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[[6, -6, 6, 5],\n [-6, -9, 6, -2],\n [6, 6, 0, -3],\n [5, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
274
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 7, 6, -8],\n [0, 4, -12, -6],\n [0, 0, -11, -4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
484
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 4, 1, 0],\n [4, -9, 0, 4],\n [1, 0, 10, -9],\n [0, 4, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
607
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, -5, -4],\n [2, -1, 4, 7],\n [-5, 4, 10, 4],\n [-4, 7, 4, 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"
}
] |
266
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 6, -6, -4],\n [6, -8, 0, -6],\n [-6, 0, 3, 2],\n [-4, -6, 2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
780
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 5, 10, -3],\n [-3, -8, -10, -8],\n [-3, 8, 1, 5],\n [-11, 9, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
137
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -7, 9, 10],\n [0, -7, -7, 5],\n [0, 0, -1, 4],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -2, 0, -3],\n [-2, 5, -1, -2],\n [0, -1, -8, 4],\n [-3, -2, 4, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
233
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -7, 9, -12],\n [-1, 5, 0, -4],\n [10, -4, -10, -3],\n [-5, 5, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
644
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 4, 3, 7],\n [0, 11, 2, 0],\n [0, 0, 8, 12],\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"
}
] |
40
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -7, -12, 6],\n [0, -1, -8, 3],\n [0, 0, 4, 3],\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"
}
] |
960
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -5, -6, -12],\n [-12, -8, 2, 9],\n [-5, 12, 7, -2],\n [-7, 1, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
220
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 2, -5, 4],\n [2, -11, 8, 0],\n [-5, 8, -9, 4],\n [4, 0, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
752
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -4, -1, 0],\n [0, -5, 7, 7],\n [0, 0, 2, -1],\n [0, 0, 0, -4]]\nRound to the nearest integer, then take the result 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[[-3, -12, 7, -11],\n [0, -6, 3, -3],\n [0, 0, -2, -9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
108
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -3, -2, -2],\n [-3, -9, -2, -2],\n [-2, -2, -4, 7],\n [-2, -2, 7, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
465
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -9, -11, 0],\n [7, -3, 4, -6],\n [12, 10, -2, -8],\n [-7, 6, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
220
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 4, -11, 3],\n [-6, 5, -10, -11],\n [9, 8, 2, 0],\n [-5, 11, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
982
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -11, -3, -11],\n [8, 0, 12, 5],\n [-2, -4, 8, 11],\n [10, 9, -2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
246
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -1, -11, 2],\n [-1, 3, 8, 8],\n [-11, 8, -2, -2],\n [2, 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"
}
] |
730
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -3, -5, -11],\n [-6, -1, 11, 8],\n [-2, 8, 5, -2],\n [8, -7, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
178
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 1, 1, -9],\n [0, 2, -5, 12],\n [0, 0, 10, 5],\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"
}
] |
660
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 1, 0, 11],\n [1, 2, 6, -2],\n [0, 6, -4, 8],\n [11, -2, 8, 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"
}
] |
980
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 1, 8, 0],\n [1, -8, -1, -6],\n [8, -1, -11, 5],\n [0, -6, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
298
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 10, 6, -2],\n [0, 2, 7, 9],\n [0, 0, 8, -9],\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"
}
] |
192
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 10, 3, -7],\n [-10, -5, 12, 12],\n [-3, -3, -12, 11],\n [7, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
999
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -4, 8, -10],\n [-4, 2, -4, -4],\n [8, -4, 12, 0],\n [-10, -4, 0, 3]]\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[[7, 6, -3, 4],\n [0, 3, -5, 4],\n [0, 0, -5, 0],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 6, 1, -3],\n [0, -3, 10, 6],\n [0, 0, 1, -6],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
135
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 6, -9, 12],\n [0, -1, 12, 1],\n [0, 0, 6, 5],\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": "Determine the value of det(A) where A =\n[[-3, 7, 3, -3],\n [6, 8, -9, 8],\n [-10, -6, -9, 6],\n [-10, 9, 11, -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"
}
] |
766
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 11, -6, -6],\n [4, -6, -5, -3],\n [-5, 9, -9, 3],\n [9, 1, -5, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 9, -1, 8],\n [0, -8, 7, 4],\n [0, 0, 10, 8],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -4, -6, -10],\n [-4, -7, -4, 8],\n [-6, -4, -7, -8],\n [-10, 8, -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"
}
] |
608
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -4, 4, 0],\n [-12, 12, -3, -8],\n [-4, -7, -7, 5],\n [-9, 11, 10, 0]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 12, 7, -12],\n [-1, -2, -8, -1],\n [-7, -9, -5, -9],\n [-2, 4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
937
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -4, 0, 6],\n [0, 1, -10, 11],\n [0, 0, 5, 6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
875
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -3, -4, -2],\n [0, -11, -6, 5],\n [0, 0, 4, -8],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
548
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -10, 9, -2],\n [-3, -6, -12, 3],\n [9, 10, -8, -4],\n [-4, 7, -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"
}
] |
21
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 8, -8, 8],\n [-1, 10, 4, -12],\n [-2, -12, 9, 6],\n [9, -10, -8, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 1, -8, -8],\n [-7, 10, 0, 8],\n [1, -10, 5, 8],\n [2, 2, -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"
}
] |
805
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 0, 3, 5],\n [0, -12, 5, -1],\n [3, 5, 10, 0],\n [5, -1, 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"
}
] |
72
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -8, 11, 9],\n [-7, 11, 7, 1],\n [-12, -12, 8, 11],\n [6, -6, -8, 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"
}
] |
270
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 0, -6, 3],\n [0, 8, 4, 8],\n [-6, 4, -5, -2],\n [3, 8, -2, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -7, -1, -11],\n [0, 8, -9, -7],\n [0, 0, 3, -9],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 2, -2, -1],\n [2, 8, -2, -4],\n [-2, -2, -2, 2],\n [-1, -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"
}
] |
524
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -9, 0, -9],\n [-12, -8, 6, 8],\n [-2, 6, -6, 4],\n [-4, 1, 12, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
416
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -6, -9, -10],\n [0, 8, -5, 12],\n [0, 0, 11, -9],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 0, -8, -4],\n [0, 4, 2, 8],\n [-8, 2, -6, 6],\n [-4, 8, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
392
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -11, -11, -2],\n [0, -1, 0, -11],\n [0, 0, 10, -8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 4, 7, 9],\n [-2, 1, -10, -4],\n [7, 6, -1, 8],\n [-6, 2, 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"
}
] |
874
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, -4, -4],\n [4, -3, 0, -6],\n [-4, 0, -12, -11],\n [-4, -6, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
319
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, 4, 4],\n [-9, -4, -3, -8],\n [7, 7, -8, 9],\n [12, 12, -1, -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"
}
] |
305
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -1, -1, 11],\n [0, -1, -6, -3],\n [0, 0, -6, -6],\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"
}
] |
330
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 10, -2, 2],\n [10, 10, 6, 2],\n [-2, 6, 6, -1],\n [2, 2, -1, -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"
}
] |
544
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 6, -6, 4],\n [6, -11, 8, 0],\n [-6, 8, -7, -8],\n [4, 0, -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"
}
] |
640
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -9, 5, 0],\n [-9, -8, -2, -2],\n [5, -2, -6, 1],\n [0, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
477
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -3, 10, -10],\n [0, -12, 5, -7],\n [0, 0, -2, 9],\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"
}
] |
856
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 4, 6, -2],\n [4, -7, 4, 8],\n [6, 4, 10, 0],\n [-2, 8, 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"
}
] |
988
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -2, 1, -4],\n [-2, 11, -3, -6],\n [1, -3, -4, -8],\n [-4, -6, -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"
}
] |
198
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -6, 8, 8],\n [-6, 11, -3, -6],\n [8, -3, -8, 4],\n [8, -6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 0, -2, 2],\n [0, 0, 1, 3],\n [-2, 1, 11, -4],\n [2, 3, -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"
}
] |
414
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -4, -6, 0],\n [8, -5, -7, -5],\n [4, 12, -2, 10],\n [-9, -6, -10, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
572
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -5, 11, -4],\n [0, 11, 10, -5],\n [0, 0, -7, -4],\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"
}
] |
71
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -5, -2, -3],\n [-5, -10, -2, -4],\n [-2, -2, -11, 9],\n [-3, -4, 9, -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"
}
] |
144
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -6, -2, -10],\n [-5, 11, 6, 11],\n [10, -12, 7, -3],\n [7, 1, -3, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -4, -5, -6],\n [-4, -9, 1, -2],\n [-5, 1, -3, -2],\n [-6, -2, -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"
}
] |
994
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 8, 6, -7],\n [0, -9, 7, 0],\n [0, 0, 4, -7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
108
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -8, 8, 4],\n [0, -2, -6, 11],\n [0, 0, 9, 7],\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"
}
] |
134
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 0, -1, -4],\n [0, -5, 10, 2],\n [-1, 10, -8, 1],\n [-4, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -3, 0, 0],\n [-3, 9, 2, -3],\n [0, 2, 9, 5],\n [0, -3, 5, -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"
}
] |
89
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 10, -12, -3],\n [0, 10, 5, -10],\n [0, 0, -2, 0],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 6, 5, 10],\n [8, -2, 10, 11],\n [4, -1, -9, -11],\n [-5, -7, 1, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
641
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 11, -8, -11],\n [-4, 10, -8, 11],\n [-5, -12, -4, -5],\n [11, -6, -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"
}
] |
716
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -8, 11, 1],\n [-7, -8, 9, 12],\n [-4, -8, 2, -3],\n [10, -5, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
898
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 1, 5, -4],\n [1, 12, 9, 4],\n [5, 9, 0, 0],\n [-4, 4, 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"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -4, 4, 8],\n [0, -12, -9, 5],\n [0, 0, 2, -6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, 11, 5],\n [0, 3, 2, 11],\n [0, 0, -7, -6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
126
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -6, -3, -3],\n [0, -7, -1, -4],\n [0, 0, -4, -3],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
336
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -12, -5, 4],\n [-12, -8, -10, 4],\n [-5, -10, 9, -8],\n [4, 4, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 7, -10, -11],\n [0, 10, -7, 10],\n [0, 0, 12, 4],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -9, -4, -2],\n [0, -12, -12, -3],\n [0, 0, 6, 10],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -9, -10],\n [0, 6, 9, -2],\n [0, 0, -9, -9],\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"
}
] |
296
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 3, -1, -3],\n [-5, -3, -9, -10],\n [3, -6, -3, -7],\n [3, 10, 7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
986
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -3, 0, 2],\n [0, -6, -9, 7],\n [0, 0, 9, -6],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -1, 10, -10],\n [-1, 11, 0, -2],\n [10, 0, -2, 6],\n [-10, -2, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 10, 2, 6],\n [0, 5, -10, -6],\n [0, 0, -12, -6],\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"
}
] |
320
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 5, -4, -8],\n [-10, 6, -10, 12],\n [-9, -6, -8, 1],\n [-10, 6, -12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
974
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -8, 2, -4],\n [0, -10, 6, -7],\n [0, 0, -2, -8],\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"
}
] |
440
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -11, 12, 9],\n [0, -8, 1, -9],\n [0, 0, 12, -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"
}
] |
112
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 9, 5, 2],\n [0, 0, -2, 1],\n [-7, -4, 6, 12],\n [8, 5, 8, 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"
}
] |
333
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -11, -9, -6],\n [0, 5, -1, -11],\n [0, 0, -8, 2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -7, 8, 8],\n [0, 3, 3, -3],\n [0, 0, -8, -10],\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"
}
] |
784
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -8, -10, -2],\n [-8, 2, -4, -3],\n [-10, -4, -5, 0],\n [-2, -3, 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"
}
] |
356
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -1, -6, -7],\n [0, -1, 8, 9],\n [9, 0, -4, -6],\n [-5, 8, -3, 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"
}
] |
818
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -2, -2, -2],\n [-2, -4, 3, -2],\n [-2, 3, 9, 0],\n [-2, -2, 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"
}
] |
932
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 7, 12, -3],\n [0, 1, 6, -6],\n [0, 0, 6, -2],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 2, -6, 3],\n [2, -3, 12, 4],\n [-6, 12, -9, -10],\n [3, 4, -10, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
797
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -12, -8, -5],\n [0, -3, -4, 9],\n [0, 0, 3, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -8, -5, -11],\n [-3, 1, 3, 11],\n [-5, -5, -12, -2],\n [2, 8, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
656
|
MATH
|
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