messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 0, 8, -1],\n [0, -2, -1, 4],\n [0, 0, 4, -10],\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"
}
] |
80
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 7, 6, -12],\n [0, -12, 6, -8],\n [0, 0, -8, 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"
}
] |
968
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -1, -6, -10],\n [0, -11, 4, -10],\n [-12, -2, 4, 10],\n [0, -11, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 11, 8, 10],\n [0, 8, 0, -5],\n [0, 0, 3, -7],\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"
}
] |
432
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -11, -11, -11],\n [-5, 2, -4, 6],\n [3, 5, 8, -5],\n [-2, -6, 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"
}
] |
950
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 6, -4, 2],\n [6, -10, 0, -6],\n [-4, 0, -2, 1],\n [2, -6, 1, -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"
}
] |
836
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -7, 2, -7],\n [0, 2, 10, 5],\n [0, 0, -5, 12],\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"
}
] |
910
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 11, 11, 11],\n [0, 6, -10, -8],\n [0, 0, -9, 1],\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"
}
] |
184
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, -8, -6],\n [4, -3, 4, -4],\n [-8, 4, -3, -8],\n [-6, -4, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
593
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -8, 11, 0],\n [-8, -12, -4, 0],\n [11, -4, -10, -11],\n [0, 0, -11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 5, -6, -3],\n [-11, -2, -7, 10],\n [-9, 2, -11, -9],\n [4, 9, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
716
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -3, 6, -2],\n [-3, -10, 4, 2],\n [6, 4, 3, -4],\n [-2, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
708
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 7, 2, 7],\n [7, 0, -4, -2],\n [2, -4, -9, -3],\n [7, -2, -3, 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"
}
] |
850
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -4, -3, -7],\n [0, 4, 11, 10],\n [0, 0, -12, 12],\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"
}
] |
112
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -3, -5, 11],\n [9, 11, -10, 10],\n [1, -12, 7, 0],\n [0, 12, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 10, 1, -2],\n [10, -6, 4, 4],\n [1, 4, -10, -4],\n [-2, 4, -4, 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"
}
] |
816
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 6, 5, -3],\n [0, -3, 0, 5],\n [0, 0, 4, -7],\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"
}
] |
76
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 4, 2, -10],\n [4, 0, 6, -6],\n [2, 6, -3, -2],\n [-10, -6, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 9, -3, 0],\n [9, -2, -4, 8],\n [-3, -4, -4, -4],\n [0, 8, -4, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
222
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 6, 1, -2],\n [11, -12, 4, 0],\n [6, 2, -10, 6],\n [-12, -9, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
728
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, -10, -7],\n [4, -6, 0, 1],\n [-10, 0, 6, 10],\n [-7, 1, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 12, -5, -6],\n [12, 3, -1, 8],\n [-5, -1, -11, 4],\n [-6, 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"
}
] |
261
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 8, -10, -4],\n [-11, -4, -1, 7],\n [10, -2, 0, -3],\n [-11, 1, 11, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
235
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 12, -5, 8],\n [0, 7, -6, -7],\n [0, 0, 1, -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"
}
] |
336
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 2, -2, 0],\n [2, 3, -10, 0],\n [-2, -10, 2, 0],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
778
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 0, 7, 2],\n [0, 9, -2, 7],\n [0, 0, 3, 9],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
595
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 4, 0, -10],\n [4, -12, 4, 6],\n [0, 4, -11, -2],\n [-10, 6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
148
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -1, 4, -2],\n [0, -2, -11, 8],\n [0, 0, -4, 11],\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"
}
] |
664
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 0, -7, 2],\n [0, -6, -1, 5],\n [-7, -1, 3, -6],\n [2, 5, -6, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
839
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -2, 1, 8],\n [-2, -7, -3, 10],\n [1, -3, -4, 2],\n [8, 10, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
284
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 4, -2, 0],\n [4, 6, 6, -3],\n [-2, 6, 10, -2],\n [0, -3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 5, 6, -2],\n [5, -4, 8, -2],\n [6, 8, -10, -4],\n [-2, -2, -4, 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"
}
] |
212
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 2, -10, 6],\n [0, 2, 1, 5],\n [0, 0, 9, -1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
980
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -7, -8, -7],\n [0, 8, 6, -11],\n [0, 0, -4, -9],\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"
}
] |
520
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -8, -7, 9],\n [0, -7, 7, 1],\n [0, 0, 7, -12],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
118
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -1, -9, 10],\n [-3, 4, 0, 0],\n [-1, 12, 2, 9],\n [7, 6, 1, 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"
}
] |
985
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -4, 2, -1],\n [0, -4, 8, -1],\n [0, 0, -4, -2],\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"
}
] |
136
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -8, -4, 0],\n [0, 1, -10, 1],\n [0, 0, -10, 11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
180
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 3, 2, 6],\n [3, 3, -6, 2],\n [2, -6, 0, -11],\n [6, 2, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
891
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -12, 11, -7],\n [0, 11, -1, 5],\n [0, 0, -2, -7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
736
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -11, -2, 0],\n [-11, -10, 4, 0],\n [-2, 4, -7, 5],\n [0, 0, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
413
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 4, 6, 6],\n [4, 4, -2, 2],\n [6, -2, -2, 0],\n [6, 2, 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"
}
] |
324
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -1, 2, 7],\n [-1, 12, 6, -6],\n [2, 6, -7, 2],\n [7, -6, 2, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
185
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 7, -4, 2],\n [7, 3, -2, -4],\n [-4, -2, -3, -7],\n [2, -4, -7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
142
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -2, -9, 4],\n [-2, 11, -2, 2],\n [-9, -2, -1, -4],\n [4, 2, -4, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 4, -2, 6],\n [4, 4, -2, 8],\n [-2, -2, 9, 4],\n [6, 8, 4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 5, -7, -10],\n [7, -6, -9, 1],\n [-8, -4, -1, 6],\n [1, -5, 7, -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"
}
] |
243
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 10, -11, -8],\n [0, -2, -9, -2],\n [0, 0, -8, -4],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
976
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 7, 3, -7],\n [-3, 9, 11, -12],\n [-11, -11, 11, 0],\n [0, -8, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
140
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, -5, -2],\n [8, 9, 12, 0],\n [-2, -5, 9, -11],\n [12, -1, -11, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
955
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, -9, 1],\n [0, -7, -8, 2],\n [0, 0, -8, 12],\n [0, 0, 0, -6]]\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[[4, -1, -4, 3],\n [0, 4, 5, 3],\n [0, 0, 11, -10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
472
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, 9, 4],\n [-10, 7, 7, 8],\n [12, 0, -7, -10],\n [-4, -7, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 1, -12, 12],\n [0, 2, 8, -12],\n [0, 0, 9, 6],\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"
}
] |
72
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 4, -6, -2],\n [4, -8, 0, -7],\n [-6, 0, 4, -8],\n [-2, -7, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
324
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 3, -9, 7],\n [4, -8, -10, 1],\n [-3, 6, -10, 8],\n [-12, 3, -12, 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"
}
] |
595
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -1, -11, 3],\n [0, -11, 5, -7],\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"
}
] |
700
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -7, -7, -6],\n [-7, 7, -1, -2],\n [-7, -1, -3, 0],\n [-6, -2, 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"
}
] |
428
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -7, 6, 3],\n [0, 1, 9, -3],\n [0, 0, 2, 4],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 10, 10, 1],\n [10, -9, -4, 8],\n [10, -4, 4, 6],\n [1, 8, 6, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 4, -4, -5],\n [0, -12, -8, -2],\n [0, 0, 6, -2],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -1, -4, 5],\n [0, 5, -8, 7],\n [0, 0, 8, -7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -10, -1, 2],\n [-10, 0, 0, -5],\n [-1, 0, 7, 4],\n [2, -5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -5, -8, 3],\n [0, 5, 5, 12],\n [0, 0, 1, 10],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
950
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -10, 6, 1],\n [-6, 7, -3, 5],\n [-11, 6, 0, 7],\n [10, -9, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
243
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -4, -5, 8],\n [0, -1, 4, 2],\n [0, 0, 5, 10],\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"
}
] |
700
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 6, -11, -10],\n [-1, -5, 11, -4],\n [-12, 7, -10, -4],\n [7, 9, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
207
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 1, 0, -5],\n [0, -12, -2, 5],\n [0, 0, -9, -12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
272
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -9, -8, 2],\n [0, 11, -9, 10],\n [0, 0, -3, 6],\n [0, 0, 0, -8]]\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[[9, -10, -7, 4],\n [-3, -2, 11, -5],\n [-11, 3, -2, 11],\n [-5, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
319
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 1, 11, 2],\n [-5, 0, -2, -5],\n [-3, -10, -12, -1],\n [-5, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, -11, 10],\n [6, 5, 8, 2],\n [-7, -4, 9, 5],\n [1, -9, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 0, -11, -2],\n [3, -7, -3, -6],\n [4, 4, 2, -7],\n [10, 2, -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"
}
] |
38
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 2, 7, -2],\n [2, 2, 8, -6],\n [7, 8, -1, -4],\n [-2, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -10, -7, -5],\n [0, -12, 0, -10],\n [0, 0, 9, -11],\n [0, 0, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -8, -1, -2],\n [-8, 10, 0, 5],\n [-1, 0, 4, 4],\n [-2, 5, 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"
}
] |
641
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 3, -4, 11],\n [0, -8, -1, 4],\n [0, 0, 7, -12],\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"
}
] |
504
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -7, 5, -2],\n [10, -12, 12, 5],\n [-8, 3, 4, -5],\n [-2, 7, -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"
}
] |
2
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -7, 1, 10],\n [0, 10, 6, 8],\n [0, 0, 4, 4],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -8, -6, -3],\n [-8, 6, 3, 2],\n [-6, 3, 2, -7],\n [-3, 2, -7, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
997
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -6, 0, -3],\n [-6, 10, 10, -4],\n [0, 10, -6, 2],\n [-3, -4, 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"
}
] |
384
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -3, -6],\n [0, 10, 6, 4],\n [-3, 6, -4, 5],\n [-6, 4, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
386
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, -8, 7],\n [0, 3, 0, -11],\n [0, 0, -10, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
970
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -9, 0, -3],\n [0, 8, -7, 6],\n [0, 0, -8, -4],\n [0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, 2, -4],\n [2, 5, 5, -8],\n [2, 5, -5, 6],\n [-4, -8, 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"
}
] |
144
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 9, -2, 6],\n [-2, -9, -12, -8],\n [-5, 12, -4, 12],\n [-8, -5, -4, 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"
}
] |
832
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 6, -12, 12],\n [-10, -7, -7, -5],\n [-11, 12, 11, -1],\n [-12, 10, 6, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -3, -2, -2],\n [-3, 7, -4, -6],\n [-2, -4, 3, 2],\n [-2, -6, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
316
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -2, -4, -4],\n [-2, -3, 4, -11],\n [-4, 4, -9, 0],\n [-4, -11, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -12, 0, 4],\n [10, -11, -12, -12],\n [12, -10, 1, 7],\n [10, -4, 6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
588
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 0, -6, 12],\n [12, -5, 0, -1],\n [6, 9, 9, 3],\n [1, 3, -6, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
332
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 5, -4, 0],\n [0, -10, -3, 7],\n [0, 0, 10, -1],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -1, 1, 0],\n [-1, 7, 2, 2],\n [1, 2, 1, -4],\n [0, 2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
250
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, 0, -3],\n [-6, 2, 2, 0],\n [0, 2, -5, -6],\n [-3, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
714
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -5, 11, -6],\n [0, 9, -10, 12],\n [0, 0, 5, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
300
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 0, -4, -1],\n [0, 8, 7, -2],\n [-4, 7, 8, -8],\n [-1, -2, -8, -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"
}
] |
445
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 1, -7, -11],\n [-9, 7, 11, 7],\n [-1, -8, -4, -6],\n [-3, -6, 5, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
776
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, -2, 12],\n [2, 8, -2, -8],\n [-2, -2, -7, 12],\n [12, -8, 12, -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"
}
] |
432
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 0, -7, -11],\n [0, -6, 4, 9],\n [0, 0, -4, 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"
}
] |
440
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -12, -1, -6],\n [0, 2, -1, -4],\n [0, 0, 3, -10],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
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