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[[-9, 7, -6, 4],\n [0, -5, 6, -12],\n [0, 0, 10, -11],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
250
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 12, 1, 11],\n [0, -11, -6, 4],\n [0, 0, -8, 2],\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"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -3, -11, -4],\n [10, 10, 4, 10],\n [-6, -9, 11, 10],\n [-1, -12, 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"
}
] |
492
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, 6, -4],\n [0, -2, 8, -7],\n [0, -2, 3, 4],\n [-6, 6, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
168
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -3, 1, 10],\n [-5, -7, -8, 5],\n [-7, -12, -4, -5],\n [-7, 8, 1, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
981
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 1, 7, 3],\n [1, 11, 9, 2],\n [7, 9, 7, 4],\n [3, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 12, 5, -7],\n [0, -12, -10, 4],\n [0, 0, 7, -8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
740
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 2, -6, 11],\n [0, -3, 5, 11],\n [0, 0, 9, 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"
}
] |
732
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -5, 2, 3],\n [3, 7, -8, -1],\n [3, 12, 6, -9],\n [-4, -7, 4, -12]]\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[[5, -3, -1, 6],\n [0, -4, -10, 2],\n [0, 0, 4, -10],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -3, 0, 8],\n [4, 6, -8, -2],\n [-3, 12, 10, 1],\n [6, -4, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
504
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -1, -5, 4],\n [-1, 10, -5, -9],\n [-5, -5, 6, -8],\n [4, -9, -8, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
705
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 9, -6, -5],\n [10, -2, -3, -6],\n [-7, -8, 6, -5],\n [0, -9, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
393
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -8, 5, -5],\n [0, -7, -4, 10],\n [0, 0, -10, -9],\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"
}
] |
890
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -10, 3, 8],\n [0, -6, -3, 3],\n [0, 0, 9, -2],\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"
}
] |
270
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 6, 1, -2],\n [6, -11, 3, -8],\n [1, 3, -5, 4],\n [-2, -8, 4, 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"
}
] |
455
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, 9, 10],\n [0, 7, 1, -6],\n [0, 0, -12, -4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
64
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 4, -4, -7],\n [-9, -12, -12, 11],\n [2, -12, 10, -7],\n [2, -4, 5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
376
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -2, -2, -5],\n [-2, -10, 8, -2],\n [-2, 8, 7, 0],\n [-5, -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"
}
] |
70
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 2, 2, 8],\n [2, 0, -1, 4],\n [2, -1, 1, -1],\n [8, 4, -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"
}
] |
461
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -3, 9, 3],\n [0, -9, 9, -12],\n [0, 0, 1, -10],\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"
}
] |
540
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -7, 0, 6],\n [-7, 2, 12, 2],\n [0, 12, 1, 5],\n [6, 2, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
177
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 6, -5, -3],\n [0, -2, -5, 11],\n [0, 0, -8, -9],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
896
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -11, 9, 4],\n [0, -7, 2, -7],\n [0, 0, 3, -2],\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"
}
] |
617
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 5, 3, 1],\n [0, 4, 9, -1],\n [0, 0, -8, -10],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 1, -9, 4],\n [0, 4, 1, 10],\n [0, 0, 6, -4],\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"
}
] |
592
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 3, -6, -2],\n [-8, -3, 7, 4],\n [-12, 9, -12, 3],\n [-11, -8, 4, -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"
}
] |
883
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 12, 2, -2],\n [6, -12, 10, 3],\n [9, 8, -8, 0],\n [-1, -1, 5, 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"
}
] |
130
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -5, 12, 3],\n [0, 2, -11, 3],\n [0, 0, 5, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, -7, -4],\n [-4, -8, -6, -4],\n [-7, -6, -4, -7],\n [-4, -4, -7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 5, -2, -2],\n [0, -12, -12, 11],\n [4, -7, -9, -8],\n [1, 9, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 5, -3, -9],\n [0, -6, 5, -8],\n [0, 0, 10, -5],\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"
}
] |
20
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -9, 5, -11],\n [0, -1, -8, -9],\n [0, 0, -7, -3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
776
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 2, -8, -8],\n [2, 2, 0, -4],\n [-8, 0, -9, -8],\n [-8, -4, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
382
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 5, 4, 5],\n [5, -6, 2, -2],\n [4, 2, 11, -2],\n [5, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
416
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -5, 8, -10],\n [-8, 10, -12, 12],\n [6, 4, -7, 1],\n [7, -6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
590
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 8, -8, -10],\n [10, 9, 12, 8],\n [-3, -10, -12, -3],\n [0, 4, -6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -11, 4, 8],\n [-7, 8, 6, -10],\n [-9, 1, -2, -12],\n [-2, 11, -11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -6, 4, 6],\n [-6, 3, -6, 3],\n [4, -6, 10, 10],\n [6, 3, 10, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
974
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 8, 3, -12],\n [0, 6, 4, 12],\n [0, 0, 8, -12],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 10, 2, 2],\n [10, 9, -1, 1],\n [2, -1, -5, 6],\n [2, 1, 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"
}
] |
340
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 12, 9, 10],\n [0, -11, -8, 10],\n [0, 0, -1, -7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
604
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 4, 8, -2],\n [4, -9, -10, -4],\n [8, -10, 12, -5],\n [-2, -4, -5, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
492
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -10, 5, -6],\n [0, 6, -4, -6],\n [0, 0, -12, 8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -10, 4, -4],\n [-1, 5, -3, 2],\n [6, 4, -8, 3],\n [4, 1, 10, 6]]? 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[[10, 4, -2, -4],\n [4, 1, -6, 2],\n [-2, -6, -1, 4],\n [-4, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
988
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, -3, 10],\n [12, -12, 8, -7],\n [-3, 10, 11, 9],\n [9, 8, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
930
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 0, 0],\n [0, 0, -2, 4],\n [0, -2, 6, 1],\n [0, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 6, -8, 0],\n [-1, 10, 10, 4],\n [0, -4, 3, 6],\n [-2, -3, -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"
}
] |
932
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -4, 2, -3],\n [-4, -3, 8, -3],\n [2, 8, 4, 10],\n [-3, -3, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
296
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -1, -2, -3],\n [-1, -7, -2, -5],\n [-2, -2, 9, 2],\n [-3, -5, 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"
}
] |
854
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -5, 6, -11],\n [0, -6, 3, -4],\n [0, 0, -5, 8],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
270
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -8, 3, -10],\n [0, -5, 3, -2],\n [0, 0, 7, -12],\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"
}
] |
840
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 1, -1, 10],\n [-10, 6, 3, -10],\n [3, -8, -5, 11],\n [11, -1, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
837
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, -1, 3],\n [10, -2, -3, 2],\n [-1, 1, 7, -8],\n [9, -10, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
621
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -10, -3, 7],\n [10, -11, -12, -6],\n [5, -10, -1, -12],\n [-7, 7, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
191
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -10, -4, -6],\n [8, 3, 7, -10],\n [-7, -11, -8, -8],\n [3, 2, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
864
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 9, 3, 2],\n [2, 2, 9, -7],\n [-7, -2, 5, -8],\n [1, 5, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -1, 10, -9],\n [-3, -1, 9, -3],\n [-2, 0, -2, -11],\n [2, 3, -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"
}
] |
223
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, 12, -10],\n [-9, -2, 3, -12],\n [-6, 9, 0, 10],\n [0, -8, -6, -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"
}
] |
120
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 9, 1, -6],\n [-12, -12, 12, -12],\n [4, 8, 7, 2],\n [2, -6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, 11, -1],\n [0, 12, -4, 9],\n [0, 0, -5, -8],\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"
}
] |
300
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -9, 10, -9],\n [3, -9, -5, 8],\n [-3, -9, -10, 6],\n [-7, 5, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
255
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 4, 2, -1],\n [0, -4, 3, -9],\n [0, 0, 1, -6],\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"
}
] |
24
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -3, -6, 1],\n [-4, 5, 0, -10],\n [-2, 9, -9, -9],\n [-1, 11, 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"
}
] |
566
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 5, 3, -7],\n [0, 1, 3, 11],\n [0, 0, 9, -9],\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"
}
] |
891
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -7, -3, 7],\n [0, -3, 6, 12],\n [0, 0, 1, -5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
928
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -12, 6, 1],\n [10, 3, -5, 8],\n [8, -5, 3, 9],\n [-11, 2, 1, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
938
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -6, 4, 2],\n [-6, 8, -6, -8],\n [4, -6, 12, 8],\n [2, -8, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
816
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -3, -4, 3],\n [-2, -6, -11, 2],\n [-9, -4, -4, -5],\n [-6, -11, -10, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
349
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -5, -5, 7],\n [-5, -11, 6, -3],\n [10, -3, 2, -8],\n [0, -4, 9, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -8, -9, 9],\n [0, -6, 0, -4],\n [0, 0, -7, 1],\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"
}
] |
160
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, 2, -9],\n [-6, 0, -5, -12],\n [-8, -2, -9, 5],\n [-4, -4, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
516
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -3, 3, 0],\n [-3, 4, -2, 2],\n [3, -2, -2, 2],\n [0, 2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
292
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -3, -3, 12],\n [0, 7, 2, 2],\n [0, 0, -9, 6],\n [0, 0, 0, 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"
}
] |
79
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 4, -3, 7],\n [0, 11, -12, -9],\n [0, 0, 5, 4],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
525
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, -8, 0],\n [9, 3, -2, -1],\n [-8, 11, -10, 10],\n [4, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
388
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -9, 10, -11],\n [0, 10, 8, 7],\n [0, 0, -6, -1],\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"
}
] |
720
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 1, -4, -2],\n [6, 6, 8, 10],\n [-7, 12, -10, -9],\n [-5, -11, 6, -4]]? 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": "What is the determinant of the matrix:\n[[-2, -9, -10, -7],\n [0, 2, -8, -11],\n [0, 0, 2, -6],\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"
}
] |
952
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -9, 7, 4],\n [-9, 7, 6, 10],\n [7, 6, -9, -4],\n [4, 10, -4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
498
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 5, -8, 8],\n [5, 10, 1, -5],\n [-8, 1, 10, 0],\n [8, -5, 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"
}
] |
586
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -6, 2, 0],\n [11, 1, -3, -9],\n [-1, 8, -7, 7],\n [11, -12, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
813
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, 0, 4],\n [0, 11, -2, 10],\n [0, -2, 10, 10],\n [4, 10, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
126
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -2, -2, -4],\n [-2, -5, -8, -6],\n [-2, -8, 1, 2],\n [-4, -6, 2, 8]]\nRound to the nearest integer, then take the result modulo 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[[5, 6, -9, 7],\n [0, -3, 3, -9],\n [0, 0, 11, -6],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -1, -7, -3],\n [0, 5, 9, 7],\n [0, 0, -7, -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"
}
] |
160
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 0, 0, -8],\n [0, 6, 4, 8],\n [0, 4, 7, 8],\n [-8, 8, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
872
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, -12, -9],\n [10, 2, 3, 12],\n [-4, -8, -6, -6],\n [-10, 12, -6, 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"
}
] |
708
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 3, 10, -6],\n [11, -12, -6, 6],\n [-6, -8, -3, 11],\n [6, -7, -2, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
361
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 5, -9, -6],\n [0, -6, -5, 2],\n [0, 0, 4, -3],\n [0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -11, -11, 6],\n [0, -9, -11, 12],\n [0, 0, -6, -7],\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"
}
] |
544
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 3, -9, 0],\n [4, -3, 4, 0],\n [6, -7, -8, 5],\n [10, 8, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 5, 9, -9],\n [-11, -6, 3, 7],\n [10, 8, -10, 12],\n [-1, -2, 5, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
364
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 9, 6, -2],\n [0, -11, -3, 2],\n [0, 0, -10, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 5, 2, -8],\n [5, 1, 4, 0],\n [2, 4, 12, 8],\n [-8, 0, 8, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
384
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -4, -5, 5],\n [-3, 7, 5, 3],\n [9, 0, -9, 5],\n [1, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
594
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 0, -3, 8],\n [0, 2, -6, -4],\n [-3, -6, -2, -1],\n [8, -4, -1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
444
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -10, -1, 6],\n [0, 9, -7, 3],\n [0, 0, -1, 0],\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"
}
] |
99
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -12, -2, -2],\n [0, 7, -11, -6],\n [0, 0, -12, -3],\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"
}
] |
740
|
MATH
|
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