messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 2, -10, 10],\n [0, 10, -11, 11],\n [0, 0, -6, 5],\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"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 10, 10],\n [6, 11, -3, 7],\n [0, 8, 1, 7],\n [-2, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
832
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 4, -7, 12],\n [0, 2, 0, 5],\n [0, 0, -9, -8],\n [0, 0, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
704
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, -12, -6],\n [1, -1, 5, 11],\n [-3, 7, -11, 1],\n [-12, -3, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
808
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 1, 4],\n [2, 0, -2, 2],\n [1, -2, 10, -8],\n [4, 2, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
876
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 11, -10, 10],\n [2, 10, 4, -3],\n [-9, -4, 9, -6],\n [-11, -4, 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"
}
] |
875
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 4, -11, 11],\n [5, 5, -10, 8],\n [-9, 0, -4, -11],\n [-2, 4, 10, 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"
}
] |
798
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -12, 1, 5],\n [0, -3, 6, -2],\n [0, 0, 7, 5],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 9, 6, 1],\n [-10, 0, 6, -5],\n [-4, -8, -7, 10],\n [-8, -3, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
146
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -6, 6, 2],\n [0, 2, 5, -5],\n [-6, 6, -3, 8],\n [-1, -6, 2, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
490
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -10, -2, 6],\n [-10, -6, 9, 10],\n [-2, 9, 7, 9],\n [6, 10, 9, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
241
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, 10, 0],\n [-4, 10, -12, 3],\n [10, -12, 12, 12],\n [0, 3, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
820
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -12, -2, 10],\n [0, 7, 9, 8],\n [0, 0, 6, 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"
}
] |
588
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -7, -12, -10],\n [-7, -12, -2, 3],\n [-12, -2, -7, 6],\n [-10, 3, 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"
}
] |
839
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 2, -11, -10],\n [0, -8, 0, -3],\n [0, 0, -6, 4],\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"
}
] |
184
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, 0, 2],\n [-6, 5, 6, -1],\n [0, 6, 6, 6],\n [2, -1, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
824
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 4, 1, -9],\n [0, 2, 6, 4],\n [-5, -8, 4, 4],\n [-11, -10, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
890
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, -10, 6],\n [0, -7, -1, 6],\n [0, 0, 5, 12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
845
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 2, -1, -12],\n [-8, -9, 12, -1],\n [4, 5, 6, 4],\n [6, 2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
612
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 2, 3, -2],\n [2, -7, 2, 6],\n [3, 2, -3, -2],\n [-2, 6, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
172
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -5, 6, 5],\n [4, 1, 10, 0],\n [-8, -6, 11, 8],\n [1, -7, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
578
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -4, 4, 3],\n [-4, -11, -2, 5],\n [4, -2, -12, 4],\n [3, 5, 4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 0, 0],\n [-6, -2, 2, 1],\n [0, 2, -1, 8],\n [0, 1, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
317
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 4, 10, -5],\n [-9, 1, 11, 5],\n [-11, 0, 1, 7],\n [-12, 7, 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"
}
] |
615
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, 3, -2],\n [-1, -11, -4, -5],\n [3, -4, 3, -5],\n [-2, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, -2, 7],\n [-3, 2, -12, 6],\n [0, -2, -2, 11],\n [8, -12, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 7, 4, 12],\n [0, -11, 8, 3],\n [0, 0, 9, 5],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
316
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 9, 5, -2],\n [0, -1, -3, -11],\n [0, 0, -5, 2],\n [0, 0, 0, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
910
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 1, 10, 7],\n [0, -5, -9, -8],\n [0, 0, 1, -6],\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"
}
] |
180
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -2, 7, -7],\n [3, 2, -4, 7],\n [7, 11, -1, -12],\n [0, 0, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
728
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -3, 12, 2],\n [5, 6, 6, -3],\n [5, -12, 3, -4],\n [-4, -6, 7, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
830
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -7, -1, -4],\n [-7, 5, 4, -2],\n [-1, 4, 5, 3],\n [-4, -2, 3, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
835
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -12, -10, 4],\n [0, 7, 11, -6],\n [0, 0, -7, 8],\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"
}
] |
980
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -3, -1, 2],\n [0, -12, -5, -10],\n [0, 0, -3, -3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -8, 7, -1],\n [0, -2, 0, -4],\n [0, 0, -11, -2],\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"
}
] |
648
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -10, 4, 10],\n [-10, 9, -7, 2],\n [4, -7, -5, -6],\n [10, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, -11, -4],\n [10, -12, 5, -2],\n [-1, -3, 4, -6],\n [-8, 7, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
444
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 6, -4, 2],\n [6, -8, 6, 6],\n [-4, 6, 8, 4],\n [2, 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"
}
] |
592
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 0, 0, -2],\n [0, 10, -6, 12],\n [0, 0, 2, -1],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -11, -5, 6],\n [0, 12, -12, -10],\n [0, 0, -7, 2],\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"
}
] |
8
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -7, -10, -4],\n [0, -7, 5, 8],\n [0, 0, 12, 8],\n [0, 0, 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"
}
] |
992
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, 5, -3],\n [-2, -7, -8, -5],\n [5, -8, -3, -5],\n [-3, -5, -5, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
482
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 7, -3, 1],\n [-1, 11, 5, 4],\n [12, 10, -8, 9],\n [-12, 5, -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"
}
] |
834
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, -7, -3],\n [-2, 11, 6, 10],\n [-7, 6, 7, 2],\n [-3, 10, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
172
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 5, -3, 7],\n [0, -12, -6, -2],\n [0, 0, -8, -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"
}
] |
232
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 6, -3, -6],\n [0, -9, -5, -5],\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"
}
] |
840
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 0, -6, 2],\n [0, 6, -6, 0],\n [-6, -6, 7, -2],\n [2, 0, -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"
}
] |
804
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 6, 6, 11],\n [0, -12, 3, -8],\n [0, 0, 1, -2],\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"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -6, 2, 2],\n [-6, 10, -6, -4],\n [2, -6, 3, -2],\n [2, -4, -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"
}
] |
164
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 4, -2, 4],\n [4, 12, 0, 0],\n [-2, 0, -11, -3],\n [4, 0, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 0, 8, 6],\n [0, 4, 3, 0],\n [8, 3, 6, 6],\n [6, 0, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -8, 2, 5],\n [-8, 7, 0, -7],\n [2, 0, 9, -7],\n [5, -7, -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"
}
] |
467
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 12, 9, -3],\n [1, -10, 10, -8],\n [-6, 1, 6, 4],\n [5, -7, -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"
}
] |
944
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -1, -4, 4],\n [-1, 0, -8, -4],\n [-4, -8, -6, -2],\n [4, -4, -2, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
172
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 4, -6, -8],\n [0, -10, -12, -5],\n [0, 0, -10, -2],\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"
}
] |
0
|
MATH
|
[
{
"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 [3, -12, -8, 0],\n [-2, -8, 10, 2],\n [-5, 0, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
322
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 8, -5, 8],\n [8, 4, 2, -4],\n [-5, 2, 5, -4],\n [8, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, -5, 11],\n [0, 9, 10, -2],\n [0, 0, -1, 10],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 4, 6, 3],\n [0, 2, 11, -2],\n [0, 0, -1, 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"
}
] |
928
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 2, -2, -2],\n [2, 1, 0, 10],\n [-2, 0, -9, 0],\n [-2, 10, 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"
}
] |
736
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -8, -12, 2],\n [11, -6, -2, 0],\n [7, -10, 5, -1],\n [-7, -3, 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"
}
] |
678
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -8, -4, 0],\n [-8, -6, -3, -1],\n [-4, -3, -4, 0],\n [0, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
710
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 6, 12, 2],\n [0, 5, -1, -8],\n [0, 0, 7, -6],\n [0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
220
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -9, -2, 10],\n [0, 3, 7, -6],\n [0, 0, 7, 11],\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"
}
] |
630
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -5, 0, 6],\n [-5, 7, -4, -1],\n [0, -4, -10, 1],\n [6, -1, 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"
}
] |
316
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, -9, -3],\n [-7, -4, -8, -1],\n [-4, 10, 3, 2],\n [11, 8, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
148
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -5, -12, 0],\n [-11, -3, -12, -12],\n [-11, -5, -12, 8],\n [6, 8, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
752
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 4, 6, 10],\n [4, -3, 8, -10],\n [6, 8, 4, 10],\n [10, -10, 10, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
804
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 9, 2, -1],\n [9, 8, 7, -5],\n [2, 7, 1, 2],\n [-1, -5, 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"
}
] |
77
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -4, 2, -5],\n [-4, -1, 2, -10],\n [2, 2, 9, -8],\n [-5, -10, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
485
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -11, -1, 8],\n [3, 6, 8, 3],\n [0, 3, -4, -2],\n [-10, 4, 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"
}
] |
472
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 8, 8, 8],\n [8, 8, -2, 1],\n [8, -2, -8, 10],\n [8, 1, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -4, 4, -7],\n [9, -2, 4, 1],\n [-6, 9, 9, -4],\n [-7, 3, -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"
}
] |
112
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 8, -6, 4],\n [0, 1, -10, -12],\n [0, 0, 9, 12],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
450
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -2, -2, -7],\n [-2, -3, 1, -4],\n [-2, 1, 4, -2],\n [-7, -4, -2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
559
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, 4, 5],\n [0, -8, -3, 0],\n [0, 0, 1, 7],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 7, 11, 12],\n [0, -3, -11, 5],\n [0, 0, 4, 0],\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"
}
] |
480
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 6, 2, -2],\n [6, -1, 8, -6],\n [2, 8, -9, 0],\n [-2, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
336
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, 0, 6],\n [-2, -1, -2, 9],\n [0, -2, 10, -2],\n [6, 9, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
976
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -8, 7, 3],\n [0, 7, -6, -8],\n [0, 0, 12, 11],\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"
}
] |
952
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -6, 4, 7],\n [0, 2, 4, 9],\n [0, 0, 7, 8],\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"
}
] |
378
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, -6, -2],\n [2, -11, -2, 1],\n [-6, -2, -6, 6],\n [-2, 1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -6, 6, 10],\n [0, 10, -6, 4],\n [0, 0, 3, -9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -6, -8, 6],\n [10, 10, 3, 12],\n [8, -3, 0, -3],\n [-4, 7, -11, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
608
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -11, 10, 9],\n [0, 12, -8, 0],\n [0, 0, -3, 7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
748
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 2, 6, 4],\n [2, 7, -8, -2],\n [6, -8, -12, -2],\n [4, -2, -2, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
932
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 11, -11, -12],\n [0, 8, 5, 7],\n [0, 0, -8, -4],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -6, 12, 5],\n [2, 1, -9, -2],\n [-4, -8, -3, 7],\n [5, 6, 3, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
736
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -7, 4, -2],\n [1, 0, 5, 11],\n [10, -7, -6, 2],\n [-6, 5, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
398
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 2, -3, -1],\n [2, 9, -4, 4],\n [-3, -4, -3, -10],\n [-1, 4, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
633
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -1, -6, 12],\n [0, 11, 1, 9],\n [0, 0, 7, -5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, 8, -1],\n [0, -12, -1, 4],\n [0, 0, 2, -1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 8, -4, 0],\n [8, 0, 2, -5],\n [-4, 2, 5, 2],\n [0, -5, 2, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
783
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 4, -2, 7],\n [-3, 7, -9, 3],\n [8, -5, 11, 8],\n [-5, 6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
109
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 4, 0],\n [0, 10, 8, -6],\n [4, 8, 5, 4],\n [0, -6, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
196
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, 10, -2],\n [-2, -8, -11, -6],\n [10, -11, -11, -4],\n [-2, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
592
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 8, -4, 10],\n [0, 12, 3, 6],\n [0, 0, -2, 6],\n [0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
136
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 11, -2, -2],\n [12, 7, -11, -4],\n [-3, -5, -3, -11],\n [-6, 4, 10, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
158
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 1, 8, -9],\n [-7, -8, 0, -5],\n [11, 12, 12, -4],\n [-5, -6, 11, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 9, -4, -2],\n [9, 0, 0, 6],\n [-4, 0, -6, -2],\n [-2, 6, -2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
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