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, 12, -2, -8],\n [0, 5, 1, -3],\n [0, 0, -8, -1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 11, -7, 10],\n [2, -6, 6, 1],\n [1, -1, 2, 6],\n [5, 11, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
203
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 7, -5, -5],\n [0, -10, -4, 1],\n [0, 0, -3, 3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 3, -2, 11],\n [6, -1, -9, -4],\n [-12, 9, -8, 4],\n [-9, -10, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
885
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 8, 4, -9],\n [0, 4, 2, 1],\n [0, 0, -1, 8],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
956
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -2, 7, 11],\n [0, 7, 8, 9],\n [0, 0, -8, 12],\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"
}
] |
880
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 12, 4, 11],\n [0, 10, -8, 8],\n [0, 0, -9, 4],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 8, -12, 4],\n [12, -1, 10, -11],\n [7, -1, 6, -2],\n [12, -9, 5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
171
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -1, 7, -12],\n [0, -3, -4, -5],\n [0, 0, -8, -4],\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"
}
] |
480
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, 0, 2],\n [0, 4, 6, 0],\n [0, 6, -9, 4],\n [2, 0, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 6, 0, 5],\n [0, -8, 11, 1],\n [-1, 6, 10, 5],\n [-2, 4, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -6, 10, -11],\n [6, -7, 6, -12],\n [-7, 3, 3, 1],\n [6, 8, -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"
}
] |
225
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 2, 8, -5],\n [9, 12, 0, -2],\n [-7, -6, 8, 9],\n [12, -1, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -11, -2, -2],\n [0, 1, 5, -7],\n [0, 0, -2, -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"
}
] |
928
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 6, 12, -1],\n [9, -7, 3, 8],\n [12, 2, -9, 12],\n [9, -11, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
213
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 9, 0, 2],\n [0, -2, 4, -12],\n [0, 0, 8, -10],\n [0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
704
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 8, 9, 1],\n [8, -8, 4, 2],\n [9, 4, 5, -7],\n [1, 2, -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"
}
] |
32
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 1, 6, 11],\n [0, -10, -3, 11],\n [0, 0, 3, -1],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -1, -11, -4],\n [0, 5, -5, 6],\n [0, 0, 11, 1],\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"
}
] |
620
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 6, 12, 0],\n [-1, 5, -9, 8],\n [6, 4, 4, 4],\n [8, -2, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
468
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, 9, -10],\n [0, -12, -5, 4],\n [0, 0, -5, -10],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 4, -4, 1],\n [4, 11, 8, 6],\n [-4, 8, -11, -4],\n [1, 6, -4, -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"
}
] |
413
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, 4, -2],\n [0, 5, -8, -8],\n [4, -8, 11, 4],\n [-2, -8, 4, 0]]\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"
}
] |
44
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 11, -4, 4],\n [0, -2, 9, -6],\n [0, 0, -8, 6],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -2, 2, 2],\n [-2, 11, -6, 1],\n [2, -6, -10, 0],\n [2, 1, 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"
}
] |
454
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -10, -7, 0],\n [-11, -7, 9, 8],\n [4, -4, -8, 5],\n [3, -12, -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"
}
] |
365
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, -6, -6],\n [12, -5, -10, -9],\n [-12, -1, -5, 12],\n [10, 11, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
830
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 0, 3, -11],\n [0, 4, 3, 9],\n [0, 0, -4, 12],\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"
}
] |
112
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 9, -6, -11],\n [0, 4, 0, -8],\n [0, 0, 5, -5],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 11, -1, 11],\n [0, -5, 4, 7],\n [0, 0, -6, -10],\n [0, 0, 0, -5]]\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[[4, -6, 1, 4],\n [0, 5, 7, -10],\n [0, 0, 5, 11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -3, 8, 0],\n [-3, -7, -6, -8],\n [8, -6, -9, 0],\n [0, -8, 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"
}
] |
204
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 4, -4, 8],\n [0, 11, 12, -3],\n [0, 0, -2, -3],\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"
}
] |
132
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -2, 1, 8],\n [-2, 8, 6, 3],\n [1, 6, -2, -2],\n [8, 3, -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"
}
] |
493
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 2, -2, -1],\n [2, -3, 6, -7],\n [-2, 6, -2, 8],\n [-1, -7, 8, 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"
}
] |
358
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -4, 9, 0],\n [0, 9, 12, -2],\n [0, 0, -11, 5],\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"
}
] |
624
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, 9, 7],\n [0, 9, 5, 3],\n [0, 0, -6, -3],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
730
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -10, -12, 8],\n [-6, -12, 5, -9],\n [3, -12, -12, 12],\n [4, -1, -11, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
478
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 7, 8, 3],\n [0, 5, 10, -5],\n [0, 0, -7, -12],\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"
}
] |
680
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -6, 2, 6],\n [-6, 9, 6, -3],\n [2, 6, -5, -3],\n [6, -3, -3, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
296
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -11, 7, -8],\n [0, 9, -5, -5],\n [0, 0, -6, 2],\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"
}
] |
540
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 4, 0, -10],\n [4, -6, -2, -8],\n [0, -2, 0, 4],\n [-10, -8, 4, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -2, 12, 0],\n [-2, -1, 0, -6],\n [12, 0, 0, -1],\n [0, -6, -1, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
604
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -3, 5, -10],\n [8, -8, 2, -5],\n [9, 6, 10, 7],\n [-7, -8, 8, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
574
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 0, -10, 5],\n [0, 11, 4, 9],\n [0, 0, 12, -5],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 9, 1, 2],\n [0, 4, 1, -11],\n [0, 0, -2, 9],\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"
}
] |
608
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -1, -2, 9],\n [0, -2, 4, 2],\n [0, 0, -12, -1],\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"
}
] |
864
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 8, -5, 9],\n [-12, -11, -8, -8],\n [3, 3, -1, 8],\n [10, 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"
}
] |
473
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -4, 8, 5],\n [7, 8, 10, -8],\n [-6, -9, 8, -11],\n [-4, -6, 12, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
556
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -8, -2, -5],\n [0, -1, 6, 7],\n [0, 0, -6, -5],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
988
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 1, 6],\n [11, -2, -12, -6],\n [-7, -10, -3, -7],\n [-12, 1, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
703
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -3, 2, 0],\n [-3, 10, 7, -10],\n [2, 7, -11, -8],\n [0, -10, -8, 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"
}
] |
647
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, 10, 8],\n [8, -8, -3, -8],\n [11, 9, 3, -9],\n [-3, 1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
738
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 5, 10, 1],\n [5, 9, 7, -2],\n [10, 7, 5, 6],\n [1, -2, 6, 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"
}
] |
9
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 2, -8, 10],\n [0, 11, 11, 7],\n [0, 0, -2, -8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
822
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 7, 6, 0],\n [7, -3, 8, 2],\n [6, 8, 0, 1],\n [0, 2, 1, 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"
}
] |
118
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 2, 3, 10],\n [2, -6, 11, -1],\n [3, 11, 0, 7],\n [10, -1, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
961
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, 6, 0],\n [0, -6, 6, 4],\n [6, 6, 4, 4],\n [0, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
536
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -6, -1, -1],\n [-6, -11, 0, -1],\n [-1, 0, -6, -7],\n [-1, -1, -7, -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"
}
] |
261
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -10, -5, 7],\n [0, -6, -3, 10],\n [0, 0, -8, -7],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
592
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 2, 0, 4],\n [2, 0, 2, -8],\n [0, 2, -11, 10],\n [4, -8, 10, -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"
}
] |
120
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 0, 0, 2],\n [0, -1, 2, -1],\n [0, 2, -4, 4],\n [2, -1, 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"
}
] |
32
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 9, 4, 3],\n [9, -11, 0, -2],\n [4, 0, 12, 6],\n [3, -2, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
348
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -3, -3, 7],\n [0, 5, -8, 6],\n [0, 0, -11, 8],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 9, 2, -2],\n [9, 12, -7, 0],\n [2, -7, 2, 3],\n [-2, 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"
}
] |
960
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -12, 2, 2],\n [0, 7, 3, 6],\n [0, 0, 9, 10],\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"
}
] |
913
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 8, -11, 0],\n [1, 10, -8, 4],\n [0, -10, -2, 7],\n [6, -1, 7, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
361
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 3, -8, -3],\n [0, -9, 11, -2],\n [0, 0, 3, 1],\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"
}
] |
135
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -2, -2, 2],\n [-2, -9, 0, -6],\n [-2, 0, -2, -2],\n [2, -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"
}
] |
652
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -2, -10, 8],\n [7, -12, 10, -6],\n [3, 6, -4, 2],\n [12, -11, -11, 8]]\nRound to the nearest integer, then take the result 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[[2, -1, -9, 8],\n [0, 4, -6, -4],\n [0, 0, -12, -11],\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"
}
] |
848
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, 1, -10],\n [2, -1, -5, -9],\n [5, 0, 7, -4],\n [4, -4, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
681
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -2, -1, 0],\n [9, -8, -9, -2],\n [-9, -4, 10, -6],\n [4, -2, -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"
}
] |
998
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 2, -4, 8],\n [2, -6, -7, -2],\n [-4, -7, -3, 6],\n [8, -2, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
157
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 7, -4, -7],\n [7, 10, 4, -2],\n [-4, 4, 2, 0],\n [-7, -2, 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"
}
] |
376
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, -4, 6],\n [4, -3, -3, -2],\n [-4, -3, -6, 2],\n [6, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
748
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -12, 2, -2],\n [0, -2, -11, 7],\n [0, 0, -4, 0],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
136
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, -5, -10],\n [-1, -7, -4, 9],\n [-5, -4, 9, -5],\n [-10, 9, -5, 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"
}
] |
43
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -1, 3, 3],\n [0, 6, 12, -4],\n [0, 0, -12, -12],\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"
}
] |
984
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -2, 2, 3],\n [-12, -1, 3, -1],\n [8, 2, 2, 8],\n [-2, -7, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -2, -4, 6],\n [-2, 2, 6, 4],\n [-4, 6, 5, -2],\n [6, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
162
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 7, 8, 6],\n [-5, -5, 4, -8],\n [-3, 10, -6, 3],\n [6, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 10, 8, -5],\n [10, -10, 0, 2],\n [8, 0, 6, -1],\n [-5, 2, -1, 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"
}
] |
438
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -4, -4, -4],\n [-4, 12, 0, 0],\n [-4, 0, 6, 9],\n [-4, 0, 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"
}
] |
232
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 1, -1, 3],\n [1, -3, -12, 0],\n [-1, -12, -2, -1],\n [3, 0, -1, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
122
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, 7, -4],\n [-1, -4, 3, 1],\n [7, 3, -9, -2],\n [-4, 1, -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"
}
] |
402
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 1, 8, -12],\n [-1, 6, 7, 9],\n [4, -12, 9, -12],\n [-1, 4, -5, 7]]\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[[6, -10, -3, 2],\n [0, 2, -6, 12],\n [0, 0, -9, 10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
108
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -4, -11, 6],\n [-6, -4, 10, 1],\n [-2, 0, -11, -10],\n [8, 1, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
369
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 6, 0, 5],\n [0, 6, -1, -12],\n [0, 0, 3, 7],\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"
}
] |
874
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 1, -8, 12],\n [-12, 3, 0, -4],\n [-10, 11, 11, 11],\n [0, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 1, 4, -2],\n [1, 3, -4, 0],\n [4, -4, 5, 0],\n [-2, 0, 0, 0]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -1, -1, 3],\n [-3, 12, -4, 7],\n [5, 6, -10, 3],\n [11, -2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -1, 12, -5],\n [-2, 11, 4, -7],\n [9, 7, -5, 4],\n [-2, -3, 12, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
835
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -11, -6, 5],\n [0, -9, 7, 4],\n [0, 0, 3, 8],\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"
}
] |
810
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, 8, 9],\n [0, 5, 12, -12],\n [0, 0, 11, -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"
}
] |
350
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -4, -5, -5],\n [0, 3, -10, 8],\n [0, 0, -2, -9],\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -6, -5, 3],\n [-2, -4, 7, -5],\n [5, 2, -2, -2],\n [-3, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
682
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 1, -2, -6],\n [1, 1, 2, -4],\n [-2, 2, -6, 0],\n [-6, -4, 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"
}
] |
614
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -2, -4, 4],\n [0, -8, -9, -6],\n [0, 0, -9, -2],\n [0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
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