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[[4, 3, -10, 3],\n [10, 12, 10, 5],\n [-7, 1, 12, -2],\n [-1, 9, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
886
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -7, 0, 5],\n [-11, 1, -3, 1],\n [5, -10, -2, 10],\n [-5, 3, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
367
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -2, -4, -1],\n [-1, -5, -5, 10],\n [4, -4, -7, -11],\n [0, -4, 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" } ]
660
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 2, 1, 6],\n [2, 11, -10, 1],\n [1, -10, 2, 7],\n [6, 1, 7, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -5, 12, -2],\n [0, 6, -6, 5],\n [0, 0, -1, 2],\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" } ]
420
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -7, -8, -2],\n [-1, 12, -7, -1],\n [-9, -8, -1, 7],\n [-5, -7, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 4, -2, 2],\n [4, 4, -5, -4],\n [-2, -5, -1, 4],\n [2, -4, 4, -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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -12, 9, -12],\n [1, 11, 7, -10],\n [-3, -3, -5, -1],\n [10, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
71
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 11, -11, 3],\n [-11, -1, -1, -1],\n [-6, 9, -8, -4],\n [11, -6, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
290
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, 12, -12],\n [12, 11, -3, 3],\n [-5, 0, -2, 0],\n [3, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
797
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, -8, 0],\n [0, 12, 0, 7],\n [0, 0, 4, -9],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
944
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -12, 7, -10],\n [0, 7, 9, -3],\n [0, 0, -8, 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" } ]
280
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 0, -5, 12],\n [0, 12, -7, -4],\n [-5, -7, 0, 0],\n [12, -4, 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" } ]
928
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 3, -2, 2],\n [3, 5, -3, 6],\n [-2, -3, 8, -8],\n [2, 6, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
349
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 6, -10, 6],\n [0, 6, -2, 10],\n [0, 0, -12, 11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -6, -4, -12],\n [0, -9, 6, -1],\n [0, 0, -1, -6],\n [0, 0, 0, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
496
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -7, -5, 1],\n [5, -6, -9, 0],\n [11, 8, 10, -10],\n [-9, 4, 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" } ]
953
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -7, -11, 7],\n [-1, 0, -2, 4],\n [11, -3, -1, 1],\n [5, -11, 6, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
290
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -12, 6, 4],\n [0, 4, -8, 8],\n [0, 0, -9, -3],\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" } ]
408
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 12, 4, 8],\n [0, -1, -12, 8],\n [0, 0, -9, 1],\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" } ]
820
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -10, 9, 10],\n [4, -12, -8, 12],\n [10, -2, -1, -12],\n [11, -4, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, 4, 10],\n [-5, 0, 4, 7],\n [-5, -12, -4, -3],\n [12, 2, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -7, -6, 6],\n [-7, 1, -8, 4],\n [-6, -8, 7, -7],\n [6, 4, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
604
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 0, 4, 6],\n [0, -5, -4, -10],\n [4, -4, -11, -8],\n [6, -10, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 6, 2, -4],\n [6, 3, 5, -5],\n [2, 5, 10, -6],\n [-4, -5, -6, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
510
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 8, -2, -2],\n [0, 6, -6, -7],\n [0, 0, 2, -5],\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" } ]
180
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -11, -4, 12],\n [-11, 11, 10, -12],\n [-4, 9, -12, -6],\n [-1, -1, 9, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
884
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -10, 8, -4],\n [-10, -7, 0, 9],\n [-10, 8, -7, 8],\n [-4, -4, -2, 5]]\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[[-9, -12, 10, 9],\n [-10, 12, -2, 12],\n [-12, 12, 6, 5],\n [5, -5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
522
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 8, -2, -8],\n [8, -2, 2, -8],\n [-2, 2, -4, 2],\n [-8, -8, 2, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
776
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -9, 12, -9],\n [1, -10, 8, 5],\n [-6, 12, 9, 0],\n [11, 0, 8, -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" } ]
86
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -7, -7, 7],\n [0, -2, -4, -4],\n [0, 0, -5, -10],\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" } ]
30
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 3, -6, 12],\n [1, -7, -6, -8],\n [11, 3, -9, -2],\n [-7, 6, -6, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
989
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 6, 12, -3],\n [0, 10, 0, -9],\n [0, 0, -11, 6],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 4, -8, -4],\n [4, 1, -3, -5],\n [-8, -3, 8, 2],\n [-4, -5, 2, -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" } ]
296
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -6, 2, 5],\n [2, -10, 7, 3],\n [8, -1, 6, -3],\n [1, 8, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
463
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 1, 8, 0],\n [0, 6, 3, -7],\n [0, 0, 10, -8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
380
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -2, 4, -2],\n [-2, -2, 0, 2],\n [4, 0, -2, 2],\n [-2, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -2, -8, -9],\n [-1, -5, 12, 0],\n [2, -6, 10, -9],\n [-11, 6, 3, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
238
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 3, -8, -12],\n [0, -4, -1, 4],\n [0, 0, 4, 10],\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" } ]
952
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 2, -6, 2],\n [2, 5, -5, 1],\n [-6, -5, 5, 8],\n [2, 1, 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" } ]
749
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -7, 3, 8],\n [0, -6, -4, 5],\n [0, 0, 4, 10],\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" } ]
808
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 2, -2, -11],\n [2, 4, -2, -2],\n [-2, -2, 3, 2],\n [-11, -2, 2, -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" } ]
228
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -11, -8, -7],\n [9, 4, 10, -3],\n [5, 7, 4, 0],\n [12, 6, -2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
958
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 6, 0, -2],\n [6, -9, -8, -7],\n [0, -8, -10, 2],\n [-2, -7, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
794
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -12, 8, 10],\n [-12, -6, -9, 12],\n [8, -9, -5, -2],\n [10, 12, -2, 6]]\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[[2, 8, 4, -2],\n [8, -10, -9, -8],\n [4, -9, -6, 0],\n [-2, -8, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 10, -9, 6],\n [0, -5, 5, 1],\n [0, 0, 5, 12],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
375
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -2, -8, 0],\n [-2, -5, 2, 8],\n [-8, 2, 1, 1],\n [0, 8, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
267
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 11, 12, 7],\n [0, 9, -8, -12],\n [0, 0, 9, 10],\n [0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
595
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, 10, -4, -2],\n [2, -4, -6, -10],\n [0, -2, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -3, -5, -10],\n [-3, -1, -2, 4],\n [-5, -2, -5, -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" } ]
204
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -1, 3, -6],\n [1, -6, -9, 7],\n [-12, -4, -4, 10],\n [-11, 11, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -10, 0, 6],\n [8, 2, -10, 4],\n [3, -12, 3, 2],\n [-12, 3, -12, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
620
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -2, -8, -8],\n [-2, -4, 4, 0],\n [-8, 4, 12, 3],\n [-8, 0, 3, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
116
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 1, -8, -6],\n [1, -9, 2, 4],\n [-8, 2, 8, 5],\n [-6, 4, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
777
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -2, -2, 3],\n [-2, 9, 10, 9],\n [-2, 10, 6, 0],\n [3, 9, 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" } ]
870
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 5, 1, 12],\n [0, 4, 10, -1],\n [0, 0, 7, -8],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, -3, 1],\n [0, 5, 6, 3],\n [0, 0, 10, 9],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
750
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -4, -8, 2],\n [-4, 5, -6, 0],\n [-8, -6, 12, -8],\n [2, 0, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 5, -12, 7],\n [-6, -7, -10, -12],\n [5, 5, -1, 2],\n [-5, 0, 11, -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" } ]
65
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -3, -4, -8],\n [-3, -3, 0, 0],\n [-4, 0, -3, 4],\n [-8, 0, 4, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
386
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 6, 3, -12],\n [12, -6, -1, 2],\n [-3, 12, 11, -7],\n [6, -7, -5, -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" } ]
773
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -5, 6, -1],\n [-5, 2, 2, 4],\n [6, 2, 0, 2],\n [-1, 4, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 12, 5, -7],\n [8, -7, -8, -1],\n [-11, 5, 2, -7],\n [-6, -8, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
661
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 5, -12, -8],\n [-5, 0, -9, 6],\n [-2, 2, -6, -6],\n [-10, -1, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -3, -12, 3],\n [0, -9, 5, 2],\n [0, 0, 7, 6],\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" } ]
236
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 0, 8, 6],\n [-12, 4, -5, 10],\n [-9, 5, 4, 2],\n [6, 10, 1, -7]]\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[[7, -4, -1, 10],\n [-4, 0, 2, 3],\n [-1, 2, -8, 4],\n [10, 3, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
697
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 0, 4, -7],\n [0, -4, -6, -10],\n [4, -6, -9, 8],\n [-7, -10, 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" } ]
216
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -4, -8, 4],\n [-4, 1, -6, -10],\n [-8, -6, 10, 4],\n [4, -10, 4, 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" } ]
944
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -10, 11, 6],\n [0, -4, 6, -5],\n [0, 0, 6, 6],\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" } ]
576
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 8, -9, -2],\n [8, -10, 2, 9],\n [-9, 2, 7, -1],\n [-2, 9, -1, -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" } ]
555
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, -8, -2],\n [-2, 10, 8, -4],\n [-8, 8, 9, -1],\n [-2, -4, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
272
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 8, -10, 2],\n [-9, 1, 7, 12],\n [-9, 8, 4, 3],\n [-3, -1, 5, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -7, 5, -3],\n [11, 10, -1, 7],\n [6, 8, 9, 2],\n [2, 5, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -11, -3, -5],\n [0, -2, -9, -11],\n [0, 0, 9, 9],\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" } ]
352
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 1, 0],\n [0, -3, -7, -5],\n [0, 0, 7, -7],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
231
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 7, -10, 5],\n [0, 10, -5, 3],\n [0, 0, -2, -9],\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": "What is the determinant of the matrix:\n[[-5, -8, -2, 9],\n [-9, -4, -9, -8],\n [-5, 9, 2, 3],\n [12, -8, -10, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
341
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 6, 7, 10],\n [0, -9, -7, -8],\n [0, 0, 9, 8],\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" } ]
290
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 0, -1, -10],\n [0, 7, 2, 0],\n [-1, 2, 8, -4],\n [-10, 0, -4, -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" } ]
68
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -12, -1, -7],\n [-4, -5, -4, -12],\n [-1, 4, 10, -11],\n [12, -7, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
621
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -4, 6, -7],\n [0, 9, -11, -6],\n [0, 0, 2, -5],\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" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -9, -7, 0],\n [-6, -9, -8, -4],\n [11, 10, -1, 7],\n [-7, 1, -10, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
351
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 5, -1, 3],\n [5, -11, -2, -2],\n [-1, -2, 9, -8],\n [3, -2, -8, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
125
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -12, 1, 5],\n [3, -4, 4, -3],\n [9, -10, 12, 4],\n [1, -5, 10, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
863
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 6, 7, -11],\n [0, 1, -11, -3],\n [0, 0, 9, 6],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 5, 0, 8],\n [0, 5, 6, 1],\n [0, 0, 8, 10],\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" } ]
800
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -10, -4, 8],\n [-10, 1, 5, -2],\n [-4, 5, -12, 0],\n [8, -2, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
786
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -7, -6, -5],\n [0, 12, 11, 7],\n [0, 0, 1, 11],\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" } ]
324
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -11, 1, -4],\n [10, 10, 1, 3],\n [5, 11, -5, 12],\n [11, 2, 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" } ]
44
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 9, 8, -4],\n [0, -3, 0, 12],\n [0, 0, -9, 10],\n [0, 0, 0, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
648
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 2, 1, 10],\n [-5, -2, 9, -8],\n [-8, 10, 8, 4],\n [-11, 1, 2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
348
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -4, 4, -8],\n [0, 9, -6, -1],\n [0, 0, 2, 7],\n [0, 0, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
568
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 4, 8, 10],\n [4, -11, 0, -6],\n [8, 0, 3, 6],\n [10, -6, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
834
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 8, -1, 10],\n [8, -6, 4, 0],\n [-1, 4, 9, 7],\n [10, 0, 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" } ]
720
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -5, 0, -12],\n [0, 10, -10, 9],\n [0, 0, 11, 3],\n [0, 0, 0, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -6, -4, -12],\n [7, 11, -6, 3],\n [-12, 6, -4, -9],\n [-4, -10, 9, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
781
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, -7, -7],\n [0, 9, 11, -1],\n [0, 0, 8, 12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH