messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -5, 0, 4],\n [-6, 12, 5, -4],\n [-11, 3, 11, -4],\n [11, 3, 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"
}
] |
970
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -8, 8, 1],\n [0, -8, -3, 2],\n [0, 0, 4, -10],\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"
}
] |
24
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -8, 2, 1],\n [-8, 1, -3, -5],\n [2, -3, -9, -8],\n [1, -5, -8, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
667
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -3, 3, -6],\n [0, 5, 3, 11],\n [6, -2, 5, 5],\n [10, -10, -11, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
464
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 4, 0, 4],\n [4, -12, -4, -10],\n [0, -4, -1, 6],\n [4, -10, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
328
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, 0, 4],\n [0, -3, -2, 6],\n [0, -2, 1, -4],\n [4, 6, -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"
}
] |
699
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 7, 2, -11],\n [0, 7, -6, 4],\n [0, 0, 7, -2],\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"
}
] |
715
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 12, -2, 10],\n [0, 9, 7, 5],\n [0, 0, 11, -6],\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"
}
] |
990
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -2, 11, -1],\n [0, -3, 8, -4],\n [0, 0, -8, 0],\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"
}
] |
416
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 1, -8, -12],\n [-2, 5, -4, -11],\n [-7, -1, -3, 4],\n [2, -6, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 10, -12, -6],\n [0, -12, 10, 7],\n [0, 0, 12, -5],\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"
}
] |
816
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, -1, 6],\n [-4, 5, -6, 7],\n [-1, -6, 5, 0],\n [6, 7, 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"
}
] |
848
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, -8, 4],\n [-7, 1, -6, -11],\n [6, -3, 7, 3],\n [-2, -7, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 11, -5, -5],\n [0, -3, 3, -8],\n [0, 0, 9, -6],\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"
}
] |
28
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -6, -6, -6],\n [-6, 6, 7, -2],\n [-6, 7, 6, -3],\n [-6, -2, -3, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -3, -9, -5],\n [0, -11, 8, -10],\n [0, 0, -5, 1],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -6, 6, -8],\n [-6, -12, 4, 6],\n [6, 4, -6, -3],\n [-8, 6, -3, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 11, -3, 4],\n [0, -5, -10, 6],\n [-12, -2, -9, -4],\n [6, -4, 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"
}
] |
964
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 1, 0, 2],\n [1, 11, 1, -6],\n [0, 1, -11, 6],\n [2, -6, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
523
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -11, 1, 8],\n [-9, -9, 1, -5],\n [-2, -12, 5, 12],\n [4, 0, -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"
}
] |
941
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 8, -9, 9],\n [0, 10, -9, -4],\n [0, 0, -5, 3],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 2, 4, 0],\n [2, -5, 11, 0],\n [4, 11, -2, 2],\n [0, 0, 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"
}
] |
32
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 7, -12, -12],\n [-6, 2, 1, 12],\n [7, 11, 0, 10],\n [7, -1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
394
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -6, 5, 4],\n [0, 8, -12, 5],\n [0, 0, 2, 5],\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"
}
] |
464
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 8, 4, -4],\n [8, -12, -1, -4],\n [4, -1, 9, -4],\n [-4, -4, -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"
}
] |
636
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 10, 4, -3],\n [-2, -3, -7, 8],\n [3, 5, 7, 11],\n [-2, -8, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, 5, 7],\n [0, -5, -8, 7],\n [0, 0, -11, 11],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
330
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, -1, -8],\n [12, -12, 12, 8],\n [12, 0, -3, 6],\n [-3, -7, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -6, -4, -5],\n [-6, 1, -3, 2],\n [-4, -3, 2, 9],\n [-5, 2, 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"
}
] |
743
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 6, 2, -2],\n [6, -1, 8, -6],\n [2, 8, 2, -10],\n [-2, -6, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
444
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, 11, 4],\n [-5, -3, -6, -10],\n [-11, -5, 11, -7],\n [8, -6, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
753
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, -2, 2],\n [0, 9, 8, 9],\n [-2, 8, -1, 10],\n [2, 9, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
756
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 4, 6, -8],\n [4, 10, -2, 0],\n [6, -2, 10, 8],\n [-8, 0, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
976
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -3, 0, -2],\n [0, 9, -7, 2],\n [0, 0, -1, -10],\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"
}
] |
54
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 10, 4, -11],\n [0, 6, -5, 4],\n [0, 0, -12, -4],\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"
}
] |
624
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, -9, -3],\n [8, 7, -7, 8],\n [-11, 4, 2, -9],\n [10, -1, 2, -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"
}
] |
8
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 0, 6, 2],\n [0, -12, 8, 8],\n [6, 8, -6, 4],\n [2, 8, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
672
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -8, -6, -2],\n [-8, 12, 6, -2],\n [-6, 6, 0, 6],\n [-2, -2, 6, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
304
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -1, 7, 4],\n [0, -10, -6, 1],\n [0, 0, 9, -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"
}
] |
600
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, 4, 9],\n [0, -1, 2, 11],\n [0, 0, 5, 0],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -6, 11, -12],\n [0, -2, -2, -12],\n [0, 0, 10, 4],\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"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -12, 10, -10],\n [12, 3, -10, 6],\n [-1, -8, -4, 7],\n [-9, 5, -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"
}
] |
972
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 12, 4, 7],\n [0, -8, 9, -2],\n [0, 0, 2, 0],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
896
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -4, 9, 4],\n [0, -11, -3, -10],\n [0, 0, -10, -11],\n [0, 0, 0, -1]]\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[[-8, 11, -9, -2],\n [0, 12, -12, -12],\n [0, 0, 7, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -11, 7, 5],\n [-10, -12, 10, -10],\n [-5, -2, 2, -7],\n [6, -10, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
206
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -7, -12, -5],\n [0, 1, 4, 7],\n [0, 0, 1, 11],\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"
}
] |
7
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 1, -2, 2],\n [12, 5, -5, 4],\n [2, 6, 5, 1],\n [0, 2, -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"
}
] |
788
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 0, -12, -11],\n [0, -6, 4, 10],\n [0, 0, -12, 8],\n [0, 0, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
304
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 3, -12, -6],\n [-9, 9, 6, 7],\n [1, -10, 2, 10],\n [0, 9, 4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 5, -9, 12],\n [1, 8, -8, 0],\n [-6, -8, 7, 12],\n [7, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
531
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, 0, 4],\n [-4, 0, -1, -4],\n [0, -1, -10, -6],\n [4, -4, -6, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
464
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 4, 10, 4],\n [4, 2, 8, 0],\n [10, 8, -9, 2],\n [4, 0, 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"
}
] |
136
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 2, 5, 10],\n [10, 9, 4, -6],\n [9, 10, -2, 1],\n [4, 1, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
877
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 1, -10, 8],\n [-7, -7, 2, 3],\n [-1, -4, -8, -3],\n [-5, -1, -7, 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"
}
] |
50
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 11, -7, 9],\n [3, 2, 7, 9],\n [5, -11, -11, 9],\n [7, 1, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
328
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -1, 2, 2],\n [-1, -1, -6, -4],\n [2, -6, 10, -4],\n [2, -4, -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"
}
] |
944
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -4, 12, 10],\n [0, 4, -2, 9],\n [0, 0, 1, -4],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
712
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -7, -3],\n [-2, -1, 0, 0],\n [-7, 0, -3, -4],\n [-3, 0, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
969
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -9, 5, 12],\n [0, 6, 2, -5],\n [0, 0, -7, 3],\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"
}
] |
304
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -12, 1, 6],\n [-12, -1, -5, -6],\n [1, -5, 5, 6],\n [6, -6, 6, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
339
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 11, -5, 0],\n [-5, 11, -11, -5],\n [-3, -5, -3, -8],\n [-12, 3, -10, -1]]? 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": "Compute |A| for the matrix A =\n[[-12, -7, -1, -10],\n [-7, 11, 8, -10],\n [-1, 8, -2, 1],\n [-10, -10, 1, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
196
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, 7, 2],\n [6, -12, 5, -12],\n [10, -11, 1, -5],\n [-3, -4, 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"
}
] |
77
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -5, -5, -11],\n [11, -4, -5, 7],\n [-7, 11, 3, 2],\n [-6, 4, 4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
510
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 9, 8, -5],\n [0, -10, 12, -11],\n [0, 0, -12, 3],\n [0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 3, 6, -2],\n [10, 10, -2, 0],\n [2, 9, -1, -6],\n [-9, 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"
}
] |
900
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 5, -3, 3],\n [1, -11, -1, -6],\n [-6, 10, -9, 3],\n [7, -3, 4, -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"
}
] |
542
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 2, -10, -9],\n [0, 9, 1, -8],\n [8, -2, -6, -6],\n [-11, -9, -6, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
714
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 11, -3, -5],\n [0, 6, 3, 10],\n [0, 0, -10, 7],\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"
}
] |
780
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -8, 9, 6],\n [0, 6, 11, 1],\n [0, 0, 10, -9],\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"
}
] |
880
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 3, -4, 6],\n [3, 1, 10, -1],\n [-4, 10, 7, 9],\n [6, -1, 9, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
337
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 1, 4, 6],\n [1, 5, -3, -6],\n [4, -3, 5, 3],\n [6, -6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
383
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -10, -4, 2],\n [-10, -3, 8, 4],\n [-4, 8, -1, -1],\n [2, 4, -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"
}
] |
740
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 11, 6, -4],\n [0, 6, -12, 12],\n [0, 0, 9, -3],\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"
}
] |
168
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -1, 4, 10],\n [0, -4, -9, 1],\n [5, 11, -6, 1],\n [-5, -9, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
566
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 12, -12, 3],\n [0, 11, 11, 10],\n [0, 0, 10, -9],\n [0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 2, -8, 10],\n [2, -4, -9, -11],\n [-8, -9, -1, 8],\n [10, -11, 8, 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"
}
] |
479
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, -11, -12],\n [-11, 0, 3, -3],\n [-5, -11, -6, -6],\n [4, -6, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
904
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, -10, -3],\n [0, 11, 1, -3],\n [0, 0, -6, 6],\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"
}
] |
848
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 10, -12, 6],\n [0, -12, 12, 2],\n [0, 0, 5, -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"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 9, 0, 10],\n [-4, 2, 4, 9],\n [-2, -11, 4, 10],\n [-8, 2, 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"
}
] |
315
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 10, 5, -2],\n [1, -9, 8, -12],\n [0, -12, -12, -5],\n [11, 10, 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"
}
] |
497
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -5, 4, 4],\n [1, -11, -12, -1],\n [1, 4, 2, -3],\n [6, -12, -4, 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"
}
] |
2
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 7, 1, 0],\n [8, 5, -2, -7],\n [8, -6, -10, 6],\n [-3, -8, 3, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
450
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 6, 7, -12],\n [7, 2, 2, 6],\n [1, -1, 11, -3],\n [4, -8, 1, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
658
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -1, 4, 6],\n [1, -6, 6, 12],\n [-9, 1, 12, -11],\n [3, 0, -8, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
62
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -2, -2, 12],\n [-7, 0, 10, 8],\n [0, -4, 6, 12],\n [9, -3, -12, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -12, -3, 7],\n [0, 4, -9, 11],\n [0, 0, 11, -3],\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"
}
] |
388
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 0, 5, -3],\n [4, 6, -10, 1],\n [7, -6, 4, -10],\n [-6, -10, -7, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
846
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -5, -8, 8],\n [-5, -4, -4, -2],\n [-8, -4, -1, 2],\n [8, -2, 2, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
83
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -2, -8, -5],\n [-2, 10, -4, 0],\n [-8, -4, 0, -1],\n [-5, 0, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
554
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -1, -5, -5],\n [5, 0, -7, 11],\n [6, -9, 1, 3],\n [0, -2, -6, -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"
}
] |
636
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -8, -6, 2],\n [-8, 5, -7, 2],\n [-6, -7, 0, 2],\n [2, 2, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
281
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 3, 4, -6],\n [9, 7, 9, -9],\n [-1, -11, 6, 0],\n [-3, -5, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
576
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 1, 1, 0],\n [1, 0, -2, 5],\n [1, -2, -11, -3],\n [0, 5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
166
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -3, 0, 2],\n [-3, -7, 4, 0],\n [0, 4, 3, 4],\n [2, 0, 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"
}
] |
157
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -11, 10, 3],\n [7, -5, 12, -11],\n [-4, 2, 5, 3],\n [3, 4, -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"
}
] |
898
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 1, 3, 4],\n [1, -4, 6, 2],\n [3, 6, -9, 4],\n [4, 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"
}
] |
468
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -4, 2, -10],\n [-4, 0, -4, 2],\n [2, -4, -3, -9],\n [-10, 2, -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"
}
] |
456
|
MATH
|
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