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[ { "content": "What is the determinant of the matrix:\n[[12, 2, 6, 8, -15],\n [0, -5, -8, -15, 13],\n [0, 0, -10, -5, 11],\n [0, 0, 0, 15, 4],\n [0, 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" ...
0
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 15, -6, 3, -6],\n [8, 4, -12, 4, 3],\n [-7, -6, 12, 9, -15],\n [-15, -8, -1, 9, -9],\n [-6, -1, 13, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
240
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, -1, 0, -8],\n [0, -11, -10, 6, -1],\n [-1, -10, -7, -10, -1],\n [0, 6, -10, 15, 6],\n [-8, -1, -1, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
64
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 10, 5, -12, -9],\n [0, -8, 3, 4, -6],\n [0, 0, -3, -15, -2],\n [0, 0, 0, -3, -10],\n [0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
120
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 14, -7, 2, -4],\n [0, 3, -11, 4, -5],\n [0, 0, -3, -15, -9],\n [0, 0, 0, 12, 3],\n [0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
112
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 6, 3, -6, 2],\n [6, 3, 0, -6, -3],\n [3, 0, 4, 0, -13],\n [-6, -6, 0, 13, -4],\n [2, -3, -13, -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" } ]
251
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 2, 7, -8, -4],\n [2, 13, 10, -1, -10],\n [7, 10, 8, 0, -2],\n [-8, -1, 0, 12, 0],\n [-4, -10, -2, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
422
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -6, 6, -8, 9],\n [0, 2, -3, -13, -7],\n [0, 0, 6, -15, 15],\n [0, 0, 0, 12, 3],\n [0, 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": "us...
960
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 14, 6, 1, -2],\n [14, 5, 10, -1, -3],\n [6, 10, -1, 4, 7],\n [1, -1, 4, -9, 4],\n [-2, -3, 7, 4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
522
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -6, -12, 3, -11],\n [0, 7, -9, -13, 4],\n [0, 0, 6, 3, -12],\n [0, 0, 0, 12, -15],\n [0, 0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
128
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 8, 5, 15, 15],\n [0, 1, -11, -6, -8],\n [0, 0, 8, -6, -13],\n [0, 0, 0, -5, 10],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
200
MATH
[ { "content": "What is the determinant of the matrix:\n[[-15, -4, -2, -2, 2],\n [-4, 15, 0, 8, -5],\n [-2, 0, 9, -12, -2],\n [-2, 8, -12, 11, 8],\n [2, -5, -2, 8, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
468
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -12, -10, 6, -6],\n [-12, 4, -7, -1, 2],\n [-10, -7, -8, -8, -11],\n [6, -1, -8, 4, -4],\n [-6, 2, -11, -4, -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}", ...
383
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 11, -9, -5, -5],\n [0, 2, -6, -5, 14],\n [0, 0, 12, -2, 2],\n [0, 0, 0, -7, -14],\n [0, 0, 0, 0, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
712
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 15, 1, -4, 0],\n [0, 10, -5, 13, -14],\n [0, 0, 14, -3, -8],\n [0, 0, 0, -15, 14],\n [0, 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" } ]
800
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 11, 8, 7, -5],\n [11, -10, 9, 4, -10],\n [8, 9, 10, 1, -10],\n [7, 4, 1, 2, -12],\n [-5, -10, -10, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
112
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 0, -7, -10, -4],\n [-1, 9, 1, -11, -14],\n [0, -2, 13, -5, 2],\n [-13, -14, -4, 5, 8],\n [-3, -12, -1, -1, 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}", ...
838
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 13, 2, -10, -8],\n [0, -6, 10, 0, -3],\n [0, 0, -2, 9, -13],\n [0, 0, 0, 13, -2],\n [0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
992
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -8, -1, 3, -11],\n [13, -7, 2, -13, -4],\n [4, -7, -11, 14, 12],\n [-5, -15, -9, -8, -5],\n [11, 6, 15, 15, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
576
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 0, 4, -2, 6],\n [0, 12, 4, -2, 10],\n [4, 4, 15, -13, 2],\n [-2, -2, -13, 5, -7],\n [6, 10, 2, -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"...
708
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -1, -4, -2, 0],\n [-5, -8, -6, -5, -2],\n [-12, 6, 14, 1, -9],\n [2, 10, 13, 10, -10],\n [10, 8, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
58
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -11, 14, 9, 1],\n [0, 8, 2, 2, 3],\n [0, 0, -2, 15, -8],\n [0, 0, 0, 13, -2],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 3, -2, 10, -2],\n [-8, -4, 12, 1, -5],\n [-2, 7, 3, 14, 9],\n [-4, 12, 14, 15, 14],\n [-2, 7, -4, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
503
MATH
[ { "content": "Determine the value of det(A) where A =\n[[14, 10, -10, 11, 5],\n [-5, -12, -2, 5, 5],\n [9, -5, 6, -13, -13],\n [6, 15, -5, 6, -3],\n [-2, -11, 9, 11, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
921
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 10, -5, 12, 0],\n [0, 5, 12, 10, -15],\n [0, 0, 12, -9, 10],\n [0, 0, 0, -7, -10],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
640
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 1, -4, 5, 6],\n [0, 3, 7, -2, -4],\n [0, 0, -14, 4, -15],\n [0, 0, 0, -3, 2],\n [0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
656
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 3, 8, 0, -11],\n [-2, -1, -9, 6, 12],\n [-15, 13, 5, 14, -7],\n [-2, -8, 14, 7, -1],\n [-10, 9, 11, 15, -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}", "rol...
709
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 10, 1, -2, -12],\n [10, 14, -4, 9, 8],\n [1, -4, 3, 4, -4],\n [-2, 9, 4, -6, -3],\n [-12, 8, -4, -3, -13]]\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"...
753
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -9, 10, -13, 1],\n [-6, -3, 11, -8, -1],\n [-10, -2, 7, -9, 15],\n [-8, 5, -10, 10, -4],\n [6, 4, -11, 13, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
852
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -2, 3, -13, -3],\n [5, 2, 4, -6, -1],\n [5, -11, -9, -10, 8],\n [0, 11, 6, -6, -8],\n [-1, -1, -6, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
392
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -13, -1, -6, 0],\n [5, -14, -1, -8, 10],\n [5, 14, -8, 6, 0],\n [14, -8, -14, -2, -7],\n [8, 11, -7, 14, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
668
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -6, -8, 0, -2],\n [-6, 0, 2, 4, 6],\n [-8, 2, 13, -7, 1],\n [0, 4, -7, -7, 8],\n [-2, 6, 1, 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" } ]
712
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 14, 5, 4, 14],\n [0, 7, 15, -12, -9],\n [0, 0, 6, 2, 14],\n [0, 0, 0, -13, -4],\n [0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
356
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -3, -10, 1, 4],\n [-3, -10, -8, 2, 6],\n [-10, -8, -11, -3, 4],\n [1, 2, -3, -6, 10],\n [4, 6, 4, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
314
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 6, -1, 2, 7],\n [10, 10, 2, -6, 9],\n [-12, 6, 3, -3, -14],\n [-10, -4, -1, -13, 7],\n [-3, -2, 7, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
604
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 1, -14, 5, -11],\n [-11, -12, 5, -2, -13],\n [9, 10, 11, -7, -3],\n [15, 4, 12, -11, -4],\n [-1, 15, 6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
355
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -4, 9, -6, -5],\n [-13, 0, 13, -2, -10],\n [14, -10, 12, -7, -2],\n [-12, 6, 2, 3, 5],\n [-9, 10, -12, 9, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
576
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -4, 10, 13, -10],\n [0, 2, 8, 11, -15],\n [0, 0, -2, -3, 0],\n [0, 0, 0, 5, 0],\n [0, 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" }...
120
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 13, 4, 4, -6],\n [0, 4, 9, 6, -14],\n [0, 0, 8, -14, -9],\n [0, 0, 0, 4, 4],\n [0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
608
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 13, 12, 2, 10],\n [0, 6, 1, -5, 8],\n [0, 0, 9, -14, 9],\n [0, 0, 0, 4, 10],\n [0, 0, 0, 0, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
344
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 5, -3, 9, 8],\n [5, -4, 11, 0, -2],\n [7, -4, -14, -12, 6],\n [7, -10, 13, -14, -14],\n [-6, 2, 10, 13, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
404
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 6, 4, -10],\n [-11, -15, 12, -6, 5],\n [-3, 9, 1, 4, -8],\n [11, -5, -1, -6, 3],\n [-15, -6, -7, -7, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
600
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 1, 3, -13, 3],\n [1, -2, -2, 8, -3],\n [3, -2, 3, 0, 2],\n [-13, 8, 0, -12, 0],\n [3, -3, 2, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
703
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 6, -14, -1, 14],\n [-13, -11, -15, -13, 4],\n [4, 3, -10, 3, 4],\n [-6, -1, 5, 5, 5],\n [10, 9, 7, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
722
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -10, 2, -1, 8],\n [-10, -1, -15, 0, 3],\n [2, -15, 0, 3, 0],\n [-1, 0, 3, -15, 0],\n [8, 3, 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" ...
803
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -1, -6, 0, 8],\n [-1, -11, -10, -10, 6],\n [-6, -10, 10, 10, 8],\n [0, -10, 10, -2, -14],\n [8, 6, 8, -14, -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}", ...
576
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -9, 12, -2, -6],\n [-9, 6, -8, 9, -4],\n [12, -8, 12, 6, 4],\n [-2, 9, 6, -6, 0],\n [-6, -4, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
836
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-13, -13, -14, -12, -6],\n [0, 8, -4, -13, 13],\n [0, 0, -3, 3, -7],\n [0, 0, 0, 5, -7],\n [0, 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":...
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-13, -2, 2, 2, -12],\n [-2, 12, -6, -8, 6],\n [2, -6, 14, -6, 0],\n [2, -8, -6, -2, -4],\n [-12, 6, 0, -4, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
880
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 9, -6, -2, 10],\n [9, -6, -7, -8, -2],\n [-3, 11, 12, -10, 15],\n [1, -5, 8, 15, 7],\n [3, -1, 1, -7, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
101
MATH
[ { "content": "Compute |A| for the matrix A =\n[[13, 2, 0, -8, 4],\n [2, -14, 5, -1, -10],\n [0, 5, 8, 8, -3],\n [-8, -1, 8, 14, -6],\n [4, -10, -3, -6, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
653
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -3, -15, 1, -6],\n [-11, -1, 6, 15, -3],\n [5, -14, -5, 0, 9],\n [3, 3, -1, 13, 10],\n [8, -13, 3, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
860
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 5, -13, 14, 6],\n [0, -7, -6, 2, 2],\n [0, 0, 3, -5, -5],\n [0, 0, 0, -14, 4],\n [0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
888
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -2, -5, -14, -9],\n [0, 6, 11, 8, -12],\n [0, 0, 8, 13, 12],\n [0, 0, 0, -15, 13],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
520
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -3, -6, 13, 11],\n [-12, -12, 11, 3, -3],\n [-5, -3, 5, -13, 1],\n [12, 3, -2, -4, -2],\n [-2, 0, -13, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
468
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 4, 10, 1, 2],\n [4, 10, 5, 1, 12],\n [10, 5, 3, 6, 6],\n [1, 1, 6, 8, 7],\n [2, 12, 6, 7, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
463
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-14, 9, 10, -8, 11],\n [0, 9, 0, 15, -14],\n [0, 0, 9, 11, 15],\n [0, 0, 0, 10, 1],\n [0, 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...
320
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -2, 0, 2, 11],\n [-2, 0, 0, -3, 7],\n [0, 0, -6, 5, -1],\n [2, -3, 5, -5, 4],\n [11, 7, -1, 4, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
82
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 2, 6, -12, 8],\n [1, -4, 4, -13, 2],\n [-2, -10, -3, 7, -12],\n [5, 10, 4, 15, 3],\n [8, 6, -5, 7, -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": ...
600
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -10, 9, 10, 3],\n [0, 11, 2, 7, 2],\n [0, 0, 3, 13, -10],\n [0, 0, 0, -8, 11],\n [0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 0, 1, -12, 8],\n [0, 4, -11, -4, -2],\n [1, -11, -2, -3, 6],\n [-12, -4, -3, 13, -2],\n [8, -2, 6, -2, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
900
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 0, -4, 0, 2],\n [0, -1, 0, -5, -3],\n [-4, 0, 12, -11, 9],\n [0, -5, -11, -9, 2],\n [2, -3, 9, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
311
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -11, -13, 10, 6],\n [0, -3, 2, 12, -6],\n [0, 0, -6, -3, -8],\n [0, 0, 0, 1, 6],\n [0, 0, 0, 0, 4]]\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[[8, 0, -11, -10, -6],\n [0, 12, -2, -4, 2],\n [-11, -2, -13, -2, 14],\n [-10, -4, -2, 2, 3],\n [-6, 2, 14, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
220
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 6, -7, 9, -6],\n [6, 14, 8, -12, -8],\n [-7, 8, 6, -2, 0],\n [9, -12, -2, 9, -4],\n [-6, -8, 0, -4, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
638
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -3, 0, 9, -11],\n [8, 2, 3, 2, 12],\n [0, 4, -12, 6, -15],\n [1, 2, -15, -14, -8],\n [4, 1, 3, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
495
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 8, -6, -10, 13],\n [-10, 2, 13, 2, 11],\n [-15, -2, 1, 0, 11],\n [1, -5, 0, -4, 9],\n [7, -3, 15, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
685
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 1, 2, -10, -5],\n [0, 12, 3, 7, 10],\n [0, 0, -10, -1, -12],\n [0, 0, 0, -3, -6],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
920
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -4, 2, 7, -5],\n [-4, -5, -6, 0, 0],\n [2, -6, 11, -3, -1],\n [7, 0, -3, -13, -3],\n [-5, 0, -1, -3, 3]]\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[[3, 0, -4, 11, 0],\n [-6, 2, 2, -10, -7],\n [7, -13, 4, -4, 3],\n [3, 0, 10, 7, 10],\n [-13, 3, -3, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
944
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 14, -5, -15, -2],\n [-7, 3, 9, -6, 1],\n [-8, 4, 3, 7, -9],\n [-3, -12, -15, -8, 7],\n [5, -14, 0, 14, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
869
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -4, -11, 8, 5],\n [-4, -3, 0, 4, -2],\n [-11, 0, 15, 6, 4],\n [8, 4, 6, 0, -2],\n [5, -2, 4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
160
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 1, -9, 6, -10],\n [0, 2, -12, 1, 5],\n [0, 0, -9, 14, 0],\n [0, 0, 0, -15, -15],\n [0, 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" ...
860
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 1, -5, 9, -13],\n [-9, -9, 7, -6, 8],\n [15, -10, -11, 3, 6],\n [15, 4, -12, 7, -11],\n [-12, 10, 15, 6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
266
MATH
[ { "content": "What is the determinant of the matrix:\n[[-13, -4, -6, -4, -7],\n [0, 5, -6, 7, 3],\n [0, 0, 5, -6, -11],\n [0, 0, 0, -3, 0],\n [0, 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" }...
950
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 15, 2, 12, -8],\n [-10, 14, 9, 5, 1],\n [-14, 6, 3, -12, 10],\n [0, -7, -14, 2, -15],\n [12, 4, 2, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
32
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -10, 14, 2, 5],\n [-6, -11, -13, 1, -1],\n [-10, -13, 0, 0, -3],\n [-7, -15, -15, -15, -14],\n [-4, -13, -12, -7, 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}"...
10
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -7, -3, 6, -12],\n [0, 5, 14, 11, -6],\n [0, 0, -5, 12, 6],\n [0, 0, 0, -3, -7],\n [0, 0, 0, 0, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -8, 0, 7, 0],\n [-8, -7, 4, -2, 5],\n [0, 4, 13, -1, -14],\n [7, -2, -1, -8, -5],\n [0, 5, -14, -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": ...
233
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 14, -3, 6, 0],\n [-5, 15, -12, 11, 15],\n [3, 13, 10, 9, 8],\n [-5, 12, 0, 4, -5],\n [15, -8, 14, -11, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
773
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -1, 8, 3, -7],\n [6, 12, -13, 11, 13],\n [8, 1, -7, -3, 3],\n [-1, -13, -1, 12, 7],\n [-1, -13, 9, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
932
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 15, 12, 12, -9],\n [5, 13, 7, 7, -12],\n [-2, -8, -9, 14, 3],\n [11, 12, 0, -3, 12],\n [7, -1, 2, -1, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
85
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -14, -15, 3, 1],\n [0, 9, -10, -3, 7],\n [0, 0, -10, -4, 3],\n [0, 0, 0, -4, 2],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 12, 5, -8, 2],\n [-10, -2, -3, 11, -5],\n [4, 8, -9, 6, -1],\n [6, 8, -8, -4, 8],\n [15, -14, -4, -15, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
304
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -3, -3, -3, 0],\n [-3, 4, -2, 12, -8],\n [-3, -2, 2, -5, 2],\n [-3, 12, -5, -1, -2],\n [0, -8, 2, -2, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
88
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 9, 0, -12, 5],\n [-1, -5, -8, 0, -8],\n [5, -14, 15, 5, 1],\n [2, 0, -1, 0, 2],\n [-2, 1, -1, -10, -13]]\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":...
173
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 5, -3, 6, 10],\n [5, -11, -2, 1, 6],\n [-3, -2, -2, -9, -1],\n [6, 1, -9, 14, 8],\n [10, 6, -1, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
309
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -11, -6, 11, -11],\n [6, -11, 2, -13, -9],\n [-14, -12, 1, 5, -4],\n [-6, -7, 6, -6, -6],\n [-4, 12, 0, 11, 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}", ...
759
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 11, -14, -12, -2],\n [0, -2, -3, -9, 8],\n [0, 0, 2, 2, -5],\n [0, 0, 0, -15, -4],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
800
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 3, -1, -4, 1],\n [0, -8, 1, 13, -14],\n [0, 0, -13, -12, 4],\n [0, 0, 0, -10, -7],\n [0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-14, -12, 2, 0, 11],\n [10, -11, -12, 11, -9],\n [-8, 6, 15, -9, 5],\n [4, -9, 2, -5, 3],\n [-4, 8, 4, 3, 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...
526
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 11, -3, -4, 5],\n [4, -11, -7, -3, -2],\n [1, -10, 0, -3, 2],\n [-3, 5, 9, 1, -14],\n [12, 13, 7, 15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
962
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 9, 1, -1, -1],\n [4, 0, 11, -10, 0],\n [7, 8, -13, 2, 10],\n [4, -11, 6, -10, -13],\n [-13, -2, 15, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
103
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 14, 12, 14, -3],\n [0, 7, -2, 1, -6],\n [0, 0, -2, 9, -14],\n [0, 0, 0, 14, -3],\n [0, 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" ...
112
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 12, -2, 2, 3],\n [1, 11, -7, 13, 12],\n [12, -13, -1, -5, -9],\n [-4, -14, 3, -15, -1],\n [10, 4, 8, -9, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
794
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -3, -2, -3, 15],\n [-3, 14, 12, 7, 0],\n [1, 15, 3, 4, 2],\n [11, 11, 2, -2, 12],\n [5, -13, -8, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
195
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -15, 14, 0, 3],\n [0, -12, -5, -3, -8],\n [0, 0, -5, 13, 9],\n [0, 0, 0, 3, -2],\n [0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
100
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 9, -13, 9, -5],\n [0, 8, -1, -13, 0],\n [0, 0, -15, -11, 13],\n [0, 0, 0, -12, 15],\n [0, 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" } ]
640
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 11, -14, 14, -10],\n [0, -6, -2, 7, 3],\n [0, 0, 15, 11, -4],\n [0, 0, 0, 14, 10],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
340
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -4, -2, -2, -9],\n [-4, -6, -2, 5, -2],\n [-2, -2, -2, 4, 5],\n [-2, 5, 4, -9, 8],\n [-9, -2, 5, 8, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
24
MATH