messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[2, 5, -3, -6],\n [0, 7, -7, -2],\n [0, 0, -11, -2],\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"
}
] |
152
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 7, -2, 10],\n [7, 11, 3, 4],\n [-2, 3, -6, -2],\n [10, 4, -2, 2]]\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": "Determine the value of det(A) where A =\n[[10, -1, 0, -7],\n [0, -4, 0, 11],\n [0, 0, 4, -6],\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"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, 4, 0],\n [4, -5, 0, -1],\n [4, 0, 7, 6],\n [0, -1, 6, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
661
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 5, 10, 9],\n [-5, -7, 10, 12],\n [3, -7, 3, 3],\n [3, -10, 5, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
247
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -10, 5, 6],\n [1, -8, 4, -3],\n [-12, 3, 0, 2],\n [0, -7, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
242
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -6, -4, -3],\n [-6, 7, 6, -1],\n [-4, 6, 11, -3],\n [-3, -1, -3, 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"
}
] |
739
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, 3, 5],\n [0, -5, -7, -6],\n [3, -7, 5, -10],\n [5, -6, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
743
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -4, 11, -8],\n [0, 10, -10, 7],\n [0, 0, -3, -4],\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"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -7, -7, 5],\n [3, 3, 10, 6],\n [1, -12, -8, -10],\n [-9, -11, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
578
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 10, 12, 10],\n [8, 4, 6, 12],\n [8, 11, 4, 8],\n [-4, 7, 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"
}
] |
504
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -6, -8, -11],\n [0, -10, -1, 6],\n [0, 0, -5, -2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 6, 1, -1],\n [9, 5, -12, -3],\n [-6, 0, -9, 1],\n [-4, 3, 9, 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"
}
] |
366
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -5, 8, -9],\n [-8, -4, -11, 12],\n [-5, 2, -2, -9],\n [-7, -5, 5, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
805
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -4, 6, -1],\n [-4, 12, -3, -4],\n [6, -3, -6, 1],\n [-1, -4, 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"
}
] |
961
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 4, -11, 4],\n [0, 9, -4, -4],\n [0, 0, -8, -9],\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"
}
] |
216
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 4, -8, -9],\n [5, 1, -12, 0],\n [-6, -7, 2, -5],\n [2, -11, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, -3, -1],\n [5, 5, 10, 9],\n [-9, -10, -10, -3],\n [11, 12, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
971
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -7, 0, -6],\n [-7, 5, 2, 3],\n [0, 2, -10, -5],\n [-6, 3, -5, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
114
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -8, -5, 10],\n [0, 8, 8, -3],\n [0, 0, 10, -2],\n [0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, -3, 11],\n [2, 12, 8, 4],\n [-3, 8, 2, 4],\n [11, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
744
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 2, 1, -2],\n [2, -12, 2, 1],\n [1, 2, -3, -2],\n [-2, 1, -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"
}
] |
588
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, -12, 8],\n [-2, 3, -4, 10],\n [-2, 8, -2, 10],\n [-2, -3, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 5, -1, -2],\n [11, 2, -1, 9],\n [-2, 0, -11, -2],\n [10, -1, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
940
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -6, -10, 12],\n [0, 4, -6, 2],\n [0, 0, -7, 12],\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"
}
] |
232
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -9, 2, -2],\n [-9, -9, -8, 2],\n [2, -8, 0, 1],\n [-2, 2, 1, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
664
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -2, -3, 2],\n [0, -6, 9, -2],\n [0, 0, 6, -9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -3, -7, -8],\n [-7, -10, -4, 11],\n [-5, 12, 1, -6],\n [0, 3, 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"
}
] |
709
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 2, 3, -2],\n [0, -9, 5, 6],\n [0, 0, 9, -1],\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"
}
] |
336
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -6, 12, -10],\n [1, 4, 7, -4],\n [2, 4, 7, 3],\n [10, -7, -10, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
534
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, 2, 10],\n [0, 9, 10, -11],\n [0, 0, 3, -4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
567
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -9, 5, -12],\n [9, -1, 12, 5],\n [-8, -8, -8, 8],\n [3, 9, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
808
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 7, 4, 6],\n [7, -11, -4, 0],\n [4, -4, -10, -2],\n [6, 0, -2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 4, -9, -12],\n [0, -10, -12, -2],\n [0, 0, -4, -11],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 6, -5, -4],\n [6, 11, -6, -4],\n [-5, -6, 5, 9],\n [-4, -4, 9, 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"
}
] |
825
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -12, 9, 2],\n [0, 12, 7, -2],\n [0, 0, -6, -10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -5, 7, 8],\n [0, -1, 8, 4],\n [0, 0, 9, 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"
}
] |
352
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -1, 10, 8],\n [3, 0, -8, 9],\n [-5, 7, -3, 2],\n [1, -7, 8, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
425
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 2, 2, 0],\n [2, 5, 6, 2],\n [2, 6, 11, -1],\n [0, 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"
}
] |
804
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -7, 12, 0],\n [7, -3, -9, -2],\n [4, 3, -6, 1],\n [-4, 10, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
368
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -6, 0, 6],\n [-6, -6, 7, 0],\n [0, 7, -9, -8],\n [6, 0, -8, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
695
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -3, -1, 0],\n [0, 1, -12, 12],\n [0, 0, 10, 12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
230
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -12, -4, -11],\n [0, 2, -9, -3],\n [0, 0, 9, -11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
990
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -11, 3, 4],\n [7, -1, -2, -10],\n [-12, -2, 3, 1],\n [-1, 10, -4, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
53
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 8, 8, -4],\n [8, 8, 0, -1],\n [8, 0, -12, -4],\n [-4, -1, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
456
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -3, -8, -9],\n [12, -5, 4, 11],\n [10, -3, 6, 0],\n [-6, -12, 10, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
526
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -8, -1, -2],\n [10, -8, -1, -8],\n [7, -8, -8, -2],\n [3, 1, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
622
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 6, 5, -10],\n [6, 5, 2, 10],\n [5, 2, 9, -4],\n [-10, 10, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 0, 9, 3],\n [0, -9, -5, -4],\n [9, -5, -7, -4],\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"
}
] |
225
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 8, -4, -12],\n [-5, -12, 11, -8],\n [-8, 11, 3, 7],\n [10, 8, -9, 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"
}
] |
620
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 4, 10, 8],\n [0, -10, -5, -4],\n [0, 0, -5, 0],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
50
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -1, -3, 5],\n [0, 9, -6, -7],\n [0, 0, -4, 1],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -5, 11, -1],\n [0, -12, 4, 8],\n [0, 0, -9, 2],\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"
}
] |
640
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 5, -12, 4],\n [-5, 12, -12, -4],\n [-2, 3, 10, 5],\n [9, 12, -5, 1]]\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[[-2, 7, -1, -7],\n [3, 10, -6, 5],\n [-5, -7, 5, 11],\n [11, -1, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
376
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -8, 0, -3],\n [0, 4, 10, -12],\n [0, 0, -10, 7],\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"
}
] |
760
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -5, -6, 5],\n [-2, -12, -1, -5],\n [9, 10, 3, 10],\n [-2, 2, -12, -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"
}
] |
865
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 7, -2, -5],\n [-1, -1, 1, 2],\n [5, -10, -7, -9],\n [-12, 12, 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"
}
] |
856
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -7, -11, -1],\n [-9, 2, 8, -7],\n [3, 3, 4, -11],\n [-6, 8, 10, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
412
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -9, 0, 7],\n [0, -6, -5, -4],\n [0, 0, 4, 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"
}
] |
56
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -4, -4, -3],\n [0, -10, 6, 7],\n [0, 0, -6, -11],\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"
}
] |
600
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -4, -8, -8],\n [0, 10, -7, -10],\n [0, 0, -12, -7],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 2, 4, -9],\n [2, -8, 8, 4],\n [4, 8, 0, -10],\n [-9, 4, -10, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
184
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 4, -9, 10],\n [-2, -3, -4, 1],\n [-4, 12, 5, 5],\n [-1, 5, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
937
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -6, -1, -7],\n [-6, 6, -6, -7],\n [-1, -6, 0, 4],\n [-7, -7, 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"
}
] |
371
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -10, 7, -11],\n [-12, 4, 2, -12],\n [2, -3, -6, -3],\n [-2, 6, 3, 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"
}
] |
24
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 3, 0, -2],\n [3, 12, -4, -2],\n [0, -4, 10, 8],\n [-2, -2, 8, -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"
}
] |
880
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 6, -6, 4],\n [6, 9, 0, 1],\n [-6, 0, 10, -6],\n [4, 1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, 7, 1],\n [-6, -2, -4, 11],\n [-2, 11, 6, 0],\n [-4, -9, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
114
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 11, 4, -2],\n [0, 1, 6, 3],\n [0, 0, -7, -10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -1, 12, 12],\n [0, -1, -1, 1],\n [0, 0, -8, -8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
256
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -7, -12, 8],\n [0, 4, -3, 4],\n [0, 0, 9, -6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 8, -7, -3],\n [9, 8, 9, 1],\n [-11, 8, -11, 0],\n [-4, 7, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
681
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, 0, -8],\n [0, -1, -7, 0],\n [0, -7, -11, -2],\n [-8, 0, -2, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -10, -2, -9],\n [-10, 7, -10, 1],\n [-2, -10, 9, 12],\n [-9, 1, 12, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
518
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 0, -1, 8],\n [6, -11, 11, -8],\n [6, 11, -7, 9],\n [12, 6, -9, -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"
}
] |
141
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 8, 0, 4],\n [8, 0, 0, 3],\n [0, 0, 2, 8],\n [4, 3, 8, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
926
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, 6, -12],\n [0, -6, 12, -12],\n [0, 0, -5, 4],\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"
}
] |
520
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -10, 2, -11],\n [7, 4, 6, 1],\n [-8, -1, -10, 7],\n [-7, 9, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 1, -12, 0],\n [1, -4, 4, 11],\n [-3, -3, 10, 1],\n [-11, 2, 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"
}
] |
452
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, -10, 8],\n [4, 8, 11, 0],\n [9, 12, 5, 2],\n [1, 12, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
786
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -7, -8, 0],\n [-7, -6, -12, 10],\n [3, 5, -3, -3],\n [4, 3, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
645
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -2, -5, -8],\n [-2, 10, -3, 0],\n [-5, -3, 8, -8],\n [-8, 0, -8, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 0, 0, 8],\n [0, 5, -5, 4],\n [0, -5, -12, 8],\n [8, 4, 8, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
653
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, 2, 1],\n [-6, 1, -4, 3],\n [2, -4, -3, 8],\n [1, 3, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
55
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -8, 0, 0],\n [-8, 7, -2, 10],\n [0, -2, 2, 12],\n [0, 10, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
556
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, 3, -4],\n [2, 2, 6, 2],\n [3, 6, -1, 4],\n [-4, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -12, -1, -6],\n [0, 6, -6, -2],\n [0, 0, -2, -1],\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"
}
] |
420
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 1, 6, -3],\n [1, 1, -5, -2],\n [6, -5, -4, 7],\n [-3, -2, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -3, 0, -2],\n [-3, 7, 0, -1],\n [0, 0, -1, 4],\n [-2, -1, 4, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
265
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 0, 0, 4],\n [0, -6, 5, 4],\n [0, 5, -12, 3],\n [4, 4, 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"
}
] |
152
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -3, -10, -1],\n [-3, 10, 10, 9],\n [-10, 10, 5, 2],\n [-1, 9, 2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
136
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -4, -3, 8],\n [-4, 2, -2, -12],\n [-3, -2, -9, 2],\n [8, -12, 2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
870
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 2, -2, -10],\n [2, -1, -2, 4],\n [-2, -2, 0, 0],\n [-10, 4, 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"
}
] |
736
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -2, -2, 0],\n [-2, -3, -2, 0],\n [-2, -2, -8, 2],\n [0, 0, 2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 6, -1, 1],\n [0, 1, -1, -8],\n [0, 0, 1, 2],\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"
}
] |
879
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -6, 4, -6],\n [0, 2, -7, 2],\n [0, 0, 12, -8],\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"
}
] |
456
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 11, -4],\n [2, 5, 4, -2],\n [11, 4, -6, 3],\n [-4, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
809
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -1, -6, 6],\n [-1, 6, 7, 1],\n [-6, 7, 5, -7],\n [6, 1, -7, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
687
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -8, -4, -6],\n [-8, 11, -2, 4],\n [-4, -2, -4, 0],\n [-6, 4, 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"
}
] |
936
|
MATH
|
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