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[ { "content": "Compute |A| for the matrix A =\n[[2, -10, 6, 4],\n [-1, 10, -7, 9],\n [-7, -9, -5, -12],\n [-5, -9, -6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
236
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 0, 2, 6],\n [0, -5, 6, 3],\n [2, 6, 1, 7],\n [6, 3, 7, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
111
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 3, 7, -8],\n [0, 8, 0, 7],\n [0, 0, -10, 4],\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" } ]
40
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -7, 0, -6],\n [-7, 2, 2, -6],\n [0, 2, 0, 4],\n [-6, -6, 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" } ]
160
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 11, 12, 3],\n [-12, 3, 3, 6],\n [0, -4, -11, -3],\n [-2, -4, -2, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -1, 10, -3],\n [-1, 2, 0, -4],\n [10, 0, -1, 5],\n [-3, -4, 5, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
186
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -3, -7, 12],\n [0, 6, -10, -1],\n [0, 0, 11, -9],\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" } ]
472
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 8, 12, 1],\n [8, 2, 6, 0],\n [12, 6, 11, 9],\n [1, 0, 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" } ]
986
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, 4, -2],\n [2, -11, -4, 6],\n [4, -4, 4, -2],\n [-2, 6, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
936
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 2, -1, -2],\n [2, -11, -4, -11],\n [-1, -4, 3, -2],\n [-2, -11, -2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
395
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -1, -7, 9],\n [-10, -9, -3, 6],\n [11, -12, -6, -8],\n [-8, -10, -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" } ]
102
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, -11, 6],\n [8, -8, -11, -3],\n [-11, 8, 9, -7],\n [2, 10, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
494
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 7, 0, -6],\n [7, -4, -1, -11],\n [0, -1, 10, 6],\n [-6, -11, 6, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
948
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, 8, -12],\n [0, -12, 3, -9],\n [0, 0, -4, 4],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -6, -9, 9],\n [-2, 7, -4, -2],\n [-7, 0, 12, 11],\n [-4, -1, -11, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -6, -11, 0],\n [-6, -10, 3, -1],\n [-11, 3, 4, 0],\n [0, -1, 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" } ]
233
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -7, 1, 4],\n [-7, -6, 0, -2],\n [1, 0, 1, 5],\n [4, -2, 5, -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" } ]
663
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, 0, -2],\n [-2, -6, -2, -2],\n [0, -2, 4, 6],\n [-2, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
448
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -5, 11, 3],\n [0, -10, -3, 6],\n [-11, -4, -6, -6],\n [-12, 6, -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" } ]
532
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 2, -6, 4],\n [2, -2, 0, -7],\n [-6, 0, -7, -9],\n [4, -7, -9, 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" } ]
67
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 5, 7, -5],\n [0, -3, -3, 2],\n [0, 0, 6, 1],\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" } ]
920
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, -8, -6],\n [6, -10, 0, 2],\n [-1, 1, -5, 11],\n [8, 11, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
380
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -10, 8, 1],\n [6, 10, -2, 0],\n [-3, -4, -3, 9],\n [-8, 5, 1, 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" } ]
170
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 3, 5, 10],\n [0, 7, -7, -10],\n [0, 0, -2, 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" } ]
496
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -6, 12, -3],\n [-6, 12, -8, -4],\n [12, -8, 11, 2],\n [-3, -4, 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" } ]
688
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -4, 2, -11],\n [0, -2, -11, -9],\n [0, 0, -7, -9],\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" } ]
140
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 3, 8, 8],\n [0, -2, 9, -1],\n [0, 0, 12, 6],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 12, 8, -4],\n [0, 2, 5, 8],\n [0, 0, -11, 3],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
648
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 9, -9, -7],\n [0, 10, -1, 10],\n [0, 0, -5, 8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -10, 11, -4],\n [-3, -10, -6, -5],\n [-8, 5, 1, -12],\n [7, -7, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
668
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, 7, 10],\n [4, 4, 3, -1],\n [7, -9, 5, 9],\n [-7, 0, -11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
191
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -4, 7, 6],\n [0, 4, 0, 11],\n [0, 0, 7, 4],\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" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -2, 0],\n [2, 4, 2, -1],\n [-2, 2, 6, 4],\n [0, -1, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 7, -9, 5],\n [-10, 6, -7, -5],\n [-2, 3, 10, -4],\n [12, -8, -5, 9]]? 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[[3, 6, 11, 0],\n [-11, -8, 10, 11],\n [8, 6, -12, 2],\n [10, -5, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
314
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -12, 11, 8],\n [11, -3, 2, 2],\n [5, 5, -4, 12],\n [10, 4, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
580
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -12, 6, -4],\n [0, -2, 3, 4],\n [0, 0, -11, -5],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 2, -8, 4],\n [-8, -3, 1, -9],\n [0, 7, -8, 10],\n [3, -7, -5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
888
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -8, -9, 2],\n [-8, -7, -4, 2],\n [-9, -4, 3, 2],\n [2, 2, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -12, 5, -4],\n [0, 12, 12, 8],\n [0, 0, -3, -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" } ]
16
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -11, -9, -9],\n [-2, 1, -5, -8],\n [-4, 12, 11, 8],\n [6, -4, 3, 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" } ]
582
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 6, 3, -11],\n [6, -3, 4, 2],\n [3, 4, 5, -8],\n [-11, 2, -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" } ]
166
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 4, -3, 4],\n [0, 1, -2, -2],\n [0, 0, -11, 10],\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" } ]
944
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -8, -1, -12],\n [0, 4, -11, 5],\n [0, 0, 12, 1],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 1, 2, 4],\n [11, 3, -5, -6],\n [-7, 7, -11, 8],\n [-10, 11, 8, -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" } ]
654
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 3, -1, 10],\n [0, -9, 3, -6],\n [0, 0, 7, -8],\n [0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
984
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 3, 1, 8],\n [0, -8, 7, 3],\n [0, 0, 1, 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" } ]
784
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -3, -10, 12],\n [-5, -5, 10, 5],\n [-11, -12, 12, 3],\n [-7, -1, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -9, 7, 5],\n [0, 4, 0, 10],\n [0, 0, -5, -5],\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" } ]
780
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, -7, 9],\n [-9, 0, -2, -10],\n [1, -3, -2, 8],\n [0, -1, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -10, -3, 11],\n [-10, 7, -7, -6],\n [-5, 0, 10, -6],\n [-6, 2, 5, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
463
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 1, -1, 9],\n [0, 5, 8, 11],\n [0, 0, 8, 1],\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" } ]
200
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, -9, 9],\n [0, -3, 2, -8],\n [0, 0, -5, 7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -5, -2, -7],\n [-5, 9, 1, 1],\n [-2, 1, 1, -6],\n [-7, 1, -6, 1]]? 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": "What is the determinant of the matrix:\n[[1, 0, -9, 2],\n [0, 11, -4, 0],\n [-9, -4, -12, 4],\n [2, 0, 4, -2]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 4, -5, 8],\n [-6, 3, -8, 3],\n [-12, -2, -5, -11],\n [-11, 3, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
159
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 10, 0, 4],\n [10, -2, -6, 2],\n [0, -6, 10, 10],\n [4, 2, 10, 0]]? 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": "Compute |A| for the matrix A =\n[[-4, 4, -8, 9],\n [7, 10, -11, -6],\n [12, 3, 8, -2],\n [-3, -2, 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" } ]
532
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -10, -6, 4],\n [-10, -4, -10, 0],\n [-6, -10, -4, 4],\n [4, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -11, -2, 4],\n [0, 5, -9, -6],\n [0, 0, -2, -9],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -3, -3, -10],\n [-7, 12, 0, -2],\n [-4, 0, 7, 2],\n [-4, -2, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
254
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -3, 6, 8],\n [-3, 9, 4, 6],\n [6, 4, 10, 8],\n [8, 6, 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" } ]
18
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 8, -3, 8],\n [-7, -2, 1, 8],\n [-2, -10, 8, 8],\n [-7, -7, 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" } ]
644
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, 0, -3],\n [6, 6, 2, 4],\n [0, 2, -2, 2],\n [-3, 4, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
728
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 6, -12, -2],\n [-11, 6, 6, -12],\n [10, -4, 3, -12],\n [-4, 12, -3, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 7, 6, 8],\n [-2, 6, 10, -3],\n [-9, -11, -1, 11],\n [-3, 9, 2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
326
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -4, 2, -3],\n [-12, -1, 3, 12],\n [-10, -9, 7, -10],\n [7, 9, -12, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
550
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 3, 4, 5],\n [0, -10, 3, 12],\n [0, 0, 3, -2],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -7, 3, 10],\n [7, 3, -8, -9],\n [-10, 3, -10, -6],\n [-10, 9, -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" } ]
582
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, -12, -10],\n [-7, -11, 7, -3],\n [-7, 2, -9, 4],\n [-10, 4, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
363
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 6, 1, -7],\n [0, 6, -7, -2],\n [0, 0, -12, -3],\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" } ]
816
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -12, 11, 9],\n [2, 6, 4, -6],\n [3, 5, 1, 6],\n [-7, -8, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
676
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 2, 2, -4],\n [2, 10, 10, 4],\n [2, 10, -4, 2],\n [-4, 4, 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" } ]
840
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -2, -3, 1],\n [-2, 7, 0, 6],\n [-3, 0, -2, -7],\n [1, 6, -7, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
484
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 9, -2, 4],\n [1, 1, -12, 0],\n [-1, 10, 1, 4],\n [9, 5, -8, 5]]\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[[-5, -2, 1, 0],\n [-2, -5, 6, -4],\n [1, 6, 8, -6],\n [0, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -1, 7, 9],\n [12, -9, 11, -10],\n [-8, -9, 8, -4],\n [6, 3, 6, -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
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, -1, -2],\n [-1, 4, -6, 6],\n [-1, -6, 9, 1],\n [-2, 6, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -4, 9, 10],\n [0, -1, -8, -2],\n [0, 0, 7, -2],\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" } ]
748
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -9, -9, -6],\n [7, -9, -4, -6],\n [10, 4, -1, -8],\n [2, 7, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
718
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 9, 9, -8],\n [0, -7, 2, 12],\n [0, 0, -2, -11],\n [0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
378
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 6, -3, 10],\n [-6, -3, -9, -9],\n [5, -10, -1, -10],\n [-4, -7, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 1, -12, 8],\n [6, -11, 0, -5],\n [6, -8, 9, 10],\n [-10, -2, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
858
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 2, 5, 0],\n [2, -1, -2, 5],\n [5, -2, -5, -1],\n [0, 5, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
275
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -6, -5, -4],\n [-6, -9, 0, 4],\n [-5, 0, -12, 0],\n [-4, 4, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 0, -4, 4],\n [0, 10, -2, -6],\n [-4, -2, -8, 6],\n [4, -6, 6, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -2, -3, -11],\n [0, 11, -10, -10],\n [0, 0, 10, -2],\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" } ]
680
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 12, -1, 0],\n [12, -12, 2, 12],\n [-1, 0, 8, 10],\n [7, 4, 11, 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" } ]
236
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 5, -8, 4],\n [5, -10, -3, -4],\n [-8, -3, 11, -1],\n [4, -4, -1, -12]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, 11, 9],\n [0, 10, -4, 8],\n [0, 0, -11, 4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 8, -6, -6],\n [8, 9, 2, 4],\n [-6, 2, -11, 6],\n [-6, 4, 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" } ]
917
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 5, -3, 6],\n [0, 7, -9, -4],\n [0, 0, 9, 6],\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" } ]
165
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 2, -7, 12],\n [0, 7, -8, 5],\n [0, 0, -11, -11],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
924
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 7, -6, 4],\n [0, -5, -10, -11],\n [0, 0, -1, 10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 5, -9, -3],\n [0, 8, 4, -2],\n [0, 0, 3, 0],\n [0, 0, 0, -9]]\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, 12, 10, -7],\n [0, 1, 8, -9],\n [0, 0, 3, 5],\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" } ]
958
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, 11, -9],\n [12, 1, -11, -2],\n [-7, 10, 6, -4],\n [-2, -7, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
401
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -6, 1, -1],\n [-6, -9, 1, -9],\n [1, 1, 3, 4],\n [-1, -9, 4, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 5, -6, -3],\n [0, 2, -6, 5],\n [0, 0, -5, 2],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 12, -12, -10],\n [0, -3, -12, 7],\n [0, 0, 12, 5],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH