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[ { "content": "Determine the value of det(A) where A =\n[[-4, 1, 3, 7],\n [-6, -11, 6, 2],\n [-1, 8, -6, -1],\n [-5, -8, -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" } ]
652
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 4, -2, -6],\n [4, 7, -6, -2],\n [-2, -6, -4, 2],\n [-6, -2, 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" } ]
352
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 5, 2, 1],\n [5, -1, -2, -1],\n [2, -2, -7, -6],\n [1, -1, -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" } ]
875
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -10, 7, 0],\n [-10, 12, 5, -10],\n [7, 5, 5, 7],\n [0, -10, 7, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
576
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -3, 1, -7],\n [0, 11, 11, -4],\n [0, 0, 12, -8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
744
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -9, -5, 2],\n [-10, 3, -5, -2],\n [-11, -9, 6, 12],\n [-6, -9, -12, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
556
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 0, 3, -11],\n [4, -5, -5, 8],\n [1, -10, 9, 4],\n [11, -8, -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" } ]
214
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -6, -7, -8],\n [6, 1, 6, 7],\n [11, -9, 8, 6],\n [2, 3, 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" } ]
314
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -8, -8, -11],\n [-10, 9, 3, -2],\n [-3, 11, -8, -2],\n [-10, -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" } ]
134
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -7, -9, 5],\n [9, -3, 1, -10],\n [-5, 9, -9, 0],\n [-12, 7, -8, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
220
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 9, 8, -10],\n [10, 7, -6, -12],\n [5, 1, 4, 11],\n [3, 7, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
483
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -8, 6, 9],\n [-4, 4, -3, -8],\n [-6, -5, 7, 4],\n [8, -4, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -8, 2, -3],\n [-11, 3, -10, -10],\n [-2, -6, -6, -12],\n [-8, -4, 5, 12]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -1, -3, -9],\n [-8, -10, -12, -6],\n [-2, -11, -2, 2],\n [-1, 12, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
890
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 1, -5, 9],\n [4, -12, 2, 7],\n [-7, -1, -4, -12],\n [-5, 12, -9, -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" } ]
641
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -2, -8, 6],\n [-2, 3, -1, 1],\n [-8, -1, -8, 3],\n [6, 1, 3, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
119
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, -4, -2],\n [-4, 6, 1, -2],\n [-4, 1, 6, -4],\n [-2, -2, -4, 8]]\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[[-11, -1, 0, 10],\n [0, -4, -12, -3],\n [0, 0, 1, -6],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 5, 4, -7],\n [0, -2, -4, 2],\n [0, 0, 1, -12],\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" } ]
112
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 1, -1, 8],\n [0, -4, -5, 2],\n [0, 0, -8, -9],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
384
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 10, -5, 2],\n [10, -10, 0, 1],\n [-5, 0, -3, 4],\n [2, 1, 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" } ]
571
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 0, -8, -11],\n [0, -4, 2, -7],\n [0, 0, 4, 8],\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" } ]
744
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -10, -7, -10],\n [0, -7, -7, 3],\n [0, 0, 12, -11],\n [0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 4, -10, 8],\n [-12, 1, 2, 2],\n [-10, 2, -4, 11],\n [-3, -9, 7, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
830
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 6, 2, 10],\n [12, -4, -2, 0],\n [5, 6, -9, 0],\n [2, 12, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 0, 0, 0],\n [0, -10, -3, -6],\n [0, -3, 9, 5],\n [0, -6, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
668
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 8, 1, 2],\n [8, -9, -2, 0],\n [1, -2, -3, -1],\n [2, 0, -1, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
685
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, -11, 1],\n [-9, -1, -5, -8],\n [-9, 12, -12, -10],\n [-10, 1, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
349
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, 10, 4],\n [2, 4, 3, -6],\n [3, 8, -3, 3],\n [2, -11, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
425
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -1, 6, 8],\n [-1, -3, -3, 3],\n [6, -3, 4, 1],\n [8, 3, 1, 6]]? 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": "What is the determinant of the matrix:\n[[3, 4, -10, 0],\n [4, -6, -4, 11],\n [-10, -4, 7, -6],\n [0, 11, -6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
891
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -8, -8, -12],\n [12, 11, 4, 0],\n [-10, 8, 2, 4],\n [10, 1, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -6, 12, -11],\n [-8, -11, -3, -5],\n [-9, 7, -10, 7],\n [-11, 1, -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" } ]
994
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, 4, -2],\n [0, 9, 0, -5],\n [4, 0, -2, 3],\n [-2, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
82
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 12, 2, -10],\n [-3, -11, -2, 7],\n [10, 2, -1, -2],\n [-7, 4, -11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
196
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 2, 6, -6],\n [2, 0, 4, 6],\n [6, 4, 0, -2],\n [-6, 6, -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" } ]
32
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -5, 10, -11],\n [-8, 11, 0, -1],\n [-9, 5, -2, 11],\n [1, 3, 5, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 8, -5, 11],\n [5, -6, -10, 1],\n [-1, -10, 8, 11],\n [8, 12, -11, 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" } ]
88
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -5, -2, -8],\n [-6, -6, -4, -9],\n [-7, 9, -4, -4],\n [-8, -1, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
194
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 10, 11, -7],\n [0, -5, 8, 3],\n [-12, 3, -10, 9],\n [-6, -1, -12, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
650
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 3, -6, 10],\n [6, -8, -3, 1],\n [-11, 0, -4, 4],\n [-10, -6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
789
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 2, -2, 12],\n [-5, -2, -7, 3],\n [-10, -11, 12, -8],\n [0, 11, -6, 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" } ]
992
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -2, 7, 10],\n [0, 1, 2, 6],\n [0, 0, 1, 12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
934
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 11, -2, -2],\n [0, 5, -3, 9],\n [0, 0, 8, -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" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 8, -4, 6],\n [8, -8, -10, 4],\n [-4, -10, 8, 0],\n [6, 4, 0, 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" } ]
544
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 10, 10, -9],\n [5, -5, -4, -10],\n [10, -12, -4, -1],\n [7, 7, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
954
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -3, -2, 5],\n [0, -5, 4, -5],\n [0, 0, -7, -6],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
790
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 5, -7, 4],\n [9, -5, 8, 10],\n [-3, 1, -4, 10],\n [-11, 8, 8, -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" } ]
766
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 2, -6, -10],\n [0, 9, 12, 6],\n [0, 0, -12, 1],\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" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -6, 9, 7],\n [3, -6, -10, -2],\n [9, 9, 4, -4],\n [6, 11, 5, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
718
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -5, -10, 11],\n [0, -2, 0, 1],\n [0, 0, -1, -2],\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" } ]
900
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 10, 9, -5],\n [6, 0, 6, -1],\n [6, -3, 9, 2],\n [5, -3, 11, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
685
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -11, -5, -9],\n [0, 1, 7, -12],\n [0, 0, -1, 0],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
982
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -12, -7, -10],\n [11, 1, -9, -5],\n [-7, 10, -1, 6],\n [10, 10, -10, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 9, 12, -12],\n [0, -8, -1, -11],\n [0, 0, 12, -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" } ]
832
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -8, -6, 10],\n [-8, -9, -2, 2],\n [-6, -2, -10, -4],\n [10, 2, -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" } ]
824
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -9, -6, 6],\n [5, -1, -9, 10],\n [5, -6, -10, -8],\n [-5, -12, 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" } ]
90
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -2, 0, 1],\n [-2, 0, 0, -2],\n [0, 0, 9, 2],\n [1, -2, 2, 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" } ]
88
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -5, 11, -3],\n [0, 2, 3, 8],\n [0, 0, -9, -9],\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" } ]
504
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, 11, 0],\n [0, 7, -2, 0],\n [0, 0, 1, 6],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
378
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 4, 5, 2],\n [-9, 2, 12, 7],\n [-8, 9, 6, -5],\n [-6, -8, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -1, -10, -3],\n [0, -4, -2, 6],\n [0, 0, 2, -11],\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" } ]
744
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 0, 7, -6],\n [0, 3, 10, 12],\n [0, 0, 8, 3],\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" } ]
40
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -9, 3, -3],\n [-4, 9, 2, -1],\n [-2, -1, -2, -6],\n [-12, 4, 7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
417
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 1, -7, 2],\n [0, 10, 5, 7],\n [0, 0, -6, -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" } ]
460
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 10, 9, 12],\n [0, 1, 4, 12],\n [0, 0, -4, 7],\n [0, 0, 0, 1]]\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[[-5, 12, 6, -1],\n [-12, -5, -5, 9],\n [-3, 8, -9, 7],\n [-4, 6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
486
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 2, 2, -12],\n [1, -2, 1, -12],\n [-3, -9, -9, 5],\n [-4, -12, 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" } ]
518
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 8, -10, 1],\n [-8, 11, 10, 8],\n [12, 9, -8, -1],\n [0, -11, 5, 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" } ]
301
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 8, 7, -2],\n [8, -2, 7, -2],\n [7, 7, -3, -1],\n [-2, -2, -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" } ]
180
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 5, -9, 0],\n [-6, -8, -3, -1],\n [5, -12, 12, 9],\n [-12, 9, -10, 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" } ]
6
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 7, 11, -4],\n [-7, -3, 1, -1],\n [11, 9, 2, -9],\n [0, -4, 8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 9, -12, -5],\n [12, 4, -12, -7],\n [-2, 1, 5, -5],\n [10, -3, 9, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
312
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 6, -6, 0],\n [6, 8, 0, -4],\n [-6, 0, 2, 4],\n [0, -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" } ]
480
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -2, 0, 0],\n [-2, -6, -6, -4],\n [0, -6, -9, 0],\n [0, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -3, 3, -4],\n [0, 3, 8, -9],\n [0, 0, -2, 11],\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" } ]
66
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -5, 5, 0],\n [-5, -2, -6, 4],\n [5, -6, 3, 1],\n [0, 4, 1, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
427
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 7, -2, -2],\n [7, 2, 2, 0],\n [-2, 2, 12, -6],\n [-2, 0, -6, -11]]\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[[-11, 4, 3, -3],\n [0, -1, -10, -11],\n [0, 0, 8, 2],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
384
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -3, 3, -10],\n [0, -5, -5, 7],\n [0, 0, -2, 7],\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" } ]
550
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 8, 0, -6],\n [8, 12, -2, -3],\n [0, -2, -5, 2],\n [-6, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
628
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 2, -4, 9],\n [-3, -6, 6, -4],\n [-5, -9, -1, 10],\n [11, -5, 9, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
802
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, 12, 4],\n [-6, 8, -8, -11],\n [-9, -10, -2, 6],\n [-3, 8, -12, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
612
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -10, -7, -11],\n [0, 1, -5, 0],\n [0, 0, 1, -8],\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" } ]
36
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 1, 3, -11],\n [12, -7, 11, -3],\n [0, -3, -11, -6],\n [-8, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
616
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 0, -11, -1],\n [9, -9, -2, -1],\n [11, 2, 0, 1],\n [2, -3, 10, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
916
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, 10, 2],\n [-4, 0, -4, 0],\n [10, -4, -9, -6],\n [2, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 3, -11, -1],\n [6, -2, 7, -2],\n [-11, 9, 5, 7],\n [9, -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" } ]
784
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, -7, 9],\n [0, -5, -12, -1],\n [0, 0, 3, -6],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
450
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 11, 6, -4],\n [3, 12, -9, 0],\n [10, 12, -12, 2],\n [7, -12, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
248
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 7, -10, 6],\n [7, -3, 1, -9],\n [-10, 1, 1, 8],\n [6, -9, 8, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
293
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 4, -9, -5],\n [0, 3, 8, -6],\n [0, 0, 4, -2],\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" } ]
480
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, -4, -4],\n [0, 4, -6, 0],\n [-4, -6, -9, 3],\n [-4, 0, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
996
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, -4, 12],\n [0, -3, -6, -3],\n [0, 0, -4, -9],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 4, 7, 0],\n [4, -3, 8, -1],\n [7, 8, 11, -10],\n [0, -1, -10, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
806
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 4, 5, -4],\n [4, 0, -2, 4],\n [5, -2, -4, 3],\n [-4, 4, 3, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
544
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 12, 11, -12],\n [-6, -6, 1, 11],\n [-2, -10, -12, 4],\n [4, -12, -11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
384
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 0, 10, -6],\n [-11, 4, 5, 5],\n [11, 7, 12, 10],\n [7, -12, 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" } ]
513
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 5, 0, 12],\n [0, -9, -1, 3],\n [0, 0, -2, 5],\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" } ]
280
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 8, -5, -8],\n [8, -4, 5, 2],\n [-5, 5, -9, 3],\n [-8, 2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
798
MATH