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[ { "content": "Compute |A| for the matrix A =\n[[1, -10, 6, 6],\n [0, 2, 9, -6],\n [0, 0, -5, -7],\n [0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 5, -7, 8],\n [-7, -10, 11, 4],\n [12, -4, -10, -11],\n [-6, -12, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
504
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 11, 11, -5],\n [0, 12, 3, 1],\n [0, 0, 8, -2],\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" } ]
808
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 1, 0, 9],\n [10, -3, 3, 9],\n [-1, -9, 0, 11],\n [6, 5, 7, 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" } ]
632
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -7, -4, 0],\n [-7, 0, -6, -8],\n [-4, -6, -3, 4],\n [0, -8, 4, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
246
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -9, 2, -5],\n [-5, 4, -12, -5],\n [6, -4, -3, 5],\n [-6, -10, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -8, 4, 6],\n [7, 12, -7, -11],\n [0, 3, -11, -4],\n [1, 6, -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" } ]
631
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 4, -1, -5],\n [0, 6, -10, -3],\n [0, 0, -9, -6],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 1, -4, 4],\n [2, -4, -11, 1],\n [-5, 1, 3, 10],\n [-2, -6, 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" } ]
624
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -8, -10, -5],\n [11, 10, 7, -12],\n [-4, 7, 4, -3],\n [-12, -8, -6, -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" } ]
206
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -10, -11, -2],\n [0, 1, -2, -9],\n [0, 0, 5, -3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 5, 5, -3],\n [-5, 4, 5, -11],\n [0, 1, -6, 10],\n [-5, 1, 11, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
785
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 8, 9, -11],\n [10, -5, 2, 10],\n [-2, -6, 3, -12],\n [-1, -1, -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" } ]
197
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -1, -3, 2],\n [-1, 1, 4, 4],\n [-3, 4, -12, 2],\n [2, 4, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 10, -3, -8],\n [10, -8, 1, -2],\n [-3, 1, -11, -4],\n [-8, -2, -4, -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" } ]
536
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 3, -6, 0],\n [-5, -11, 11, -8],\n [-8, 7, 6, 1],\n [11, -8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 3, 8, 0],\n [0, 11, 11, -5],\n [0, 0, -8, -2],\n [0, 0, 0, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -6, 4, 6],\n [-6, -8, -4, -7],\n [4, -4, -8, 2],\n [6, -7, 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" } ]
512
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 5, 8, -6],\n [12, 3, -8, -10],\n [-3, 3, -12, -12],\n [-3, -7, 10, 12]]? 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": "What is the determinant of the matrix:\n[[6, 8, -2, -11],\n [0, -1, 9, -7],\n [0, 0, 12, -2],\n [0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
208
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 8, -7, -9],\n [-6, -3, 5, 6],\n [-12, -12, -1, 11],\n [9, 11, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
743
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 1, -9, 12],\n [1, -7, 9, -2],\n [0, -5, 2, 0],\n [0, -4, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 10, -1, -10],\n [-10, 10, 12, 12],\n [6, 7, -8, -11],\n [2, 11, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 2, -12, 9],\n [-3, -3, 7, 3],\n [-2, -11, -7, 6],\n [-5, 1, 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" } ]
726
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 1, -8, 7],\n [-10, 10, -11, -11],\n [9, -8, 4, 6],\n [-9, -11, -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" } ]
718
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 3, 8, 2],\n [0, 3, 1, 4],\n [0, 0, 5, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 10, 4, -8],\n [0, 12, 5, 10],\n [0, 0, 10, -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" } ]
240
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, 2, 0],\n [-4, -1, -7, -3],\n [2, -7, 11, -4],\n [0, -3, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 2, -8, -5],\n [2, 0, -2, -6],\n [-8, -2, -1, 1],\n [-5, -6, 1, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
276
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -1, -2, 6],\n [2, 11, -5, 8],\n [-7, -7, 11, -4],\n [7, 8, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -12, 3, 7],\n [0, -3, -5, 8],\n [0, 0, 7, -11],\n [0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -9, 2, -11],\n [8, 3, 0, 4],\n [-7, 1, 4, -2],\n [4, -9, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
161
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -4, 11, -2],\n [-1, -8, 9, -1],\n [-1, -2, 10, 4],\n [-10, -10, 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" } ]
578
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -4, 0, 7],\n [0, -1, 3, -4],\n [0, 0, -1, -2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 11, -2, 2],\n [11, 2, 2, 4],\n [-2, 2, -3, 2],\n [2, 4, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -1, 4, -6],\n [-1, 1, -4, -4],\n [4, -4, -1, 6],\n [-6, -4, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
283
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -3, -12, 4],\n [4, -6, 12, 1],\n [11, 4, 2, 8],\n [8, 0, 9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -3, 0, -6],\n [-3, 5, -5, -4],\n [0, -5, -11, 6],\n [-6, -4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
944
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 2, 6, 0],\n [2, -3, 2, 3],\n [6, 2, -5, 4],\n [0, 3, 4, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
536
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -7, -4, -3],\n [12, 12, 4, -12],\n [6, 11, 2, -11],\n [-2, 8, 10, -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" } ]
280
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 10, -9, 2],\n [-3, 11, -12, 12],\n [7, -7, 0, -2],\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" } ]
22
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 9, -5, -1],\n [12, -3, 2, -2],\n [-11, 5, -10, 10],\n [-7, 1, 3, 11]]? 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": "Determine the value of det(A) where A =\n[[11, 0, -5, -6],\n [-1, -1, -1, -8],\n [1, -11, -6, -7],\n [-4, 7, 5, 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" } ]
354
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -10, -7, -12],\n [0, -2, 3, -3],\n [0, 0, -9, 12],\n [0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
136
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -2, -9, 5],\n [-8, -11, 11, 0],\n [9, -9, 6, 11],\n [6, -1, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, -2, 9],\n [-1, 10, -4, -2],\n [-2, -4, 12, -10],\n [9, -2, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
596
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -2, 4, -1],\n [8, -5, 10, -7],\n [-1, -7, 10, -1],\n [-3, 7, -5, 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" } ]
601
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 2, 5, 10],\n [6, 12, 9, -7],\n [9, 9, 4, 4],\n [-2, -8, -12, -7]]\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": "Compute |A| for the matrix A =\n[[8, -12, -8, 6],\n [-12, -4, 10, 0],\n [-8, 10, 12, -5],\n [6, 0, -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" } ]
928
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -5, 4, -12],\n [4, -4, 5, -7],\n [11, 7, -5, 2],\n [-6, -9, 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" } ]
989
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -11, 8, 5],\n [-6, 11, -6, 6],\n [12, 5, -12, -11],\n [5, -12, -6, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 2, 2, -5],\n [2, -9, -1, 2],\n [2, -1, 5, 8],\n [-5, 2, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 7, 3, -9],\n [0, -10, 6, -10],\n [0, 0, -12, -5],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
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 [-9, 7, -9, -5],\n [7, 1, 6, 11],\n [11, 0, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
758
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 4, -6, 1],\n [4, 0, -4, 8],\n [-6, -4, -11, 5],\n [1, 8, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -8, 10, 10],\n [-8, 10, -12, 9],\n [10, -12, -1, 2],\n [10, 9, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
513
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -7, 3, 1],\n [0, 8, 1, -11],\n [0, 0, 10, -9],\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" } ]
440
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 4, 6, 2],\n [4, 0, -7, -10],\n [6, -7, -7, 0],\n [2, -10, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 5, -12, 4],\n [0, -4, 10, 11],\n [0, 0, -12, 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" } ]
296
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -7, -4, 6],\n [-7, 2, -12, -9],\n [-4, -12, -2, -12],\n [6, -9, -12, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -4, -5, -1],\n [-3, 10, -3, 1],\n [6, 6, 11, 9],\n [8, 5, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
614
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, 8, 2],\n [6, 11, -3, 1],\n [8, -3, -2, -4],\n [2, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
134
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -4, 2, 2],\n [-4, 12, -4, -11],\n [2, -4, -11, -2],\n [2, -11, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
963
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -4, 7, -8],\n [0, 7, 10, 10],\n [0, 0, 9, 7],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
316
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, -6, 8],\n [6, 11, -2, 2],\n [-6, -2, 1, -3],\n [8, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
420
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -6, -4, 2],\n [6, 12, 4, 9],\n [-6, -6, -11, -12],\n [-9, -3, 10, 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" } ]
589
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -6, -12, 11],\n [9, -6, 5, 11],\n [-3, -12, 5, -1],\n [-4, -11, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
298
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 12, -12, -12],\n [0, -8, -3, 8],\n [0, 0, -10, 10],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 11, -8, 1],\n [0, -12, -4, 7],\n [0, 0, -2, -7],\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" } ]
864
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 6, -11, -8],\n [-7, 4, -12, -12],\n [-11, 1, 7, -7],\n [-6, -8, -11, 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" } ]
325
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -11, -12, 3],\n [-11, 4, 1, -10],\n [0, 8, -8, -4],\n [3, 2, -5, 11]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, -3, -12],\n [9, -12, 4, 0],\n [-11, -10, -7, -2],\n [11, 7, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
470
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 1, 5, 6],\n [0, 2, 3, 7],\n [0, 0, 2, 9],\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" } ]
976
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 0, -4, 4],\n [0, 0, -8, 2],\n [-4, -8, -9, 6],\n [4, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
488
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 0, -4, 3],\n [0, -1, -3, -12],\n [0, 0, 11, 7],\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" } ]
154
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 9, 4, -4],\n [0, 2, -12, -4],\n [0, 0, 5, -6],\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" } ]
760
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -4, -12, 2],\n [8, -3, 9, -7],\n [-9, 2, 3, 11],\n [10, -9, 2, 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" } ]
738
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, 1, 3],\n [0, -6, 5, 4],\n [0, 0, 5, 9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -10, 11],\n [0, -2, 4, 0],\n [0, 0, -11, 8],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -7, 2, 6],\n [-7, 0, -3, 1],\n [2, -3, 1, 2],\n [6, 1, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
369
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, -4, -10],\n [0, -5, -6, -12],\n [0, 0, -12, 11],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 10, 5, -2],\n [-4, -1, -10, -5],\n [-1, 3, 6, 9],\n [-4, -8, -7, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
281
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -11, 0, -6],\n [-9, 12, -7, 1],\n [10, 11, 6, 3],\n [6, -9, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
286
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -7, 1, 9],\n [0, 9, 1, -3],\n [0, 0, -12, -9],\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" } ]
680
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 3, 3, 12],\n [-9, 2, -2, -8],\n [2, 10, 0, 9],\n [-5, 9, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 11, -2, 5],\n [-6, 0, -1, -10],\n [8, -9, 0, -2],\n [-5, -12, 9, 12]]? 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[[7, -12, -4, 7],\n [0, -5, 12, 7],\n [0, 0, -8, 8],\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" } ]
960
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -2, -5, -1],\n [-8, -9, -11, -5],\n [12, -6, -2, 2],\n [-3, -6, 7, -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" } ]
316
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 7, 7, -8],\n [10, -6, 12, 4],\n [-2, -10, -10, 3],\n [0, 4, -12, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
304
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -4, 6, 6],\n [0, 5, -4, -7],\n [0, 0, 12, 1],\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" } ]
980
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 7, 2, 5],\n [0, -10, -7, -10],\n [0, 0, -4, 5],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 3, -12, -9],\n [0, -2, 1, 2],\n [0, 0, -3, -11],\n [0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 3, -9, -5],\n [0, 10, -4, 3],\n [0, 0, -3, 0],\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" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 8, 0, -12],\n [5, -6, 11, 7],\n [8, 0, -8, -1],\n [1, 7, 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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 11, -12, 12],\n [0, 4, -10, 5],\n [0, 0, -1, -4],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -12, 7, -6],\n [0, -1, -2, 7],\n [0, 0, -7, 5],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 9, -3, -10],\n [-8, -1, -12, -6],\n [0, 10, 10, -12],\n [8, 8, 11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
852
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 10, 2, 3],\n [10, 7, 2, -11],\n [2, 2, 5, 1],\n [3, -11, 1, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
659
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -1, 2, 1],\n [0, 7, -8, 4],\n [0, 0, -11, 7],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
623
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -2, 1, -6],\n [-2, -3, 2, -5],\n [1, 2, -9, 6],\n [-6, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH