 1],\n [-5, -3, -3, 0],\n [12, -3, -2, 3],\n [1, 0, 3, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
846
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 4, 3, -3],\n [-5, -5, -8, 4],\n [-10, 9, -11, -5],\n [-12, -4, -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"
}
] |
791
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, 2, -2],\n [-2, 11, 0, -6],\n [2, 0, -3, 4],\n [-2, -6, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, -6, 10],\n [0, 2, -3, 10],\n [0, 0, 4, 4],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -12, -6, -8],\n [0, -7, 5, 0],\n [0, 0, -7, 6],\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"
}
] |
147
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -6, -6, 3],\n [1, -12, -10, 1],\n [-9, -9, -8, 6],\n [5, 3, -3, 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"
}
] |
490
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 8, -3, -12],\n [0, -1, -7, 0],\n [0, 0, -8, 8],\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"
}
] |
960
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -8, 12, 10],\n [0, 2, 4, 1],\n [0, 0, -3, 1],\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"
}
] |
676
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 2, 4, 10],\n [-11, -11, 2, -8],\n [-10, -7, -7, 1],\n [-4, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
882
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -7, 9, 10],\n [11, -7, -9, 0],\n [2, -12, 2, 9],\n [-5, 7, -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"
}
] |
65
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -1, -7, 4],\n [0, -10, -6, 0],\n [0, 0, -7, 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"
}
] |
760
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 5, -9, 11],\n [0, 10, 2, -8],\n [-8, 0, -6, 7],\n [-2, -1, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
70
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 8, -8, -1],\n [8, -6, -5, 2],\n [-8, -5, 10, 5],\n [-1, 2, 5, -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"
}
] |
393
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 2, 5, 4],\n [2, -2, 8, 2],\n [5, 8, -9, -1],\n [4, 2, -1, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
718
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 6, -4, -8],\n [0, -6, -6, 12],\n [0, 0, 5, 12],\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"
}
] |
640
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 9, -10, 4],\n [-3, -11, 8, 7],\n [9, -10, 6, 4],\n [7, -5, -11, 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"
}
] |
197
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 1, -1, 8],\n [1, -11, 0, -8],\n [-1, 0, -1, -2],\n [8, -8, -2, -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"
}
] |
922
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 7, 2, -6],\n [-7, 4, -10, 4],\n [11, 5, -10, -9],\n [3, -5, -1, -11]]\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[[7, 6, -2, 0],\n [6, 12, -1, -10],\n [-2, -1, -6, 2],\n [0, -10, 2, 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"
}
] |
294
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 1, -11, -6],\n [0, -8, -4, 11],\n [0, 0, 2, 1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, -7, 4],\n [0, 12, 4, -8],\n [0, 0, 6, 2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 4, 0, -4],\n [4, -4, 0, -2],\n [0, 0, -11, -4],\n [-4, -2, -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"
}
] |
276
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 12, 10, -12],\n [0, -9, -12, -6],\n [0, 0, -11, 0],\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"
}
] |
110
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -8, -1, -12],\n [4, 12, -12, 9],\n [-10, 5, -7, -6],\n [-2, -11, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
684
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 4, 0, 1],\n [4, 4, 0, 6],\n [0, 0, 3, -5],\n [1, 6, -5, 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"
}
] |
560
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -9, 0, -10],\n [0, -5, 2, 5],\n [0, 0, -10, -2],\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"
}
] |
750
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -12, -4, 2],\n [-12, 0, 3, 6],\n [-4, 3, 4, -2],\n [2, 6, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
112
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 3, 2, 0],\n [3, -8, -2, -8],\n [2, -2, 2, -6],\n [0, -8, -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"
}
] |
428
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 11, -6, -12],\n [0, -8, 11, 9],\n [0, 0, -12, 1],\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"
}
] |
928
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 9, -6, 2],\n [-6, -11, 9, 1],\n [6, -7, 3, 1],\n [-10, -6, -7, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
464
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -8, 7, 12],\n [3, -8, -8, -6],\n [3, -10, -3, 4],\n [-8, 7, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 5, 3, 5],\n [-8, -5, 6, -3],\n [-8, -6, 1, -5],\n [6, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
126
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -7, -9, -8],\n [-2, 9, 2, 6],\n [-12, 6, -3, -3],\n [-9, -3, 9, 12]]? Round to the nearest integer, then express your answer 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[[11, 2, -2, -4],\n [2, -9, 4, 1],\n [-2, 4, -5, -2],\n [-4, 1, -2, -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"
}
] |
561
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 7, 9, 7],\n [-1, -3, 1, -2],\n [7, -3, 0, -5],\n [-5, 12, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
475
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -10, -2, 0],\n [-10, 2, -8, -5],\n [-2, -8, 10, 8],\n [0, -5, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
602
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 7, -7, 7],\n [2, 12, -9, -11],\n [5, -8, 5, -12],\n [-7, -4, -11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
558
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 1, 7, -10],\n [3, 10, 10, -4],\n [0, 0, 11, 5],\n [0, -8, -11, -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"
}
] |
509
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -12, 4, -6],\n [0, -4, 6, 11],\n [0, 0, -7, 11],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 0, -5, -6],\n [0, -3, -6, 1],\n [0, 0, 5, 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"
}
] |
60
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 6, -6, 3],\n [11, 11, 3, -4],\n [3, -1, -12, -8],\n [-1, -5, 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"
}
] |
368
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 8, 1, 2],\n [0, -4, 1, 9],\n [0, 0, -5, 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"
}
] |
540
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 11, 10, -7],\n [-6, 12, 8, 1],\n [-5, -9, 8, 3],\n [12, 10, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
358
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, -3, 1],\n [0, -2, -5, -6],\n [0, 0, -7, 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"
}
] |
776
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, 1, -5],\n [2, 6, -3, -11],\n [1, -3, -10, 0],\n [-5, -11, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -4, 0, -2],\n [-4, 6, 6, 11],\n [0, 6, 9, -8],\n [-2, 11, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, -4, -10],\n [-12, -12, 11, -3],\n [8, -9, 2, -4],\n [4, -10, 9, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -9, -2, 4],\n [-2, -2, 8, 2],\n [1, 5, 0, 11],\n [-5, -10, -3, -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"
}
] |
856
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 0, 11, 1],\n [0, -7, 2, -8],\n [0, 0, -6, 3],\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"
}
] |
24
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -10, 0, 0],\n [-10, -3, 4, 7],\n [0, 4, 2, 3],\n [0, 7, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
314
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 5, 3, 4],\n [0, 5, -1, 9],\n [0, 0, 4, -7],\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"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -6, 4, 0],\n [-6, -6, 4, 7],\n [4, 4, -11, 3],\n [0, 7, 3, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
105
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 6, -6, 2],\n [6, 1, 9, -3],\n [-6, 9, 9, 7],\n [2, -3, 7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
260
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 2, -11, -10],\n [-8, 5, -3, 1],\n [4, 1, -11, 0],\n [-8, 2, 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"
}
] |
614
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 8, 2, -3],\n [8, -4, -7, 2],\n [2, -7, -1, 6],\n [-3, 2, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
67
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -5, 11, -7],\n [0, 2, -6, 2],\n [0, 0, -4, 11],\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"
}
] |
800
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, 7, -4],\n [2, -3, -2, 5],\n [7, -2, 2, 6],\n [-4, 5, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -9, -2, 1],\n [0, -3, -9, 12],\n [0, 0, -12, 2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -4, -12, -12],\n [0, -3, 9, -3],\n [-1, 5, -11, -4],\n [8, 0, 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"
}
] |
867
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -6, -2, 6],\n [-6, -12, 0, -2],\n [-2, 0, 2, 6],\n [6, -2, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
296
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -12, -2, 0],\n [0, -10, -3, -3],\n [0, 0, 10, 9],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -3, -11, -4],\n [5, 12, 5, -4],\n [-12, -6, -11, 5],\n [4, 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"
}
] |
515
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -4, 2, 0],\n [-4, -12, -3, 0],\n [2, -3, 7, -4],\n [0, 0, -4, 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"
}
] |
425
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -12, -5, -10],\n [-12, -12, 3, -10],\n [-5, 3, 0, 0],\n [-10, -10, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
756
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -6, 4, 3],\n [0, -10, 0, -11],\n [0, 0, 6, -8],\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"
}
] |
300
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 1, 1, -2],\n [1, -1, 4, -5],\n [1, 4, -12, -1],\n [-2, -5, -1, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
439
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -11, -6, 8],\n [-4, 0, 2, 3],\n [7, 3, -4, -1],\n [0, 7, 9, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
633
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -12, -8, -10],\n [8, -10, 11, 0],\n [2, 12, -11, 7],\n [-11, -9, 7, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -8, 8, -2],\n [-8, 12, 2, 6],\n [8, 2, 3, 2],\n [-2, 6, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
404
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 8, -12, 4],\n [8, 11, -9, -6],\n [-12, -9, 3, 0],\n [4, -6, 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"
}
] |
92
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 8, 4, -8],\n [8, -3, -2, 2],\n [4, -2, 2, -2],\n [-8, 2, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
140
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 5, -1, -4],\n [5, -4, 0, 0],\n [-1, 0, 3, 0],\n [-4, 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"
}
] |
667
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, 4, 8],\n [-3, -11, -9, -4],\n [4, -9, 7, 2],\n [8, -4, 2, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
403
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, 3, 7],\n [0, -3, -11, -3],\n [0, 0, 12, 6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 8, 3, 3],\n [6, 11, -1, 12],\n [-12, -6, 3, 9],\n [-12, -10, -8, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
103
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -2, -8, -6],\n [-2, -5, 0, -3],\n [-8, 0, -3, -2],\n [-6, -3, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 2, -3, -2],\n [2, -3, 9, -2],\n [-3, 9, -6, 6],\n [-2, -2, 6, 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
|
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