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[[5, 7, -3, -9],\n [-7, -1, 3, 7],\n [10, -5, -4, -2],\n [-5, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
992
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 10, 2, 9],\n [-2, -12, -4, 11],\n [-12, 4, -9, 8],\n [-7, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
802
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 0, 6, -6],\n [0, -1, -1, 2],\n [6, -1, 12, 8],\n [-6, 2, 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"
}
] |
953
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -4, 5, -3],\n [-7, 7, 9, -12],\n [-10, 4, -7, -6],\n [-8, 7, -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"
}
] |
696
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 3, -6, 7],\n [0, 3, -3, 5],\n [0, 0, 5, -4],\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"
}
] |
945
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 6, -2],\n [-6, -10, 9, 9],\n [-4, 7, -4, 4],\n [-6, 2, 12, -6]]\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[[-7, -5, -4, 2],\n [11, 12, 4, 0],\n [-1, -5, 2, 6],\n [1, 2, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
422
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, -2, -4],\n [-4, -6, 2, 11],\n [-2, 2, 1, 2],\n [-4, 11, 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"
}
] |
514
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -6, 2, 0],\n [8, -10, -4, -10],\n [-8, -7, -9, -3],\n [-6, 5, 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"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 8, -4, -3],\n [0, 3, 0, -8],\n [0, 0, 9, -10],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
323
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -2, 0, -2],\n [-2, -7, -4, -9],\n [0, -4, -9, 12],\n [-2, -9, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -1, 6, -2],\n [-1, -6, 1, -2],\n [6, 1, 2, -4],\n [-2, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
431
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -11, 0, 4],\n [0, -2, 7, 10],\n [0, 0, -3, 8],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 6, 11, -9],\n [-1, -2, 5, -8],\n [5, 12, 2, -2],\n [-12, 12, -3, 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"
}
] |
34
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, -5, 0],\n [8, 3, -9, -5],\n [-5, -9, -8, -4],\n [0, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
839
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -8, 12, 1],\n [-10, 7, 3, 0],\n [-8, -3, 2, 10],\n [-8, -10, -12, 1]]? Round to the nearest integer, then express your answer modulo 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[[-6, 8, 0, 4],\n [8, 11, -1, -2],\n [0, -1, -4, -6],\n [4, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
50
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 1, -4, 1],\n [1, 0, 2, 4],\n [-4, 2, -3, 4],\n [1, 4, 4, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
690
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 10, -12, -12],\n [0, 12, -10, -6],\n [0, 0, -2, 2],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
136
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -12, -9, 12],\n [-11, 6, 5, 10],\n [-3, -1, 12, -3],\n [5, 6, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
113
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -5, -11, -2],\n [0, 4, 4, 5],\n [0, 0, 10, -1],\n [0, 0, 0, -9]]\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[[-6, -2, 0, -2],\n [-2, -7, -6, -2],\n [0, -6, 2, 1],\n [-2, -2, 1, -5]]\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[[-4, 12, 7, 1],\n [0, -10, 5, -7],\n [0, 0, 7, 10],\n [0, 0, 0, 4]]\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[[3, 4, -12, 4],\n [4, 6, 9, -10],\n [-12, 9, -4, 7],\n [4, -10, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
148
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -10, -7, -7],\n [-12, -10, -4, 9],\n [6, -2, 2, 3],\n [6, 5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
156
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -5, -8, -4],\n [0, -5, -4, 0],\n [0, 0, 8, 11],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 3, -7, -3],\n [7, 4, -8, -2],\n [-4, 11, 0, -3],\n [9, 2, -11, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 2, -3, -2],\n [2, -2, 9, 7],\n [12, 12, -2, -12],\n [9, -11, 11, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
644
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -3, 9, 4],\n [-3, 9, 8, -5],\n [9, 8, 1, 6],\n [4, -5, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
787
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 8, 3, -9],\n [8, 11, 6, 2],\n [3, 6, -3, 0],\n [-9, 2, 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"
}
] |
903
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, 0, -8],\n [0, 5, -12, 9],\n [0, 0, -8, -7],\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"
}
] |
320
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -8, 0, -6],\n [11, 3, 6, 7],\n [-12, -12, 4, 11],\n [-2, -1, -4, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
244
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 12, -1, 9],\n [12, 11, 0, -2],\n [-1, 0, 6, 1],\n [9, -2, 1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
894
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 6, 9, 3],\n [-7, -2, 1, -8],\n [7, -7, 11, -6],\n [12, 1, -8, 0]]\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": "Determine the value of det(A) where A =\n[[-7, 12, 6, -12],\n [0, 6, -7, 1],\n [0, 0, 7, -12],\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"
}
] |
236
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -9, -6, -12],\n [0, -3, -5, 8],\n [0, 0, -7, -1],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
811
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, 1, 6],\n [-9, -3, 3, -6],\n [9, -11, 4, 11],\n [-5, 0, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
883
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -10, 5, 10],\n [0, 10, -10, -4],\n [12, 11, -10, 4],\n [1, 5, -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"
}
] |
352
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, 4, 6],\n [-8, 3, 9, -1],\n [6, 0, -3, 3],\n [2, 4, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
130
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, -2, 4],\n [-2, 8, 5, -6],\n [-2, 5, -2, 7],\n [4, -6, 7, 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"
}
] |
524
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, -4, 2, -8],\n [-4, -10, 10, -2],\n [2, 10, -5, -4],\n [-8, -2, -4, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 12, -6, 1],\n [0, -8, 7, -2],\n [0, 0, 5, 8],\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"
}
] |
440
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -3, 1, 0],\n [12, -2, -11, 8],\n [-12, 10, -1, 6],\n [-7, 10, -11, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
694
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -10, 9, 6],\n [5, -5, -6, -9],\n [12, -12, 2, 11],\n [-12, -8, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -9, 0, -2],\n [0, -12, -11, 0],\n [0, 0, 8, -2],\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"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -2, 8, -9],\n [0, 8, -12, 4],\n [0, 0, -1, 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"
}
] |
440
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -12, -12, -9],\n [0, 3, 1, -6],\n [0, 0, -10, 5],\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"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -1, 3, -5],\n [5, 0, -3, -1],\n [4, -6, 3, 7],\n [2, 10, -10, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
401
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, -11, 10],\n [-11, -2, 12, 10],\n [11, -2, -8, 3],\n [1, -3, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
861
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 4, 11, -2],\n [0, -9, 3, 8],\n [0, 0, -2, 5],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
980
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -8, 2, -4],\n [-8, -3, -4, 8],\n [2, -4, -8, 8],\n [-4, 8, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
820
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 8, 6, -9],\n [4, -10, -9, -6],\n [0, 7, 11, -10],\n [-8, 5, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, 12, -5],\n [0, 10, 2, 1],\n [0, 0, -7, 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"
}
] |
690
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 4, 9, -12],\n [4, 7, -9, 5],\n [9, -1, 7, -3],\n [-2, -11, 8, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 12, 5],\n [0, 10, -2, 9],\n [0, 0, -5, -9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -4, 4, -1],\n [-4, 0, 8, 4],\n [4, 8, 10, -6],\n [-1, 4, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
184
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 8, -9, 5],\n [-3, 0, -3, -3],\n [-10, -8, -4, -12],\n [6, 9, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
756
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 0, -9, -10],\n [0, 2, -1, 0],\n [-9, -1, 9, 11],\n [-10, 0, 11, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
668
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -2, 12, -2],\n [0, -12, -8, 5],\n [0, 0, -7, 7],\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"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 6, -5, -8],\n [12, 9, 4, 1],\n [-6, -2, 10, -8],\n [1, 3, -11, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
452
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -11, -9, -9],\n [8, -8, 5, 5],\n [-1, -6, -3, -10],\n [-10, 3, -4, -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"
}
] |
929
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -5, 11, 9],\n [0, 7, -2, 0],\n [0, 0, -11, 4],\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"
}
] |
305
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 0, 6, 4],\n [0, -12, -9, -1],\n [6, -9, 1, 0],\n [4, -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"
}
] |
653
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -3, -6, -2],\n [-3, 8, -6, -4],\n [-6, -6, -5, -11],\n [-2, -4, -11, 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"
}
] |
836
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 4, -2, 3],\n [0, 2, 3, -9],\n [0, 0, 1, 9],\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"
}
] |
936
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 7, 4, 8],\n [0, -10, 3, -12],\n [0, 0, -6, -9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, -12, -6],\n [-2, 2, -2, -4],\n [-12, -2, 9, 4],\n [-6, -4, 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"
}
] |
160
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -12, 1, -5],\n [0, -5, 1, 8],\n [0, 0, 3, -6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, -8, -8],\n [0, 7, 0, -11],\n [0, 0, 9, -1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
748
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -1, -7, -5],\n [7, 11, -5, -4],\n [-2, 5, -2, -7],\n [11, 12, -10, 5]]\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[[7, 5, 9, 4],\n [0, -9, 5, -6],\n [0, 0, 12, -7],\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"
}
] |
24
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 6, 6, -5],\n [-1, 4, 10, -11],\n [10, -11, -7, 2],\n [8, 4, -6, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -9, 9, -10],\n [2, -9, 11, 4],\n [-11, -1, -10, 10],\n [8, 11, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
561
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -5, -1, 7],\n [-5, 4, -2, -4],\n [-1, -2, -4, -9],\n [7, -4, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -11, -11, 8],\n [9, -10, 12, 5],\n [-12, -4, 1, 8],\n [-9, 0, 12, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
395
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 4, 4, -2],\n [4, -4, 2, 5],\n [4, 2, -3, 1],\n [-2, 5, 1, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
770
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 0, 3, 1],\n [0, -6, 4, 9],\n [3, 4, 1, 2],\n [1, 9, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
235
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -5, 9, 6],\n [0, -6, 8, 5],\n [0, 0, -6, -11],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, -2, 10],\n [-3, -7, 5, 8],\n [-2, 5, -4, 0],\n [10, 8, 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"
}
] |
124
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 4, -1, -4],\n [4, -5, 4, 2],\n [-1, 4, 10, -2],\n [-4, 2, -2, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
766
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 12, -2, 1],\n [-1, 12, 12, 2],\n [-2, -10, -9, 7],\n [7, -6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
740
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -8, -2, -9],\n [-8, -7, -4, -2],\n [-2, -4, 8, 6],\n [-9, -2, 6, 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"
}
] |
216
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 0, 9, -8],\n [0, -7, 0, -4],\n [9, 0, -6, -4],\n [-8, -4, -4, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
598
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -4, 1, -10],\n [2, -1, 2, 12],\n [5, 8, -2, -7],\n [-7, 9, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 12, -5, 12],\n [-8, -12, -1, -8],\n [0, 7, -11, -11],\n [10, -9, 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"
}
] |
13
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -2, 4, -3],\n [0, 6, -6, -12],\n [0, 0, 2, -5],\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"
}
] |
756
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -9, -10, -5],\n [0, -7, 2, -7],\n [0, 0, 6, -1],\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"
}
] |
24
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -8, -6, -3],\n [-8, -3, -4, 6],\n [-6, -4, 3, -6],\n [-3, 6, -6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
438
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 0, 9, 2],\n [0, 10, -4, 2],\n [9, -4, 11, -6],\n [2, 2, -6, 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"
}
] |
460
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -6, -3, 10],\n [0, -6, -3, 2],\n [0, 0, 9, 2],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
112
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -8, 8, 10],\n [0, 6, 11, -12],\n [0, 0, 4, 8],\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"
}
] |
984
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 6, 5, -10],\n [0, -1, 0, 12],\n [0, 0, -11, 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"
}
] |
230
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -1, -2, -2],\n [-1, -10, 6, -6],\n [-2, 6, -8, 11],\n [-2, -6, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
575
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 2, 7, 1],\n [2, -5, 10, 0],\n [7, 10, -12, -7],\n [1, 0, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
130
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -8, -8],\n [0, -8, 9, 2],\n [-8, 9, -4, 8],\n [-8, 2, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
589
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -11, -8, 4],\n [-10, -5, 4, 11],\n [-6, 3, -8, -10],\n [-10, 12, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
469
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -7, 6, -10],\n [0, -8, -10, -5],\n [0, 0, -3, -2],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 2, 5, -7],\n [2, -4, 2, 8],\n [5, 2, -6, 2],\n [-7, 8, 2, 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"
}
] |
756
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 11, -5, -3],\n [0, 4, -5, 9],\n [0, 0, -1, 4],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -9, -9, -6],\n [0, 10, 2, 10],\n [0, 0, -10, -11],\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"
}
] |
0
|
MATH
|
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