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[[7, -9, 1, -9],\n [-8, -9, 1, 11],\n [-9, 4, -12, 10],\n [-1, -8, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
450
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 1, 4, -3],\n [1, -1, -2, -3],\n [4, -2, -9, -2],\n [-3, -3, -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"
}
] |
158
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -7, 8, 5],\n [0, -10, -5, -2],\n [0, 0, -5, 0],\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"
}
] |
300
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -1, 1, -7],\n [-1, 7, -7, 0],\n [1, -7, 6, 3],\n [-7, 0, 3, 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"
}
] |
739
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 8, -3, -8],\n [0, 2, 2, 0],\n [0, 0, 8, 1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -7, 11, -1],\n [0, -10, -12, -7],\n [0, 0, 8, 3],\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"
}
] |
240
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 2, 6, 2],\n [2, -11, -4, -4],\n [6, -4, 10, -4],\n [2, -4, -4, 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"
}
] |
336
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -5, 8],\n [2, 5, -2, 2],\n [-5, -2, 2, 8],\n [8, 2, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -3, -7, 11],\n [0, 4, -8, -9],\n [0, 0, 4, 7],\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"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 6, 1, 8],\n [-2, 8, 6, -6],\n [6, -12, 12, 11],\n [2, 10, -6, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
284
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -9, 8, 10],\n [0, -10, 11, 1],\n [0, 0, 10, 0],\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"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 4, -4, 4],\n [1, -1, -9, 2],\n [-9, -3, -4, 2],\n [10, -5, 5, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
548
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 4, 2, 4],\n [4, 2, 7, -3],\n [2, 7, 5, 3],\n [4, -3, 3, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
363
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 6, -4, -1],\n [6, 11, 8, -4],\n [-4, 8, 10, -1],\n [-1, -4, -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"
}
] |
274
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 1, -4, 0],\n [0, -10, -6, 12],\n [-5, 8, -3, 3],\n [9, -5, -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"
}
] |
794
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 12, 11, -7],\n [11, -3, -9, -8],\n [-7, -4, 12, 10],\n [-12, -10, -10, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
917
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 1, 8, -2],\n [-9, 11, -8, 8],\n [8, -8, 3, 11],\n [4, 0, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
140
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 10, 7, -1],\n [0, -11, 2, 5],\n [0, 0, -11, -8],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
370
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 0, 1, 4],\n [0, 10, 9, 9],\n [0, 0, 7, 5],\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"
}
] |
900
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 10, 10, -6],\n [10, 5, 0, 0],\n [10, 0, -4, -10],\n [-6, 0, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 12, -10, -4],\n [-6, 11, -12, 6],\n [0, -3, 8, -12],\n [-7, 7, 1, 9]]\nRound to the nearest integer, then take the result 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[[-8, -11, 3, 1],\n [0, -6, -3, -8],\n [0, 0, -4, 9],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
272
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 3, 8, 11],\n [-3, -7, 9, -1],\n [-12, 11, 2, 4],\n [-3, -6, 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"
}
] |
49
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -12, -12, 9],\n [0, -4, 8, 7],\n [0, 0, 9, 12],\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"
}
] |
216
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -11, 2, 0],\n [-11, -9, 0, -6],\n [2, 0, 8, -2],\n [0, -6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
816
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -2, -2, -2],\n [-11, -7, -2, -3],\n [-4, -5, 10, -9],\n [-1, 10, -1, -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"
}
] |
82
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -2, 11, -12],\n [10, 5, -2, 6],\n [9, -11, 0, 6],\n [2, -9, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
387
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 3, 11, -4],\n [-10, -5, -8, 7],\n [1, 10, 8, -12],\n [-6, 2, 5, -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"
}
] |
466
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 8, 4, -3],\n [-11, 7, -4, 8],\n [9, -4, -10, -3],\n [-4, 7, 4, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
434
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 7, -6, 3],\n [7, 10, -2, 8],\n [-6, -2, 6, 4],\n [3, 8, 4, 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"
}
] |
356
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -6, 5, 2],\n [-6, -3, 10, -4],\n [5, 10, 10, 9],\n [2, -4, 9, -5]]\nRound to the nearest integer, then take the result 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[[-1, 1, 11, -3],\n [8, 2, 7, 7],\n [4, 7, -11, -7],\n [12, -9, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -2, -2, 4],\n [-2, -7, 4, 2],\n [-2, 4, -4, 1],\n [4, 2, 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"
}
] |
252
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -6, 4, 9],\n [-6, 2, -2, 8],\n [4, -2, -8, -2],\n [9, 8, -2, -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"
}
] |
316
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 7, -2, -7],\n [7, -6, -1, -2],\n [-2, -1, -9, 1],\n [-7, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
910
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -2, 1, 10],\n [11, 0, 6, 12],\n [3, -12, 12, 3],\n [-12, -12, -4, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -1, -1, -8],\n [-6, -5, -4, 5],\n [8, -9, 5, -6],\n [-12, 2, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
134
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -11, -1, 4],\n [0, -11, 6, 8],\n [0, 0, 12, 8],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
456
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 3, -10, -2],\n [8, -2, -9, 4],\n [4, -8, 1, -1],\n [9, -9, 12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 10, -10, -3],\n [10, 8, -10, -5],\n [-10, -10, 12, 2],\n [-3, -5, 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"
}
] |
848
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 10, 1, -4],\n [-5, -9, -4, 0],\n [3, -11, -2, -10],\n [-5, -8, 11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
856
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -7, -9, -8],\n [0, -4, -10, -10],\n [0, 0, 6, -4],\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"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 5, -3, -7],\n [0, 5, 0, -4],\n [0, 0, -1, 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"
}
] |
600
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -7, 4, 6],\n [-7, -6, -2, -1],\n [4, -2, 7, 11],\n [6, -1, 11, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -8, -1, -2],\n [0, 8, -8, -6],\n [0, 0, 9, 10],\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"
}
] |
80
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -7, 11, 7],\n [-4, -10, -12, -4],\n [8, -11, -10, -7],\n [-6, 11, -11, -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"
}
] |
310
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 8, 6, -6],\n [8, -3, -2, -6],\n [6, -2, -9, 0],\n [-6, -6, 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"
}
] |
803
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 7, -3, 6],\n [0, -7, -11, -10],\n [0, 0, 5, -11],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
695
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -2, -8, 6],\n [-2, 2, 2, 1],\n [-8, 2, -6, -2],\n [6, 1, -2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, -5, 3],\n [-2, -6, -2, -8],\n [-5, -2, -8, -9],\n [3, -8, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
346
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 0, 2, -3],\n [0, 10, -5, 2],\n [2, -5, 2, -4],\n [-3, 2, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
61
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 5, -2, -11],\n [0, 8, 8, -2],\n [0, 0, -8, -11],\n [0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 9, 1, 7],\n [1, 10, 7, -11],\n [7, 3, -7, -4],\n [6, -1, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
750
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, 2, -5],\n [3, 12, -9, 5],\n [-6, 12, -7, -11],\n [0, -9, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
917
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 2, 2, -4],\n [2, -10, 6, 2],\n [2, 6, 12, -1],\n [-4, 2, -1, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
934
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -10, 12, 8],\n [4, 2, -12, 5],\n [5, 11, 4, 10],\n [4, -3, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
314
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -7, -1, 2],\n [0, -4, -12, -4],\n [0, 0, 2, -11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -8, -1, 5],\n [-8, -2, -10, -4],\n [-1, -10, 9, -4],\n [5, -4, -4, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
858
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 4, 5, -10],\n [0, -7, 5, -10],\n [0, 0, -4, -3],\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[[-4, 9, 3, -7],\n [-3, 3, -10, 4],\n [-5, -5, -8, 5],\n [9, 0, -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"
}
] |
976
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 6, 11, -10],\n [-9, 3, 1, -5],\n [6, -7, -1, -6],\n [9, -2, -7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
446
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, -2, -2],\n [0, 5, -4, 6],\n [-2, -4, 8, -6],\n [-2, 6, -6, 6]]\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[[-6, -6, -2, -10],\n [5, 4, 8, 3],\n [-11, -6, 3, 4],\n [6, -5, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 0, 4, -2],\n [0, 3, 1, 2],\n [4, 1, 7, 1],\n [-2, 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"
}
] |
924
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 10, 0, 1],\n [10, -2, -2, -4],\n [0, -2, -7, 8],\n [1, -4, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
508
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 6, 6, 12],\n [-7, 4, 9, 3],\n [10, 2, -5, 0],\n [-5, -5, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
307
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -3, -11, 12],\n [12, 11, 0, -1],\n [5, -3, -9, 11],\n [-4, 5, -5, 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"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -2, -3, 0],\n [-2, 6, 4, 0],\n [-3, 4, -12, -4],\n [0, 0, -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"
}
] |
842
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, 8, 6],\n [6, -11, -2, 2],\n [8, -2, 10, 4],\n [6, 2, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -10, 4, -11],\n [0, 8, 1, 11],\n [0, 0, -12, 5],\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"
}
] |
728
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -7, 2, 6],\n [-7, 2, -2, -3],\n [2, -2, 4, 8],\n [6, -3, 8, -1]]\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[[12, 2, 0, 9],\n [2, 10, -6, 4],\n [0, -6, -4, 0],\n [9, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, -5, -3],\n [0, 11, 3, -4],\n [0, 0, -3, 10],\n [0, 0, 0, -11]]\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[[-6, 8, -2, -10],\n [0, 5, 6, -1],\n [0, 0, 5, -2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -11, 11, -10],\n [0, -12, -2, -5],\n [-1, 7, 1, 10],\n [-7, -8, 12, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
838
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 3, 7, 4],\n [3, -2, 1, 0],\n [7, 1, 5, -2],\n [4, 0, -2, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 4, 2, 0],\n [4, -1, 8, -1],\n [2, 8, 10, 1],\n [0, -1, 1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
741
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 6, -9, 4],\n [0, -4, 9, 4],\n [0, 0, 6, -7],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 3, -4, -1],\n [0, 2, -4, 12],\n [0, 0, -10, 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"
}
] |
480
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -9, -7, -3],\n [0, 1, 5, 9],\n [0, 0, 2, -7],\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"
}
] |
940
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -10, 11, -6],\n [0, 5, 11, 3],\n [0, 0, -11, 2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 3, 7, -12],\n [7, 10, -2, -9],\n [-5, 2, -6, 6],\n [0, -11, 11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
738
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, 3, -2],\n [8, 4, 6, 3],\n [3, 6, -8, 0],\n [-2, 3, 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"
}
] |
961
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 12, -12, -8],\n [0, -5, 0, -11],\n [0, 0, 5, 12],\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"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, -8, -12, -2],\n [-8, 12, 0, -3],\n [-12, 0, -3, -1],\n [-2, -3, -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"
}
] |
424
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -9, 3, -10],\n [0, 10, 0, 10],\n [0, 0, 11, 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"
}
] |
210
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -6, -4, 5],\n [-6, 0, -2, 6],\n [-4, -2, -11, 2],\n [5, 6, 2, 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"
}
] |
84
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -5, 1, -7],\n [0, -2, -1, 11],\n [0, 0, -2, -3],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -3, 3, -5],\n [0, -3, 8, 7],\n [0, 0, 6, 7],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 8, 10, -7],\n [12, 9, -11, -11],\n [-9, -5, 11, 10],\n [-10, 4, 8, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
626
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, 7, 10],\n [0, 1, 1, 6],\n [0, 0, 7, 2],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
63
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 5, -5, -11],\n [0, 12, 0, 2],\n [0, 0, 2, -8],\n [0, 0, 0, -1]]\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[[-7, -5, -9, 4],\n [9, 10, 7, -11],\n [6, 7, -5, -4],\n [-6, -12, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -2, 0, -1],\n [-11, -4, 7, 10],\n [-12, 0, -7, 2],\n [-6, 5, -10, 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"
}
] |
101
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 0, -8, -8],\n [0, 8, 12, -5],\n [0, 0, 8, 1],\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"
}
] |
584
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 9, 8, 1],\n [0, 12, -3, -5],\n [0, 0, 5, 4],\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"
}
] |
800
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 1, 2, 8],\n [1, -4, 3, -1],\n [2, 3, 6, -2],\n [8, -1, -2, -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[[-4, 4, -7, -2],\n [4, 3, 8, 1],\n [-7, 8, 8, -6],\n [-2, 1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 0, -11, -9],\n [0, -5, 0, -2],\n [0, 0, 11, -9],\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"
}
] |
260
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 7, 12, -8],\n [0, 2, -4, -2],\n [0, 0, 8, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
576
|
MATH
|
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