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[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, 0],\n [0, -3, 0],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
994
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 7, -3],\n [0, 4, 0],\n [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" } ]
976
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -5, -3],\n [2, 10, -10],\n [7, -2, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, -1],\n [-10, -6, -3],\n [-6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
747
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 5, 6],\n [5, -10, -7],\n [6, -7, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
482
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 8, -5],\n [1, -4, -9],\n [-3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
748
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 4, 0],\n [0, -9, 2],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
838
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 2, 10],\n [2, 3, 0],\n [10, 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" } ]
861
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -4, 0],\n [-4, 2, -7],\n [0, -7, -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" } ]
470
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 2, 5],\n [2, 1, -2],\n [5, -2, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
919
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 0, -7],\n [0, -8, 4],\n [0, 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" } ]
968
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -6, -1],\n [-6, -1, 0],\n [-1, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
735
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 1, -3],\n [1, -2, 4],\n [-3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
65
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -4, 4],\n [-4, 6, 2],\n [4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
694
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 6, -1],\n [0, -5, -7],\n [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" } ]
940
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 4, 0],\n [4, 10, 0],\n [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" } ]
130
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -2, 8],\n [-4, 3, -10],\n [7, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 8, 7],\n [8, -8, -8],\n [-8, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -2, 3],\n [0, 3, 3],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, -2],\n [0, 4, 6],\n [0, 0, -6]]\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[[4, -4, -3],\n [0, -3, 0],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
904
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 10, -4],\n [10, -1, -2],\n [-4, -2, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
406
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 4, -1],\n [4, -3, 2],\n [-1, 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" } ]
990
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -9, 6],\n [0, 7, 9],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
916
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 6, 3],\n [3, 6, -7],\n [10, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
340
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -7, -5],\n [-7, 2, 0],\n [-5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
919
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -1, 6],\n [-1, 7, 5],\n [6, 5, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
333
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -1, -7],\n [0, -3, 6],\n [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" } ]
952
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 8, -4],\n [8, -5, 0],\n [-4, 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" } ]
425
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 1, 7],\n [10, 8, -1],\n [-7, 4, 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" } ]
609
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -4, -10],\n [-4, -8, 4],\n [-10, 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" } ]
152
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 6, 1],\n [0, 1, -1],\n [0, 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" } ]
4
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 3, 10],\n [10, 10, -8],\n [-10, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -10, -5],\n [7, 8, 8],\n [3, 3, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
265
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -1, -4],\n [8, -7, 7],\n [10, -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" } ]
999
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -8, 0],\n [-4, -7, 7],\n [-7, 10, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
172
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 0, 6],\n [0, 8, 3],\n [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" } ]
616
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -7, 3],\n [-10, 2, 10],\n [8, -3, 7]]\nRound to the nearest integer, then take the result modulo 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[[-9, -6, -9],\n [0, 3, -4],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
189
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -1, 0],\n [-1, -5, 1],\n [0, 1, 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" } ]
203
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 5, -5],\n [-2, -4, -8],\n [0, 7, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
234
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 6, 0],\n [6, 10, 4],\n [0, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, -4],\n [-4, -3, 5],\n [-4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
368
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -9, -6],\n [3, -10, 5],\n [-5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
749
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -4, 2],\n [-4, -6, 3],\n [2, 3, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -7],\n [0, 7, -3],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
979
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -4, 3],\n [0, 10, -9],\n [-10, 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" } ]
20
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 5, 0],\n [5, 9, -2],\n [0, -2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 2, 8],\n [0, -8, -7],\n [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" } ]
968
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 5, -3],\n [5, 10, -4],\n [-3, -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" } ]
750
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, -1],\n [4, 7, 1],\n [-1, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
553
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 3, 4],\n [3, 10, -2],\n [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" } ]
934
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, -3],\n [-2, 9, 3],\n [-3, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 6, -4],\n [6, 8, 9],\n [-4, 9, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
132
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 3, -2],\n [3, 8, 5],\n [-2, 5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
278
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 10, -4],\n [-3, 5, 2],\n [-2, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
165
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 9, 0],\n [-9, -10, -7],\n [0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
916
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -4, 10],\n [-4, 2, -6],\n [-7, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
568
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 6, -6],\n [0, 4, 2],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 9, -5],\n [0, -8, -4],\n [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" } ]
608
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -10, 0],\n [-10, -6, -2],\n [0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -10, 1],\n [0, -10, 0],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -8, 2],\n [0, 2, 5],\n [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" } ]
904
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 0, -4],\n [0, -1, 0],\n [-4, 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" } ]
12
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -7, -9],\n [0, 7, -3],\n [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" } ]
951
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 3, 10],\n [0, 9, 0],\n [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" } ]
180
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 0, -4],\n [-3, 6, -5],\n [-2, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
835
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 1, -10],\n [0, 7, -4],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -5, -4],\n [-5, 10, 0],\n [-4, 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" } ]
975
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 7, -10],\n [0, 8, -1],\n [0, -7, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
943
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -1, 1],\n [0, 10, 1],\n [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" } ]
820
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -6, 5],\n [8, -7, -3],\n [-6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
612
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 1, -9],\n [-8, -1, 0],\n [-6, -3, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -3, 1],\n [-3, 8, -8],\n [1, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
613
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 3, -2],\n [8, 0, 0],\n [-4, -4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -2, -6],\n [0, 2, -2],\n [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" } ]
984
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 10, 0],\n [0, -7, -6],\n [0, 0, -4]]\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[[1, 8, -2],\n [0, 3, -4],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 1, -10],\n [0, 4, 9],\n [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" } ]
64
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -1, 2],\n [10, -2, 8],\n [10, 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" } ]
160
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 6, -1],\n [0, 8, -6],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 5, -4],\n [5, -6, 4],\n [-4, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
942
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 5, -4],\n [0, -3, -3],\n [0, 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" } ]
976
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, 2],\n [0, -7, -4],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
657
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -5, -6],\n [0, 1, -1],\n [0, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
944
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 10, 0],\n [7, 8, -1],\n [10, 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" } ]
802
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 8, 2],\n [-4, 3, -3],\n [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" } ]
178
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, -4],\n [0, 5, 3],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -10, 7],\n [-6, -9, -4],\n [-3, -9, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
267
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 3, -2],\n [0, -10, 6],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
420
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -1, 0],\n [-1, -2, -5],\n [0, -5, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 2, 4],\n [2, -5, 0],\n [4, 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" } ]
950
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 5, 9],\n [0, -6, 3],\n [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" } ]
96
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -1, 8],\n [0, -8, 3],\n [2, -3, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
263
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, 0],\n [0, 3, 1],\n [0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 8, -1],\n [8, -2, 0],\n [-1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
470
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, -10],\n [4, 8, 9],\n [-3, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
176
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, -3],\n [0, 0, 2],\n [7, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, -4],\n [-2, -4, 4],\n [-4, 4, -6]]\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[[-6, 8, 3],\n [0, -6, -8],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH