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math_arithmetic_matrix_eigenvalues_level_7

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[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-6, -12, -31, 17, 19, -13, -26, -3, 26, -9, -29, -9],\n [0, 21, -6, -33, -7, -22, -11, -26, 13, 2, 35, -22],\n [0, 0, -24, -22, -35, 32, 13, -18, 0, 28, -8, -4],\n [0, 0, 0, -3, -6, 1, 17, 33, -28, -35, -29, 26],\n [0, 0, 0, 0, -33, 22, -4, 32, 13, 2, -34, -27],\n [0, 0, 0, 0, 0, -3, -8, -10, -7, -25, -2, 12],\n [0, 0, 0, 0, 0, 0, 32, -13, 25, -9, -20, 9],\n [0, 0, 0, 0, 0, 0, 0, -12, -26, 2, 34, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, -29, 24, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -21, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-24, 25, 0, -1, 31, 27, 4, -5, 1, -31, -32, -10],\n [0, 3, 20, 18, 2, 18, -17, -10, 16, 25, 31, -14],\n [0, 0, 3, 25, 13, 25, -24, -23, 22, -25, 28, -5],\n [0, 0, 0, -34, 25, 0, 13, -9, -24, 22, -30, 8],\n [0, 0, 0, 0, -4, -3, -16, 33, 16, 6, -35, 27],\n [0, 0, 0, 0, 0, -26, -10, -4, 6, 26, -24, 4],\n [0, 0, 0, 0, 0, 0, 21, -29, -10, 23, 33, 11],\n [0, 0, 0, 0, 0, 0, 0, -4, -28, 14, 11, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, 14, -23, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, -32, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
178
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[30, -4, 22, 4, 26, -19, 6, -7, -12, 9, 14, -13],\n [-4, 35, 1, -9, -5, 20, 13, -6, 8, -4, -8, 12],\n [22, 1, -32, -6, -14, -6, -7, -4, 26, -4, 6, 4],\n [4, -9, -6, 5, -11, 4, -25, 2, 18, 34, -16, 4],\n [26, -5, -14, -11, 1, -14, -8, 25, -3, -4, -10, 8],\n [-19, 20, -6, 4, -14, -8, 3, 16, -16, -2, 28, -4],\n [6, 13, -7, -25, -8, 3, 4, -2, -6, -14, 33, -15],\n [-7, -6, -4, 2, 25, 16, -2, 35, -9, 18, 0, -34],\n [-12, 8, 26, 18, -3, -16, -6, -9, 13, 26, -1, -4],\n [9, -4, -4, 34, -4, -2, -14, 18, 26, 14, 16, -28],\n [14, -8, 6, -16, -10, 28, 33, 0, -1, 16, -5, -20],\n [-13, 12, 4, 4, 8, -4, -15, -34, -4, -28, -20, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-34, -28, 12, 2, 18, -10, -12, 13, -12, 12, 26, -8],\n [-28, 29, 0, -10, -8, 12, 3, 8, 4, 8, -24, 12],\n [12, 0, 5, -6, -10, 2, -24, -4, 6, -2, 26, -5],\n [2, -10, -6, 25, 30, 0, -14, -4, 8, -10, -2, -1],\n [18, -8, -10, 30, 32, -24, -14, 31, -6, -2, 12, -17],\n [-10, 12, 2, 0, -24, 19, -12, 18, 8, -5, 6, -11],\n [-12, 3, -24, -14, -14, -12, 16, -24, 13, -24, 2, -11],\n [13, 8, -4, -4, 31, 18, -24, 29, 17, -27, -10, 22],\n [-12, 4, 6, 8, -6, 8, 13, 17, 9, 1, 14, 6],\n [12, 8, -2, -10, -2, -5, -24, -27, 1, -14, -22, 24],\n [26, -24, 26, -2, 12, 6, 2, -10, 14, -22, 19, -24],\n [-8, 12, -5, -1, -17, -11, -11, 22, 6, 24, -24, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[20, 22, -14, -21, -16, -12, -2, -16, -25, -12, -11, 1],\n [22, -10, 4, -14, 10, 24, -2, -20, -20, 8, -5, -4],\n [-14, 4, 3, -24, -7, 20, 20, -12, -6, 13, -16, 10],\n [-21, -14, -24, 12, -2, 10, 8, 23, -7, -11, 8, -14],\n [-16, 10, -7, -2, -20, -10, 10, 21, 16, -24, -1, -28],\n [-12, 24, 20, 10, -10, -24, -18, -19, -4, 2, -13, -18],\n [-2, -2, 20, 8, 10, -18, -22, -34, -8, -11, -6, 2],\n [-16, -20, -12, 23, 21, -19, -34, -3, 22, 28, 12, -20],\n [-25, -20, -6, -7, 16, -4, -8, 22, 23, 6, -10, -6],\n [-12, 8, 13, -11, -24, 2, -11, 28, 6, -16, -4, -23],\n [-11, -5, -16, 8, -1, -13, -6, 12, -10, -4, -11, 11],\n [1, -4, 10, -14, -28, -18, 2, -20, -6, -23, 11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
529
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[29, -23, 0, 22, -16, 16, -30, -13, 6, -12, -31, -4],\n [0, -19, -9, 32, -13, -2, -15, -14, 29, -4, 26, -8],\n [0, 0, 34, -22, 19, 22, 8, 10, -22, 8, 5, -34],\n [0, 0, 0, -1, -17, 27, -28, -13, -23, -13, -5, -6],\n [0, 0, 0, 0, -7, -14, -17, 5, 2, -7, -14, -28],\n [0, 0, 0, 0, 0, 10, 28, -5, -13, 25, 14, 10],\n [0, 0, 0, 0, 0, 0, -18, 23, 34, -1, -17, -10],\n [0, 0, 0, 0, 0, 0, 0, -12, 7, 3, -11, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, -25, -27, -1, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 19, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, -19, -31, 34, 28, 30, 35, -32, -8, 2, 30, 31],\n [0, 11, -11, 30, 31, 33, 4, 14, 4, 1, 33, -19],\n [0, 0, 6, -5, -3, 7, 31, 2, 5, 27, 4, -6],\n [0, 0, 0, 7, 25, -4, -32, 9, -16, 35, 29, 24],\n [0, 0, 0, 0, -10, 26, 8, -5, -10, -31, 34, -1],\n [0, 0, 0, 0, 0, -18, 14, -16, 20, -34, -10, -13],\n [0, 0, 0, 0, 0, 0, -19, 2, -22, -22, -24, 33],\n [0, 0, 0, 0, 0, 0, 0, 30, -13, 32, -16, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -4, 30, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -34, -9, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-17, -8, 4, 21, 15, -14, 32, -28, 24, 29, 0, 35],\n [0, 29, 20, -32, 14, 3, -1, -11, 8, 11, 4, -5],\n [0, 0, 19, -20, 32, 33, 6, 5, 14, -30, 17, -19],\n [0, 0, 0, 16, -2, -16, 20, 15, 17, 13, -32, -18],\n [0, 0, 0, 0, -15, 16, 33, 5, 18, -6, 20, 5],\n [0, 0, 0, 0, 0, 12, 34, 12, -32, -12, -5, -7],\n [0, 0, 0, 0, 0, 0, 11, 19, 33, 2, -7, -24],\n [0, 0, 0, 0, 0, 0, 0, -32, 21, 18, -8, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, -7, 5, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -25, -28, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
218
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[25, -17, -4, -6, 29, -4, 21, -16, -6, 23, 26, 31],\n [0, 30, 18, -26, 2, -5, -7, -11, -4, -19, 9, 13],\n [0, 0, -16, 26, -23, 7, -15, -30, 35, 17, 16, 33],\n [0, 0, 0, -6, 7, 23, 2, -2, 10, -4, -20, 3],\n [0, 0, 0, 0, -2, 14, -25, 7, -26, -28, -17, 29],\n [0, 0, 0, 0, 0, 12, 18, -20, -6, -8, -20, 15],\n [0, 0, 0, 0, 0, 0, 8, 31, 7, -30, 28, -23],\n [0, 0, 0, 0, 0, 0, 0, -30, 1, 21, 17, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 25, -6, 7, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 21, -9, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-23, 12, 13, 22, 34, 25, -10, 3, 22, -9, 4, -5],\n [0, -21, 18, 34, -25, -6, -1, 7, 25, 4, 6, 6],\n [0, 0, 17, 8, 10, 1, 2, 2, -25, 9, 28, 8],\n [0, 0, 0, -27, 31, -34, -28, 7, -18, 16, 3, -5],\n [0, 0, 0, 0, -34, -4, 0, 19, 27, 33, 4, -12],\n [0, 0, 0, 0, 0, 2, 35, 9, -4, -4, -35, 9],\n [0, 0, 0, 0, 0, 0, -6, -14, 22, 19, 10, -10],\n [0, 0, 0, 0, 0, 0, 0, 10, -29, -2, 22, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, -22, -25, 4, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -20, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[13, -26, 12, -12, 4, -19, -22, -2, -1, -32, -28, 20],\n [-26, -16, -15, 6, 10, 2, -12, 4, -12, -9, 4, 15],\n [12, -15, -4, -8, -3, 2, -2, -32, 4, 2, -10, -10],\n [-12, 6, -8, 29, 2, 12, -11, -4, -20, -26, -2, -4],\n [4, 10, -3, 2, 12, 4, 19, 2, 23, 6, 22, -4],\n [-19, 2, 2, 12, 4, 1, -25, -19, -9, -3, -6, -16],\n [-22, -12, -2, -11, 19, -25, -33, -15, 18, 5, 20, -23],\n [-2, 4, -32, -4, 2, -19, -15, -16, 3, 4, -18, -11],\n [-1, -12, 4, -20, 23, -9, 18, 3, 17, 6, -20, 6],\n [-32, -9, 2, -26, 6, -3, 5, 4, 6, -23, -4, 0],\n [-28, 4, -10, -2, 22, -6, 20, -18, -20, -4, -21, 6],\n [20, 15, -10, -4, -4, -16, -23, -11, 6, 0, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
507
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[9, -11, 24, -16, -18, 0, 5, 14, -14, -30, -4, 5],\n [-11, -35, -26, 6, -4, 2, 18, 6, 20, -27, -1, 13],\n [24, -26, 20, -20, 1, 18, -10, -8, -14, 12, 30, 4],\n [-16, 6, -20, -24, -26, -10, 0, 2, 2, 5, -4, 0],\n [-18, -4, 1, -26, -27, 1, 25, -14, -18, -6, 5, 12],\n [0, 2, 18, -10, 1, 6, -20, -10, 7, -4, 10, 19],\n [5, 18, -10, 0, 25, -20, 28, 1, 19, 16, 14, 3],\n [14, 6, -8, 2, -14, -10, 1, -12, 8, 4, 6, 10],\n [-14, 20, -14, 2, -18, 7, 19, 8, -6, -17, -28, 34],\n [-30, -27, 12, 5, -6, -4, 16, 4, -17, -21, -18, -2],\n [-4, -1, 30, -4, 5, 10, 14, 6, -28, -18, -5, -18],\n [5, 13, 4, 0, 12, 19, 3, 10, 34, -2, -18, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
533
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, -4, 14, -2, -20, -23, -4, -13, 14, 29, -8, 10],\n [-4, -16, -2, 4, -14, 0, 6, 1, 4, -4, 24, -7],\n [14, -2, 12, -11, -2, -16, 18, 11, -6, 14, 34, 10],\n [-2, 4, -11, -8, 18, -25, -23, 2, -22, 25, -3, -12],\n [-20, -14, -2, 18, 24, 0, -26, -18, -8, 22, -6, 6],\n [-23, 0, -16, -25, 0, -5, 10, -30, 2, -6, 24, 16],\n [-4, 6, 18, -23, -26, 10, 29, 24, 4, 28, 10, 10],\n [-13, 1, 11, 2, -18, -30, 24, -12, -10, 1, 0, 0],\n [14, 4, -6, -22, -8, 2, 4, -10, 3, 13, -8, -12],\n [29, -4, 14, 25, 22, -6, 28, 1, 13, 13, -5, -14],\n [-8, 24, 34, -3, -6, 24, 10, 0, -8, -5, 8, 24],\n [10, -7, 10, -12, 6, 16, 10, 0, -12, -14, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-18, 20, -21, -1, -9, -33, -15, 3, -4, 14, -27, 14],\n [0, -32, -32, -2, -9, -21, -4, 5, 35, 25, 27, 25],\n [0, 0, 29, -4, 5, -10, 12, -20, -5, 30, -4, -26],\n [0, 0, 0, -33, 26, 31, 19, -26, 19, -14, -22, -28],\n [0, 0, 0, 0, 18, 6, -17, 4, 33, -9, 7, 16],\n [0, 0, 0, 0, 0, 13, -7, -10, -9, 31, 31, -1],\n [0, 0, 0, 0, 0, 0, -23, -7, -27, -4, -14, 22],\n [0, 0, 0, 0, 0, 0, 0, 19, -10, -23, -29, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -30, -13, -26, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 8, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-7, -6, -20, -8, 0, 9, -22, 0, -28, -14, -5, -9],\n [-6, -14, -16, 13, -1, 28, 5, -9, -8, -20, -28, 20],\n [-20, -16, 30, 2, 9, 26, 8, 20, -2, 14, -8, 2],\n [-8, 13, 2, -19, 8, -12, 1, 4, 12, 14, -27, 14],\n [0, -1, 9, 8, 20, 11, -8, -1, -2, -2, 19, 6],\n [9, 28, 26, -12, 11, 1, 2, 12, -6, -17, -16, -24],\n [-22, 5, 8, 1, -8, 2, -7, -6, 6, -2, -15, -17],\n [0, -9, 20, 4, -1, 12, -6, -35, -9, 28, -4, 19],\n [-28, -8, -2, 12, -2, -6, 6, -9, 23, -20, -5, 12],\n [-14, -20, 14, 14, -2, -17, -2, 28, -20, -14, -22, 6],\n [-5, -28, -8, -27, 19, -16, -15, -4, -5, -22, -18, 9],\n [-9, 20, 2, 14, 6, -24, -17, 19, 12, 6, 9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
539
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, 10, -24, -16, -4, -20, 18, 3, 11, -1, 4, 2],\n [10, -9, -12, -5, 1, -12, -6, 4, 12, 4, 16, -6],\n [-24, -12, 4, -4, -20, -1, 6, -7, 15, 11, 26, 12],\n [-16, -5, -4, -6, -2, 4, -8, 22, 3, 22, 30, 2],\n [-4, 1, -20, -2, 31, -8, -5, 10, -9, -8, 2, -4],\n [-20, -12, -1, 4, -8, -26, -10, 10, -1, 2, -20, 0],\n [18, -6, 6, -8, -5, -10, -34, -20, 4, 0, -13, 14],\n [3, 4, -7, 22, 10, 10, -20, 25, 12, 16, -4, -15],\n [11, 12, 15, 3, -9, -1, 4, 12, 24, 6, 26, 20],\n [-1, 4, 11, 22, -8, 2, 0, 16, 6, -34, -4, -14],\n [4, 16, 26, 30, 2, -20, -13, -4, 26, -4, -4, 6],\n [2, -6, 12, 2, -4, 0, 14, -15, 20, -14, 6, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
492
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[25, 22, 5, -12, 6, 8, -12, -22, -26, -2, 2, 22],\n [22, -30, 2, -16, 9, -16, -8, 12, -19, -6, 2, -1],\n [5, 2, -13, 14, 8, 30, 16, 8, 27, 2, -20, -16],\n [-12, -16, 14, 0, -10, -5, -10, 8, -28, -4, 2, 0],\n [6, 9, 8, -10, -26, 18, 20, 4, 15, 17, -2, 21],\n [8, -16, 30, -5, 18, 24, -18, -10, 1, -15, -18, -4],\n [-12, -8, 16, -10, 20, -18, 0, -6, -4, -4, -6, -7],\n [-22, 12, 8, 8, 4, -10, -6, 16, 2, 15, 12, -22],\n [-26, -19, 27, -28, 15, 1, -4, 2, -33, -32, 25, -27],\n [-2, -6, 2, -4, 17, -15, -4, 15, -32, 10, -17, -8],\n [2, 2, -20, 2, -2, -18, -6, 12, 25, -17, 20, -4],\n [22, -1, -16, 0, 21, -4, -7, -22, -27, -8, -4, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
110
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-29, 2, 14, 5, 16, -21, 10, 18, 19, -8, -8, -2],\n [2, 23, -30, 2, -7, 18, 8, 14, 3, -14, -33, -4],\n [14, -30, -9, -26, 5, 13, -10, 31, -16, 1, -10, -6],\n [5, 2, -26, -6, -22, 16, 14, 0, -14, 14, -18, 7],\n [16, -7, 5, -22, -32, 23, 32, 0, 3, -12, -16, -20],\n [-21, 18, 13, 16, 23, 16, 22, -2, 16, 8, -14, -6],\n [10, 8, -10, 14, 32, 22, 16, -28, -4, -10, -24, -10],\n [18, 14, 31, 0, 0, -2, -28, -1, -6, -13, 4, 7],\n [19, 3, -16, -14, 3, 16, -4, -6, 11, -14, 6, -26],\n [-8, -14, 1, 14, -12, 8, -10, -13, -14, 30, 17, 8],\n [-8, -33, -10, -18, -16, -14, -24, 4, 6, 17, 25, 8],\n [-2, -4, -6, 7, -20, -6, -10, 7, -26, 8, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
535
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[20, 8, 6, -22, -2, 9, -9, 11, 16, -6, -5, 30],\n [8, -15, 2, -12, -5, 6, 16, 19, -2, -10, 14, 12],\n [6, 2, 32, 1, -7, 31, -6, 12, -19, 24, -8, -12],\n [-22, -12, 1, 25, -16, 10, -3, 4, -6, 21, 10, -18],\n [-2, -5, -7, -16, -17, -4, 17, 19, 12, -32, 10, -20],\n [9, 6, 31, 10, -4, -30, -15, 17, 3, 14, -12, -12],\n [-9, 16, -6, -3, 17, -15, -21, -6, -22, -16, 1, -4],\n [11, 19, 12, 4, 19, 17, -6, 35, 18, 4, -30, -16],\n [16, -2, -19, -6, 12, 3, -22, 18, 12, 20, 8, -6],\n [-6, -10, 24, 21, -32, 14, -16, 4, 20, 5, 24, 18],\n [-5, 14, -8, 10, 10, -12, 1, -30, 8, 24, -31, 0],\n [30, 12, -12, -18, -20, -12, -4, -16, -6, 18, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
549
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[6, -1, -15, -12, 2, 26, -11, -16, 12, -11, -12, -6],\n [-1, -13, 18, -18, 18, 4, 25, 4, 5, 20, 22, 12],\n [-15, 18, -24, 34, -17, -2, -10, -8, 24, 0, -16, -18],\n [-12, -18, 34, -32, -1, 2, -15, -17, -8, -24, -18, -18],\n [2, 18, -17, -1, 5, -10, -28, -12, 1, 22, 12, 2],\n [26, 4, -2, 2, -10, -9, 13, 26, 20, 27, 10, 15],\n [-11, 25, -10, -15, -28, 13, -3, -4, 14, 18, -2, 10],\n [-16, 4, -8, -17, -12, 26, -4, 29, -8, 10, 4, 0],\n [12, 5, 24, -8, 1, 20, 14, -8, 23, -3, -18, 24],\n [-11, 20, 0, -24, 22, 27, 18, 10, -3, 5, -20, 4],\n [-12, 22, -16, -18, 12, 10, -2, 4, -18, -20, 32, 8],\n [-6, 12, -18, -18, 2, 15, 10, 0, 24, 4, 8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
558
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-6, 7, 4, 29, 19, 29, -10, 22, 9, 2, 3, 30],\n [7, 9, 11, -20, 12, 28, 10, -8, -6, -18, -6, -12],\n [4, 11, -19, 21, 14, 10, 21, -6, -27, 24, -28, 6],\n [29, -20, 21, 11, -4, 22, 10, -12, 0, -2, 24, -2],\n [19, 12, 14, -4, -26, -1, -18, 30, 14, -8, 24, 10],\n [29, 28, 10, 22, -1, -8, -4, -10, -34, 14, -5, 4],\n [-10, 10, 21, 10, -18, -4, -35, 1, 8, 15, -14, -11],\n [22, -8, -6, -12, 30, -10, 1, -34, -6, 6, -16, 3],\n [9, -6, -27, 0, 14, -34, 8, -6, -5, 19, 12, -5],\n [2, -18, 24, -2, -8, 14, 15, 6, 19, -22, -18, -20],\n [3, -6, -28, 24, 24, -5, -14, -16, 12, -18, 32, -8],\n [30, -12, 6, -2, 10, 4, -11, 3, -5, -20, -8, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
595
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-16, -10, 6, 2, 27, 18, -6, 6, -8, 2, -12, -4],\n [-10, 7, 0, -2, 0, 18, -26, 20, -2, -2, -9, 8],\n [6, 0, -7, 16, 20, 0, -16, -17, 0, 10, 4, 0],\n [2, -2, 16, -6, -19, -6, -10, 16, -10, -6, 26, 2],\n [27, 0, 20, -19, -10, 0, -10, -12, 17, 30, 32, -1],\n [18, 18, 0, -6, 0, 13, 18, 4, 26, -12, 15, 30],\n [-6, -26, -16, -10, -10, 18, -33, -7, -5, -12, -13, -26],\n [6, 20, -17, 16, -12, 4, -7, -8, -11, 2, -9, 21],\n [-8, -2, 0, -10, 17, 26, -5, -11, 18, 8, -2, 7],\n [2, -2, 10, -6, 30, -12, -12, 2, 8, 22, 6, 2],\n [-12, -9, 4, 26, 32, 15, -13, -9, -2, 6, -25, -11],\n [-4, 8, 0, 2, -1, 30, -26, 21, 7, 2, -11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
470
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[23, -10, 8, 9, -6, 18, 22, -3, -4, -6, -6, 15],\n [-10, 34, -22, 2, 11, -14, 19, 24, -15, 24, -2, -6],\n [8, -22, 3, 9, -10, 7, 20, -20, 9, -6, 18, 14],\n [9, 2, 9, -5, -16, -14, -14, -22, 16, 18, -27, -8],\n [-6, 11, -10, -16, -29, 3, -1, -1, 11, 26, 18, -14],\n [18, -14, 7, -14, 3, 16, -6, 0, 6, 8, 6, 18],\n [22, 19, 20, -14, -1, -6, -13, 7, 18, 10, -22, 34],\n [-3, 24, -20, -22, -1, 0, 7, 4, -32, 20, 11, -12],\n [-4, -15, 9, 16, 11, 6, 18, -32, 23, -1, 1, 20],\n [-6, 24, -6, 18, 26, 8, 10, 20, -1, -13, -17, 14],\n [-6, -2, 18, -27, 18, 6, -22, 11, 1, -17, 18, -34],\n [15, -6, 14, -8, -14, 18, 34, -12, 20, 14, -34, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
539
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-28, 15, -17, -5, -14, -3, 1, -24, 33, 28, -11, 18],\n [0, -23, -10, -14, -26, 12, 6, 23, 17, 4, 26, -30],\n [0, 0, 33, -33, -29, -24, -19, 31, 34, 0, -19, -35],\n [0, 0, 0, 35, 7, -5, -12, 1, 29, 27, 20, -18],\n [0, 0, 0, 0, 20, 12, -17, -10, 2, -11, 20, -8],\n [0, 0, 0, 0, 0, -13, 1, -25, -19, 20, 17, 31],\n [0, 0, 0, 0, 0, 0, 8, 20, 18, 17, 10, 18],\n [0, 0, 0, 0, 0, 0, 0, -3, 17, -20, -10, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -35, -31, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 7, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-25, -16, -26, -16, -8, 4, 14, 32, 6, 0, -2, 4],\n [-16, 0, 16, 9, -5, 16, 7, 20, -10, 4, 6, 1],\n [-26, 16, -2, 15, -10, -16, 6, -24, 11, -9, -16, 13],\n [-16, 9, 15, -16, -10, 2, -7, 12, -8, 0, -6, -9],\n [-8, -5, -10, -10, -11, 3, 8, -22, 0, -5, -18, -11],\n [4, 16, -16, 2, 3, -26, 2, 10, -30, 0, -31, 2],\n [14, 7, 6, -7, 8, 2, -19, 15, -4, -31, 31, -25],\n [32, 20, -24, 12, -22, 10, 15, -6, -9, 13, -12, 4],\n [6, -10, 11, -8, 0, -30, -4, -9, -27, -5, 4, 24],\n [0, 4, -9, 0, -5, 0, -31, 13, -5, -26, 12, 0],\n [-2, 6, -16, -6, -18, -31, 31, -12, 4, 12, -33, 9],\n [4, 1, 13, -9, -11, 2, -25, 4, 24, 0, 9, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
521
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-2, 31, -32, 8, -21, -28, -31, 30, 10, 29, 30, -10],\n [0, 15, 5, 15, -17, -33, 2, 34, 9, 35, 5, -11],\n [0, 0, 18, -23, 4, -15, 5, 25, -3, -7, 19, -4],\n [0, 0, 0, -5, -22, 27, 16, 18, 14, 18, -1, -6],\n [0, 0, 0, 0, -16, 35, -20, 16, 29, 34, -35, -20],\n [0, 0, 0, 0, 0, 16, 14, -19, -33, 26, -15, -3],\n [0, 0, 0, 0, 0, 0, 8, 21, 4, 20, 27, 3],\n [0, 0, 0, 0, 0, 0, 0, -11, 34, -33, -15, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, 32, 30, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, -20, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[14, -28, -24, 15, 30, 5, -14, -27, -25, -23, 20, -8],\n [0, 28, 34, 19, 1, -3, -11, -13, 24, 20, 27, -28],\n [0, 0, 26, -25, 31, 4, 4, 20, 17, -8, 6, 10],\n [0, 0, 0, -7, 16, 10, -35, 27, -20, -11, 26, -20],\n [0, 0, 0, 0, -13, 7, 8, -4, -13, -16, -17, -7],\n [0, 0, 0, 0, 0, 19, -32, 27, -24, -18, -28, -4],\n [0, 0, 0, 0, 0, 0, 35, -10, -13, 27, 30, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, -18, -13, 13, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, -5, 3, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 22, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
235
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[3, 0, 19, -2, 28, -9, 22, 20, 0, -20, -17, -5],\n [0, 24, -24, 3, -8, -4, 18, -19, 2, 12, 8, 18],\n [19, -24, 15, -12, -12, -12, 24, -1, 15, -2, 28, 8],\n [-2, 3, -12, -34, -23, 17, 4, -10, -4, -10, -2, 8],\n [28, -8, -12, -23, 3, -9, 6, 4, 7, 18, 32, 19],\n [-9, -4, -12, 17, -9, 4, -14, -12, 7, -23, -1, -1],\n [22, 18, 24, 4, 6, -14, 3, 4, -2, 3, 12, 2],\n [20, -19, -1, -10, 4, -12, 4, -7, 3, -14, -2, 16],\n [0, 2, 15, -4, 7, 7, -2, 3, 30, 2, -2, 10],\n [-20, 12, -2, -10, 18, -23, 3, -14, 2, -22, 0, -10],\n [-17, 8, 28, -2, 32, -1, 12, -2, -2, 0, -29, -18],\n [-5, 18, 8, 8, 19, -1, 2, 16, 10, -10, -18, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-20, 12, -26, -30, 18, 15, -15, -14, -14, -8, 14, 4],\n [12, 6, 6, 10, 6, -4, 20, -1, 14, -11, 7, 7],\n [-26, 6, 0, -18, 28, -16, -8, 0, 4, -15, -6, 6],\n [-30, 10, -18, 5, 16, 10, -7, 17, 26, 4, 2, 0],\n [18, 6, 28, 16, -10, 6, 18, 0, 1, -11, 0, 0],\n [15, -4, -16, 10, 6, 30, 20, 0, 14, -14, -5, 25],\n [-15, 20, -8, -7, 18, 20, -6, -11, 22, -8, 4, 18],\n [-14, -1, 0, 17, 0, 0, -11, 3, 2, -2, -16, 0],\n [-14, 14, 4, 26, 1, 14, 22, 2, 27, -17, 8, 16],\n [-8, -11, -15, 4, -11, -14, -8, -2, -17, -33, -10, 8],\n [14, 7, -6, 2, 0, -5, 4, -16, 8, -10, -8, 14],\n [4, 7, 6, 0, 0, 25, 18, 0, 16, 8, 14, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
445
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-30, -10, 14, -15, 8, 20, 4, -14, -10, 1, 10, 0],\n [-10, -34, 8, -3, 0, -8, -16, 1, 5, -10, 18, 21],\n [14, 8, 33, 11, -30, 11, -11, 18, -34, -8, -2, 4],\n [-15, -3, 11, 12, 5, -4, 8, 2, 8, -22, -20, 18],\n [8, 0, -30, 5, -1, 16, -7, 22, 2, 0, 8, 11],\n [20, -8, 11, -4, 16, -2, -2, 22, -6, 14, -12, 0],\n [4, -16, -11, 8, -7, -2, -15, -1, 2, -15, -18, -9],\n [-14, 1, 18, 2, 22, 22, -1, 17, 21, 20, 2, 7],\n [-10, 5, -34, 8, 2, -6, 2, 21, 16, 11, -12, 29],\n [1, -10, -8, -22, 0, 14, -15, 20, 11, 25, -1, -12],\n [10, 18, -2, -20, 8, -12, -18, 2, -12, -1, 27, -16],\n [0, 21, 4, 18, 11, 0, -9, 7, 29, -12, -16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
512
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-23, 19, -28, 26, -14, 20, -15, 13, -30, -1, -9, 4],\n [0, 16, 4, 7, 22, -33, -21, 9, -25, 3, -17, -16],\n [0, 0, -32, -27, -11, 11, 13, -9, -8, 26, -20, 10],\n [0, 0, 0, -26, -35, 30, -19, 11, -12, 14, -7, -23],\n [0, 0, 0, 0, -22, -26, -3, 4, -30, -19, 0, 34],\n [0, 0, 0, 0, 0, 15, 6, -17, 26, 31, -6, 2],\n [0, 0, 0, 0, 0, 0, 9, -3, -31, 26, 1, -19],\n [0, 0, 0, 0, 0, 0, 0, -3, -31, -18, 27, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, 23, -30, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 13, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
211
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-9, 5, -29, -4, -20, -34, 7, -5, 11, -3, -19, 18],\n [0, 15, 16, -29, 18, -25, 26, -6, 21, 10, 34, 30],\n [0, 0, -26, -32, 26, 7, 6, -12, -31, 32, 9, 23],\n [0, 0, 0, 13, -4, 14, 22, 16, -13, -6, 34, 35],\n [0, 0, 0, 0, 34, -1, 32, -4, 23, -1, -20, 16],\n [0, 0, 0, 0, 0, -18, -32, 21, 17, -11, 11, 16],\n [0, 0, 0, 0, 0, 0, 6, -17, 8, -6, 8, -9],\n [0, 0, 0, 0, 0, 0, 0, 20, 22, 33, -28, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 1, 18, 13, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 20, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
220
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[34, -17, -32, -31, 18, 34, 21, 16, -18, 28, -26, -13],\n [0, 16, 11, 34, -10, 34, 7, 33, 27, 30, 27, -23],\n [0, 0, 11, 0, 0, 14, 20, -17, -16, -14, -5, 26],\n [0, 0, 0, 13, 23, -32, 3, -29, 35, 13, -21, -29],\n [0, 0, 0, 0, 11, 17, -9, -31, 24, 26, 23, 25],\n [0, 0, 0, 0, 0, 29, -12, -7, -29, -19, -11, 0],\n [0, 0, 0, 0, 0, 0, 5, -11, -2, -28, 20, -6],\n [0, 0, 0, 0, 0, 0, 0, 17, -31, -18, -19, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 2, -16, 14, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 34, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
190
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[15, 18, 6, -14, 18, -6, -8, -12, -14, 10, -31, -4],\n [18, -2, 24, -30, -3, 12, -6, -9, 18, 14, 12, 6],\n [6, 24, 27, 16, -28, -30, 7, 6, 6, 0, 15, 3],\n [-14, -30, 16, 5, 11, -20, 24, 10, -14, -4, -11, -2],\n [18, -3, -28, 11, 18, -16, 15, 0, 30, 6, 0, -4],\n [-6, 12, -30, -20, -16, -4, 18, -10, 2, -4, 18, -16],\n [-8, -6, 7, 24, 15, 18, -15, -2, -12, -4, 8, -9],\n [-12, -9, 6, 10, 0, -10, -2, 32, -2, 17, 26, -10],\n [-14, 18, 6, -14, 30, 2, -12, -2, -24, 9, -19, 4],\n [10, 14, 0, -4, 6, -4, -4, 17, 9, 16, -16, 9],\n [-31, 12, 15, -11, 0, 18, 8, 26, -19, -16, -18, -4],\n [-4, 6, 3, -2, -4, -16, -9, -10, 4, 9, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
526
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[19, -31, 18, 6, -4, -10, 8, -11, 14, 6, 16, 18],\n [-31, -24, -16, -14, 14, -12, -1, 18, -8, 2, 10, -28],\n [18, -16, 15, 9, -12, -34, -31, -21, -22, -5, 32, 20],\n [6, -14, 9, 21, -1, -26, 22, 12, 14, 14, -22, 35],\n [-4, 14, -12, -1, 14, 3, 12, -32, 12, 4, -4, -14],\n [-10, -12, -34, -26, 3, -3, -28, 32, 0, -16, 18, 14],\n [8, -1, -31, 22, 12, -28, 5, -4, -16, 20, 16, 6],\n [-11, 18, -21, 12, -32, 32, -4, -7, 7, 25, 28, 9],\n [14, -8, -22, 14, 12, 0, -16, 7, -30, 8, 12, -2],\n [6, 2, -5, 14, 4, -16, 20, 25, 8, 16, -10, -3],\n [16, 10, 32, -22, -4, 18, 16, 28, 12, -10, 1, 6],\n [18, -28, 20, 35, -14, 14, 6, 9, -2, -3, 6, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
97
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, 5, 15, -25, -14, -22, 0, 5, -33, 14, -9, 15],\n [5, 30, -15, 26, 6, -2, -20, 12, -14, 30, 10, 1],\n [15, -15, 2, 31, -23, 18, -4, -33, -3, 28, -24, 22],\n [-25, 26, 31, 14, 2, -20, -1, 10, 17, 6, -10, 18],\n [-14, 6, -23, 2, -18, -2, 13, 34, 3, -18, -3, 2],\n [-22, -2, 18, -20, -2, -29, 10, 4, -10, -28, -6, -16],\n [0, -20, -4, -1, 13, 10, -32, -2, 6, -4, 8, 26],\n [5, 12, -33, 10, 34, 4, -2, -12, -3, -11, -9, 22],\n [-33, -14, -3, 17, 3, -10, 6, -3, -13, 6, 10, -4],\n [14, 30, 28, 6, -18, -28, -4, -11, 6, 27, 5, -24],\n [-9, 10, -24, -10, -3, -6, 8, -9, 10, 5, 3, -23],\n [15, 1, 22, 18, 2, -16, 26, 22, -4, -24, -23, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-6, 28, -2, 9, 18, -10, 3, 9, -5, 4, -2, -6],\n [28, -8, 16, -11, 12, 32, -12, 18, 16, -4, -12, -6],\n [-2, 16, -29, 21, 12, 2, 0, 16, -4, 12, -4, -11],\n [9, -11, 21, -26, -27, 0, 7, -24, -26, -14, -20, 18],\n [18, 12, 12, -27, 7, 7, -9, -16, 3, 14, -4, 0],\n [-10, 32, 2, 0, 7, -16, 18, 12, 6, 2, 10, -3],\n [3, -12, 0, 7, -9, 18, -23, -14, -26, 11, 8, 30],\n [9, 18, 16, -24, -16, 12, -14, 32, -5, -14, 28, 28],\n [-5, 16, -4, -26, 3, 6, -26, -5, 7, -12, -18, 21],\n [4, -4, 12, -14, 14, 2, 11, -14, -12, 19, 2, 2],\n [-2, -12, -4, -20, -4, 10, 8, 28, -18, 2, 1, 10],\n [-6, -6, -11, 18, 0, -3, 30, 28, 21, 2, 10, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
504
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[15, 5, 31, 29, -30, 1, -24, -34, 17, -11, -8, 9],\n [0, -19, 33, 20, 22, -32, 19, 13, 2, 9, -6, 1],\n [0, 0, -4, -25, 22, -1, -19, -6, -18, -6, -20, 18],\n [0, 0, 0, -32, -1, 27, 30, 3, -8, -2, -3, 14],\n [0, 0, 0, 0, -35, -28, 10, -12, 4, 15, -12, -14],\n [0, 0, 0, 0, 0, 6, 3, -1, 5, 12, 35, 8],\n [0, 0, 0, 0, 0, 0, 27, -7, -5, 28, 17, 32],\n [0, 0, 0, 0, 0, 0, 0, 11, 15, 0, -9, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, 1, 9, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 21, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
233
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-12, -2, 23, -14, -24, 22, 15, 6, -2, 2, -2, 0],\n [-2, 23, -14, 6, 0, 8, 12, 1, 30, 11, -2, -26],\n [23, -14, 20, 6, 16, -14, -4, -20, -12, -18, -28, 8],\n [-14, 6, 6, -28, -2, 16, -22, 10, -2, 15, -8, 0],\n [-24, 0, 16, -2, -6, -15, -16, 26, -2, 4, 6, 0],\n [22, 8, -14, 16, -15, 34, 0, 6, -20, -18, -14, -29],\n [15, 12, -4, -22, -16, 0, 4, -4, -20, -16, 9, 6],\n [6, 1, -20, 10, 26, 6, -4, -16, 0, 8, 15, 24],\n [-2, 30, -12, -2, -2, -20, -20, 0, 33, 28, -26, 8],\n [2, 11, -18, 15, 4, -18, -16, 8, 28, 18, -2, 0],\n [-2, -2, -28, -8, 6, -14, 9, 15, -26, -2, -10, -28],\n [0, -26, 8, 0, 0, -29, 6, 24, 8, 0, -28, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
537
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[23, 16, -2, -17, 4, -18, -8, 5, 14, -16, 22, 10],\n [16, 8, -10, -20, -22, 4, 24, 0, -14, -6, -16, -12],\n [-2, -10, 23, 19, -14, 4, 0, 18, -16, 26, 7, 6],\n [-17, -20, 19, 6, -12, -12, -24, -4, 8, -12, -16, -16],\n [4, -22, -14, -12, -10, -11, -23, 21, -15, -7, -8, 3],\n [-18, 4, 4, -12, -11, -13, -15, 0, 18, 26, 12, -8],\n [-8, 24, 0, -24, -23, -15, 32, -18, 8, 26, -5, -13],\n [5, 0, 18, -4, 21, 0, -18, 27, -2, -26, -10, -28],\n [14, -14, -16, 8, -15, 18, 8, -2, -35, 0, 32, 16],\n [-16, -6, 26, -12, -7, 26, 26, -26, 0, 5, -27, -16],\n [22, -16, 7, -16, -8, 12, -5, -10, 32, -27, -27, -4],\n [10, -12, 6, -16, 3, -8, -13, -28, 16, -16, -4, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
99
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[28, 20, 28, -12, 6, 0, 20, 8, -2, -6, 4, 18],\n [20, 9, 18, 0, 0, 0, 2, 9, -2, -3, -7, 16],\n [28, 18, 31, 8, -14, 12, 18, -8, -6, 2, 14, -8],\n [-12, 0, 8, 26, 0, -8, -22, -23, -5, -25, 22, -4],\n [6, 0, -14, 0, -18, -32, -8, 10, 10, 18, 22, -22],\n [0, 0, 12, -8, -32, -28, 13, -19, 2, 12, -8, 20],\n [20, 2, 18, -22, -8, 13, 25, 6, 4, 18, 1, 11],\n [8, 9, -8, -23, 10, -19, 6, 0, 6, 24, 10, -2],\n [-2, -2, -6, -5, 10, 2, 4, 6, 26, 18, 10, -12],\n [-6, -3, 2, -25, 18, 12, 18, 24, 18, 5, 15, 2],\n [4, -7, 14, 22, 22, -8, 1, 10, 10, 15, -28, -18],\n [18, 16, -8, -4, -22, 20, 11, -2, -12, 2, -18, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
99
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[19, 11, -14, 21, 6, -2, 24, -2, 12, 3, -2, 17],\n [11, -35, 20, -1, -8, 24, -30, -16, 7, 16, -12, -2],\n [-14, 20, -30, -3, -4, 5, -4, 2, -22, -4, 11, 8],\n [21, -1, -3, 26, -14, 29, 4, -18, 26, 18, 22, 22],\n [6, -8, -4, -14, -30, 16, 10, 12, 10, 12, 1, -2],\n [-2, 24, 5, 29, 16, 31, 17, -12, 12, -4, 13, 16],\n [24, -30, -4, 4, 10, 17, -16, 1, 20, 2, -14, 9],\n [-2, -16, 2, -18, 12, -12, 1, -12, -9, -6, 8, 2],\n [12, 7, -22, 26, 10, 12, 20, -9, -33, -2, -5, 30],\n [3, 16, -4, 18, 12, -4, 2, -6, -2, 30, 8, -4],\n [-2, -12, 11, 22, 1, 13, -14, 8, -5, 8, 20, -14],\n [17, -2, 8, 22, -2, 16, 9, 2, 30, -4, -14, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[29, 34, 14, 23, 27, -11, -26, -35, -22, -15, 22, 2],\n [0, -31, 8, 29, 21, 9, 24, 30, 11, -10, -27, 15],\n [0, 0, 3, 32, 4, 0, -15, -10, 20, 21, 23, -29],\n [0, 0, 0, 17, 10, 21, 25, 20, -7, -22, 32, 35],\n [0, 0, 0, 0, 26, -16, 20, 16, -11, 26, -19, 3],\n [0, 0, 0, 0, 0, 22, 8, -13, -19, 2, -6, -17],\n [0, 0, 0, 0, 0, 0, -10, -29, -2, 0, -30, 1],\n [0, 0, 0, 0, 0, 0, 0, 18, -26, -11, -18, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, 3, 12, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, -13, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-26, 6, -20, -33, -12, 4, 12, 22, 2, 10, 24, 0],\n [6, -25, -14, 22, 28, 4, 7, 0, 4, -6, 14, 10],\n [-20, -14, -13, -22, -11, -7, 2, -12, -22, 10, 6, 6],\n [-33, 22, -22, -19, -25, -2, -5, -19, -4, 0, 4, 14],\n [-12, 28, -11, -25, 22, 16, -12, 1, -16, 0, -8, 14],\n [4, 4, -7, -2, 16, 18, -20, -24, -5, 6, 7, 8],\n [12, 7, 2, -5, -12, -20, -12, -4, -18, 6, -9, -12],\n [22, 0, -12, -19, 1, -24, -4, -29, -29, -13, -18, -4],\n [2, 4, -22, -4, -16, -5, -18, -29, -14, 7, 8, -22],\n [10, -6, 10, 0, 0, 6, 6, -13, 7, -25, -34, -4],\n [24, 14, 6, 4, -8, 7, -9, -18, 8, -34, -8, -26],\n [0, 10, 6, 14, 14, 8, -12, -4, -22, -4, -26, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[29, 10, 16, 11, -8, -7, -12, 25, -2, -3, -4, -7],\n [10, 16, -4, -6, -7, 8, 6, -4, 13, 9, 2, -25],\n [16, -4, -33, -10, 21, -12, -13, 9, 0, 18, -5, 2],\n [11, -6, -10, -30, -12, -28, 28, 23, 23, -14, -32, -10],\n [-8, -7, 21, -12, -1, 2, -12, -11, -18, -6, 0, 2],\n [-7, 8, -12, -28, 2, -21, 28, -8, -16, 22, 8, -19],\n [-12, 6, -13, 28, -12, 28, -18, 4, -2, 0, -4, -28],\n [25, -4, 9, 23, -11, -8, 4, -19, -8, 17, 8, 4],\n [-2, 13, 0, 23, -18, -16, -2, -8, 32, 4, -33, 16],\n [-3, 9, 18, -14, -6, 22, 0, 17, 4, -9, 20, 8],\n [-4, 2, -5, -32, 0, 8, -4, 8, -33, 20, 18, -7],\n [-7, -25, 2, -10, 2, -19, -28, 4, 16, 8, -7, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-21, 0, 0, 15, -19, 5, 14, 10, -4, -28, -3, 4],\n [0, 7, 16, 12, -5, -18, 25, 20, 2, 22, 26, -14],\n [0, 16, 6, -18, 7, 0, 28, -4, 21, 10, -2, 26],\n [15, 12, -18, -23, -2, -20, -3, -2, 8, -10, -4, 20],\n [-19, -5, 7, -2, -34, 20, 13, 11, 8, -1, 14, -16],\n [5, -18, 0, -20, 20, 19, -6, -27, -8, -24, 6, 6],\n [14, 25, 28, -3, 13, -6, 27, -8, -6, -6, 6, 2],\n [10, 20, -4, -2, 11, -27, -8, -22, -12, 3, -8, 6],\n [-4, 2, 21, 8, 8, -8, -6, -12, 0, 4, -23, 14],\n [-28, 22, 10, -10, -1, -24, -6, 3, 4, 24, 24, 9],\n [-3, 26, -2, -4, 14, 6, 6, -8, -23, 24, 19, -24],\n [4, -14, 26, 20, -16, 6, 2, 6, 14, 9, -24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-30, -18, 14, -2, -12, -2, 24, 9, 12, -32, 16, -13],\n [-18, 24, -12, 0, -4, 29, 17, 26, 3, -17, 2, -6],\n [14, -12, 13, -11, 2, 22, -27, -22, 4, 28, -10, -22],\n [-2, 0, -11, 15, 8, -17, 10, -6, -10, 12, 16, -10],\n [-12, -4, 2, 8, 28, 8, -5, 24, -4, 5, -2, -14],\n [-2, 29, 22, -17, 8, 12, 2, 28, 0, -13, -7, -2],\n [24, 17, -27, 10, -5, 2, 0, 18, -28, 2, 18, 22],\n [9, 26, -22, -6, 24, 28, 18, -25, -6, 24, 8, 26],\n [12, 3, 4, -10, -4, 0, -28, -6, 10, 8, 6, -16],\n [-32, -17, 28, 12, 5, -13, 2, 24, 8, 28, 8, 10],\n [16, 2, -10, 16, -2, -7, 18, 8, 6, 8, -25, 18],\n [-13, -6, -22, -10, -14, -2, 22, 26, -16, 10, 18, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
575
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-9, 0, 5, 6, -24, -14, 9, -16, 14, 3, -14, 2],\n [0, 21, 6, 25, 0, -15, 2, 9, -28, -20, 6, -2],\n [5, 6, 24, 3, -10, -28, 2, -18, -4, -31, 0, 13],\n [6, 25, 3, 11, -4, 16, 1, 2, -16, 18, 12, 12],\n [-24, 0, -10, -4, 33, 18, -3, -19, -30, -6, -4, -20],\n [-14, -15, -28, 16, 18, -3, 20, -6, 11, 0, -8, -20],\n [9, 2, 2, 1, -3, 20, -27, -8, -14, -12, 0, 13],\n [-16, 9, -18, 2, -19, -6, -8, -27, -2, -6, 4, 3],\n [14, -28, -4, -16, -30, 11, -14, -2, -13, -31, -17, -6],\n [3, -20, -31, 18, -6, 0, -12, -6, -31, 26, -4, -2],\n [-14, 6, 0, 12, -4, -8, 0, 4, -17, -4, 9, 16],\n [2, -2, 13, 12, -20, -20, 13, 3, -6, -2, 16, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
510
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, 6, -12, 2, 0, 2, -3, 24, -5, 8, 10, 10],\n [6, 20, 24, 16, 8, -23, 9, 7, -4, -4, -28, -18],\n [-12, 24, 28, 26, -2, 14, -20, -8, -29, 5, -32, 17],\n [2, 16, 26, -6, 20, 6, -4, -7, -10, -22, 6, -5],\n [0, 8, -2, 20, 12, -12, -8, -18, -11, -20, -24, -10],\n [2, -23, 14, 6, -12, 27, -15, 14, -6, 0, 8, 6],\n [-3, 9, -20, -4, -8, -15, 19, -18, -12, 14, -16, 6],\n [24, 7, -8, -7, -18, 14, -18, 30, -15, 26, 28, -28],\n [-5, -4, -29, -10, -11, -6, -12, -15, -31, 20, -10, 4],\n [8, -4, 5, -22, -20, 0, 14, 26, 20, 24, 23, -20],\n [10, -28, -32, 6, -24, 8, -16, 28, -10, 23, 34, 15],\n [10, -18, 17, -5, -10, 6, 6, -28, 4, -20, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
123
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[6, 7, 19, -21, 21, 0, -2, 12, 2, 12, 16, 12],\n [7, -17, -2, 7, 1, 18, 25, 0, -22, 0, -2, 5],\n [19, -2, 28, 1, 2, 21, -10, -12, -10, 20, -17, -8],\n [-21, 7, 1, 30, -23, 8, -1, 8, 13, -18, 9, 6],\n [21, 1, 2, -23, -7, 0, 9, 8, 23, -10, 31, 2],\n [0, 18, 21, 8, 0, 22, -4, -18, -6, -2, -7, -1],\n [-2, 25, -10, -1, 9, -4, -31, -26, 4, -3, 18, 9],\n [12, 0, -12, 8, 8, -18, -26, -9, 13, -16, -17, -8],\n [2, -22, -10, 13, 23, -6, 4, 13, -24, 6, -2, 16],\n [12, 0, 20, -18, -10, -2, -3, -16, 6, 25, -14, -32],\n [16, -2, -17, 9, 31, -7, 18, -17, -2, -14, 16, -14],\n [12, 5, -8, 6, 2, -1, 9, -8, 16, -32, -14, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
485
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-34, -2, 23, 18, 20, -1, 2, 21, -20, 2, 13, 16],\n [-2, -19, 9, 12, 2, -22, -26, -24, 25, 6, -27, 18],\n [23, 9, -10, -18, -3, 4, -22, -6, 9, 14, -25, -14],\n [18, 12, -18, -27, 14, -6, 14, 8, 16, 0, -18, 4],\n [20, 2, -3, 14, -14, -5, -27, -1, -7, -19, -14, -27],\n [-1, -22, 4, -6, -5, -34, -16, -6, 20, -19, 30, -12],\n [2, -26, -22, 14, -27, -16, -21, 16, -6, -12, -14, -22],\n [21, -24, -6, 8, -1, -6, 16, -2, -28, -24, 16, 24],\n [-20, 25, 9, 16, -7, 20, -6, -28, 30, -3, 9, 18],\n [2, 6, 14, 0, -19, -19, -12, -24, -3, -23, 4, -4],\n [13, -27, -25, -18, -14, 30, -14, 16, 9, 4, -4, 24],\n [16, 18, -14, 4, -27, -12, -22, 24, 18, -4, 24, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-9, -12, -14, -33, -20, -6, 7, -32, 4, -20, -20, 30],\n [0, -16, 15, 21, 15, -18, 23, -8, 33, -8, -23, -30],\n [0, 0, -7, 2, 29, 20, -6, 23, 22, -26, -15, 20],\n [0, 0, 0, -21, -30, -8, 27, -7, 12, 27, 22, -15],\n [0, 0, 0, 0, -14, 8, -8, 14, 15, -35, -2, -1],\n [0, 0, 0, 0, 0, 1, 28, -35, -21, -23, -7, 19],\n [0, 0, 0, 0, 0, 0, 34, -21, 3, 33, 24, 8],\n [0, 0, 0, 0, 0, 0, 0, -1, 18, 22, 26, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 17, -33, 26, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 6, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-15, -1, 5, 12, -8, 0, -16, 16, 12, -4, -6, -21],\n [-1, 14, -15, -4, 25, 24, -4, -16, -12, 28, 9, 7],\n [5, -15, 35, 12, -10, 22, 10, 0, 0, -29, -10, -24],\n [12, -4, 12, 24, 18, 12, 6, -2, 21, -14, -15, 2],\n [-8, 25, -10, 18, -3, 8, -4, 10, 25, 5, -17, 5],\n [0, 24, 22, 12, 8, 18, -2, 16, 4, -6, -12, 15],\n [-16, -4, 10, 6, -4, -2, 18, 10, -9, 10, 13, 16],\n [16, -16, 0, -2, 10, 16, 10, 6, -12, -8, 24, 16],\n [12, -12, 0, 21, 25, 4, -9, -12, -22, -16, -12, -2],\n [-4, 28, -29, -14, 5, -6, 10, -8, -16, 2, 6, 4],\n [-6, 9, -10, -15, -17, -12, 13, 24, -12, 6, -15, -12],\n [-21, 7, -24, 2, 5, 15, 16, 16, -2, 4, -12, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
500
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[5, -20, 23, -27, 33, -26, -29, 30, -16, 27, -32, -8],\n [0, -34, 5, -8, -35, -9, 31, 3, 4, -8, -12, 15],\n [0, 0, 16, -30, 23, -24, 27, 0, -27, 31, -7, 35],\n [0, 0, 0, -14, 30, -15, 35, 5, 5, 13, -32, 29],\n [0, 0, 0, 0, 31, 17, -1, -32, 32, -25, 8, 24],\n [0, 0, 0, 0, 0, 1, 22, 7, -21, 31, -34, 35],\n [0, 0, 0, 0, 0, 0, -34, -26, 7, 7, 31, -13],\n [0, 0, 0, 0, 0, 0, 0, -28, 22, 4, -35, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -33, -2, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -11, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[23, 18, 30, -6, -13, -27, 19, -35, 20, 3, -18, 6],\n [0, -3, -6, -31, 14, 29, -26, 24, -9, -8, 9, 16],\n [0, 0, 24, 4, -21, -29, 3, 15, -29, -24, -22, -2],\n [0, 0, 0, -2, -9, -14, -18, 10, 8, -18, 1, -29],\n [0, 0, 0, 0, 16, 16, 18, 5, 6, -14, 3, -13],\n [0, 0, 0, 0, 0, 21, 21, 26, 21, 32, -11, 4],\n [0, 0, 0, 0, 0, 0, -3, -18, -6, 1, -29, -8],\n [0, 0, 0, 0, 0, 0, 0, -34, -7, 14, 23, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, 30, -1, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -4, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-25, -29, 34, 4, 12, -6, 32, 0, -3, 8, -7, -3],\n [-29, -18, 12, -2, 12, -10, 16, 14, 25, -10, -2, 24],\n [34, 12, -32, -15, 3, 0, -8, 14, 3, 14, -18, 19],\n [4, -2, -15, -19, 6, -7, -24, -12, 2, -22, 8, 4],\n [12, 12, 3, 6, 2, 0, -11, -6, -28, -7, 15, -6],\n [-6, -10, 0, -7, 0, 7, 7, 4, 8, 1, -14, -6],\n [32, 16, -8, -24, -11, 7, -25, -28, -18, -30, -19, -30],\n [0, 14, 14, -12, -6, 4, -28, 27, 14, -18, -1, 12],\n [-3, 25, 3, 2, -28, 8, -18, 14, -11, 22, -6, -17],\n [8, -10, 14, -22, -7, 1, -30, -18, 22, -2, -8, 12],\n [-7, -2, -18, 8, 15, -14, -19, -1, -6, -8, -33, 2],\n [-3, 24, 19, 4, -6, -6, -30, 12, -17, 12, 2, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
113
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-5, 0, -4, 27, -10, 29, -34, 34, 9, -11, 4, -18],\n [0, -12, 7, -4, 11, 9, -1, -27, -26, 29, 23, 21],\n [0, 0, 14, 32, -31, -7, -31, 24, 29, -8, -35, -7],\n [0, 0, 0, 28, -22, -4, -27, -25, 12, 15, -32, 5],\n [0, 0, 0, 0, 22, -35, -34, -26, -9, -23, 27, -25],\n [0, 0, 0, 0, 0, -19, 1, -9, 31, 32, 11, -2],\n [0, 0, 0, 0, 0, 0, 7, -9, 12, 33, 35, -14],\n [0, 0, 0, 0, 0, 0, 0, 19, -30, 4, -23, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, -35, 27, -24, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -25, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, 10, 10, -22, 10, -6, 28, 6, 15, 16, -3, 17],\n [10, -33, 8, -15, -5, 10, -22, -13, -29, 14, 13, -16],\n [10, 8, 30, -4, 0, 21, -8, 8, 22, 17, 1, -3],\n [-22, -15, -4, 9, -3, 9, 0, -4, -24, 25, -6, -16],\n [10, -5, 0, -3, -35, -19, 20, -2, 9, 7, -28, 8],\n [-6, 10, 21, 9, -19, -7, -18, -14, 12, 12, -14, 22],\n [28, -22, -8, 0, 20, -18, -30, 10, -20, -10, -21, -16],\n [6, -13, 8, -4, -2, -14, 10, -19, -2, -6, -30, -2],\n [15, -29, 22, -24, 9, 12, -20, -2, -17, 8, -4, -18],\n [16, 14, 17, 25, 7, 12, -10, -6, 8, -21, 5, -14],\n [-3, 13, 1, -6, -28, -14, -21, -30, -4, 5, -27, -10],\n [17, -16, -3, -16, 8, 22, -16, -2, -18, -14, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-35, 2, 12, 12, -8, 10, 0, -8, 2, 3, -4, 4],\n [2, -32, -2, 17, -11, 21, 5, -20, -15, 8, 14, -26],\n [12, -2, -34, 28, -30, 6, -2, 14, -9, -26, 10, -26],\n [12, 17, 28, -18, -7, -1, -7, -8, -6, -4, -2, 7],\n [-8, -11, -30, -7, 23, -20, 14, -6, -7, 12, 11, -14],\n [10, 21, 6, -1, -20, 21, 4, 0, 2, -7, 12, -24],\n [0, 5, -2, -7, 14, 4, 27, -2, -2, 16, -18, 3],\n [-8, -20, 14, -8, -6, 0, -2, 35, 6, 2, 7, 2],\n [2, -15, -9, -6, -7, 2, -2, 6, 26, 1, 12, 10],\n [3, 8, -26, -4, 12, -7, 16, 2, 1, 24, -1, -5],\n [-4, 14, 10, -2, 11, 12, -18, 7, 12, -1, -27, -25],\n [4, -26, -26, 7, -14, -24, 3, 2, 10, -5, -25, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[13, -12, -16, -14, -22, -22, -20, 12, -26, 22, -11, -14],\n [-12, 25, -14, -33, 6, 0, 18, 0, -5, -24, -1, 14],\n [-16, -14, -32, -32, -10, -2, -1, 8, 3, 0, -10, -9],\n [-14, -33, -32, -6, -8, -1, 10, 16, 0, 2, 4, -10],\n [-22, 6, -10, -8, -22, -26, -1, 31, -19, 16, 21, 8],\n [-22, 0, -2, -1, -26, -13, -28, -23, -10, -3, 10, -13],\n [-20, 18, -1, 10, -1, -28, 22, 18, 22, -4, 14, -22],\n [12, 0, 8, 16, 31, -23, 18, 8, 28, -2, -11, 0],\n [-26, -5, 3, 0, -19, -10, 22, 28, 10, 2, -8, 2],\n [22, -24, 0, 2, 16, -3, -4, -2, 2, -24, 3, 9],\n [-11, -1, -10, 4, 21, 10, 14, -11, -8, 3, 0, 12],\n [-14, 14, -9, -10, 8, -13, -22, 0, 2, 9, 12, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[14, -4, 27, 17, 15, 1, -9, -2, 30, -2, 12, 5],\n [-4, -12, 0, 12, 26, -12, -28, 0, -8, -6, 0, -26],\n [27, 0, 0, -8, -20, 18, -6, 8, 17, -10, -26, -22],\n [17, 12, -8, 29, -18, -19, 24, 22, 12, 4, -1, -29],\n [15, 26, -20, -18, -20, -10, -30, 6, 15, 3, 2, 10],\n [1, -12, 18, -19, -10, -8, 14, 0, 4, -8, 23, 9],\n [-9, -28, -6, 24, -30, 14, -34, -14, 15, -4, 4, 14],\n [-2, 0, 8, 22, 6, 0, -14, 35, -16, 2, 16, -11],\n [30, -8, 17, 12, 15, 4, 15, -16, 22, -14, 8, -17],\n [-2, -6, -10, 4, 3, -8, -4, 2, -14, 2, 27, 16],\n [12, 0, -26, -1, 2, 23, 4, 16, 8, 27, -15, -7],\n [5, -26, -22, -29, 10, 9, 14, -11, -17, 16, -7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[23, -24, 26, 4, -34, -11, -5, 11, 24, 5, 14, -13],\n [0, 35, -14, 20, -20, 22, 15, -30, -34, 26, 6, 7],\n [0, 0, -16, 20, 31, 23, 12, -1, -28, -4, 9, 31],\n [0, 0, 0, 29, -16, 35, 5, -35, -32, 35, -26, -7],\n [0, 0, 0, 0, 10, -18, -33, 34, -14, 19, 28, 5],\n [0, 0, 0, 0, 0, -18, 22, -35, -14, -13, -28, -7],\n [0, 0, 0, 0, 0, 0, 32, -31, -31, -11, -12, -35],\n [0, 0, 0, 0, 0, 0, 0, 1, -26, 31, -23, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, -6, -12, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -32, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
253
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[4, -6, 22, 2, 0, -7, -2, -6, -4, 20, 12, -19],\n [-6, -14, -8, 18, 4, -2, -6, -24, 1, -2, -2, 16],\n [22, -8, -1, -10, -8, -10, 8, -2, -2, -25, -24, -7],\n [2, 18, -10, 9, 0, 2, 12, -6, 1, -10, -14, -2],\n [0, 4, -8, 0, 9, -12, 24, -22, -18, 14, 11, 0],\n [-7, -2, -10, 2, -12, 32, -11, -6, 27, -23, -8, -14],\n [-2, -6, 8, 12, 24, -11, -9, 2, 6, -4, -22, 2],\n [-6, -24, -2, -6, -22, -6, 2, -30, 10, -20, 11, -12],\n [-4, 1, -2, 1, -18, 27, 6, 10, -26, 20, 19, -5],\n [20, -2, -25, -10, 14, -23, -4, -20, 20, -10, -14, -8],\n [12, -2, -24, -14, 11, -8, -22, 11, 19, -14, 26, 24],\n [-19, 16, -7, -2, 0, -14, 2, -12, -5, -8, 24, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[24, -16, 22, 7, -7, -34, -10, 23, -35, -5, 2, -14],\n [0, 11, -35, 14, 0, 9, 0, -2, -27, -32, 27, -32],\n [0, 0, 8, 4, 0, -1, 23, 29, -5, 10, 13, -30],\n [0, 0, 0, -6, -10, -33, -3, 14, -5, 32, -26, -14],\n [0, 0, 0, 0, 1, 35, 27, 15, -28, -35, -28, 19],\n [0, 0, 0, 0, 0, 9, 1, 30, 28, 0, 14, 17],\n [0, 0, 0, 0, 0, 0, 23, 10, 32, 4, -23, -27],\n [0, 0, 0, 0, 0, 0, 0, 31, 26, 34, 0, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, -32, 21, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -11, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-25, -5, -2, 2, -6, 2, -16, -10, -12, -4, -4, -10],\n [-5, 30, -14, -30, 5, 16, -16, 27, -2, 8, -26, -16],\n [-2, -14, -2, 4, -16, -12, 28, 4, 5, -18, -4, 2],\n [2, -30, 4, -30, 6, -20, -16, 1, 14, -14, 2, 14],\n [-6, 5, -16, 6, 3, 2, 1, 4, -3, -2, -16, -29],\n [2, 16, -12, -20, 2, 8, 2, -1, -6, 14, -26, 2],\n [-16, -16, 28, -16, 1, 2, 8, 9, 2, 3, -8, -18],\n [-10, 27, 4, 1, 4, -1, 9, -9, -7, 0, -4, -4],\n [-12, -2, 5, 14, -3, -6, 2, -7, 11, 20, -20, -24],\n [-4, 8, -18, -14, -2, 14, 3, 0, 20, 29, -22, 0],\n [-4, -26, -4, 2, -16, -26, -8, -4, -20, -22, -2, 8],\n [-10, -16, 2, 14, -29, 2, -18, -4, -24, 0, 8, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
102
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[0, -16, 22, 14, 8, -26, -6, -13, 2, 4, -23, -31],\n [-16, -4, -14, 20, -16, -22, -20, -8, 0, -6, 0, 32],\n [22, -14, 34, -10, -4, 2, -23, 32, 2, 24, -17, -8],\n [14, 20, -10, -14, -3, -28, -7, 6, 20, -26, -10, -13],\n [8, -16, -4, -3, 5, -20, 3, -6, -10, 24, -16, 1],\n [-26, -22, 2, -28, -20, -1, 24, -14, -1, 7, -22, 0],\n [-6, -20, -23, -7, 3, 24, -13, -2, -12, 16, -13, -12],\n [-13, -8, 32, 6, -6, -14, -2, -29, 3, 26, 26, 12],\n [2, 0, 2, 20, -10, -1, -12, 3, -33, -21, 0, 0],\n [4, -6, 24, -26, 24, 7, 16, 26, -21, 27, -18, 5],\n [-23, 0, -17, -10, -16, -22, -13, 26, 0, -18, -32, 1],\n [-31, 32, -8, -13, 1, 0, -12, 12, 0, 5, 1, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
97
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[35, -8, 13, -2, -17, -3, 0, -4, -14, -14, 20, -6],\n [-8, -8, -10, 16, 6, 8, 4, 11, -20, -6, -26, 2],\n [13, -10, -11, -17, -20, -16, 6, 0, 12, 3, 7, 2],\n [-2, 16, -17, -25, -10, -20, 2, 12, -8, -9, -18, 10],\n [-17, 6, -20, -10, 12, -21, -4, -8, 2, 14, -4, -7],\n [-3, 8, -16, -20, -21, 31, -20, 17, 13, -22, 20, 6],\n [0, 4, 6, 2, -4, -20, 1, -22, 10, 4, 22, -14],\n [-4, 11, 0, 12, -8, 17, -22, -34, -8, 28, -7, 6],\n [-14, -20, 12, -8, 2, 13, 10, -8, 1, 2, -18, -20],\n [-14, -6, 3, -9, 14, -22, 4, 28, 2, 8, -8, -13],\n [20, -26, 7, -18, -4, 20, 22, -7, -18, -8, 25, -20],\n [-6, 2, 2, 10, -7, 6, -14, 6, -20, -13, -20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, 17, 17, -19, 29, 22, 1, 6, 34, 4, -13, -13],\n [0, -29, 1, -20, 2, 4, -7, -19, -16, -11, 24, 2],\n [0, 0, 28, -15, -4, -8, -24, -13, -21, -24, -32, -1],\n [0, 0, 0, -23, 1, 8, -34, 2, 1, 23, 33, -18],\n [0, 0, 0, 0, -1, 22, -29, -27, 33, -32, -4, -31],\n [0, 0, 0, 0, 0, 16, -21, -35, 29, -25, 25, 27],\n [0, 0, 0, 0, 0, 0, 35, 12, -27, 11, 24, 16],\n [0, 0, 0, 0, 0, 0, 0, 15, -20, -4, 11, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 19, 20, -7, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 14, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-23, 2, 33, 0, -1, 3, -4, 17, 7, 4, 16, 21],\n [2, 34, 16, -6, -22, 12, -22, -22, 7, -9, 2, 6],\n [33, 16, -9, 14, -1, -2, 2, 22, 22, -2, -8, 0],\n [0, -6, 14, 14, 2, 28, 20, 12, 16, -6, 2, 2],\n [-1, -22, -1, 2, -16, -20, -6, 21, -23, -32, 32, -6],\n [3, 12, -2, 28, -20, -20, 4, -26, -14, 4, 21, -5],\n [-4, -22, 2, 20, -6, 4, -33, -16, 16, -3, -4, 0],\n [17, -22, 22, 12, 21, -26, -16, -21, -10, -8, -10, -19],\n [7, 7, 22, 16, -23, -14, 16, -10, 26, -5, -24, 12],\n [4, -9, -2, -6, -32, 4, -3, -8, -5, 1, 12, 6],\n [16, 2, -8, 2, 32, 21, -4, -10, -24, 12, -12, 6],\n [21, 6, 0, 2, -6, -5, 0, -19, 12, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
566
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[24, -2, 15, 4, -14, -20, 6, -20, -31, -30, 6, -6],\n [0, 17, -17, 15, -8, 11, -35, 32, 21, -14, 22, -23],\n [0, 0, 3, -24, -12, -18, -21, 24, -20, 11, -12, 9],\n [0, 0, 0, -20, -13, -13, 5, -18, 0, -24, 33, 15],\n [0, 0, 0, 0, 34, 2, 18, -32, 10, 27, 14, -6],\n [0, 0, 0, 0, 0, -25, -12, 15, 6, 3, -29, -18],\n [0, 0, 0, 0, 0, 0, 18, -23, 6, 8, 31, -16],\n [0, 0, 0, 0, 0, 0, 0, -31, -18, -1, -11, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, 21, -8, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -31, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
208
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, -7, -30, 22, 21, -33, -12, -17, -27, -6, 8, 17],\n [0, 24, -13, 25, -29, 8, 19, 3, 23, -31, 6, -22],\n [0, 0, -34, -17, -13, 5, -22, 11, 27, -28, -9, 4],\n [0, 0, 0, 2, -12, -8, 5, -18, 13, -10, -33, 2],\n [0, 0, 0, 0, -32, -2, 29, 20, -26, 35, 28, -23],\n [0, 0, 0, 0, 0, 2, 22, -11, 6, -3, 21, 1],\n [0, 0, 0, 0, 0, 0, -13, 30, 25, -34, -9, 12],\n [0, 0, 0, 0, 0, 0, 0, -13, -18, -14, 8, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 16, 13, 31, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
183
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[35, 10, -12, 0, 13, 12, 23, 6, 20, 9, 2, -2],\n [10, -23, -4, 20, -25, 12, 26, -19, 0, 8, 4, -18],\n [-12, -4, -21, 2, -2, -26, -12, 16, 24, 8, -31, -31],\n [0, 20, 2, -2, -16, 16, -32, -4, 21, -17, 13, -14],\n [13, -25, -2, -16, 26, 6, -6, 22, 22, -7, -7, 26],\n [12, 12, -26, 16, 6, 9, -8, 24, 5, 1, 2, -2],\n [23, 26, -12, -32, -6, -8, 18, 26, -26, 16, -18, 19],\n [6, -19, 16, -4, 22, 24, 26, 19, -11, 0, 0, 28],\n [20, 0, 24, 21, 22, 5, -26, -11, 30, 4, -20, 2],\n [9, 8, 8, -17, -7, 1, 16, 0, 4, 27, 22, 22],\n [2, 4, -31, 13, -7, 2, -18, 0, -20, 22, 4, 20],\n [-2, -18, -31, -14, 26, -2, 19, 28, 2, 22, 20, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-6, -19, -13, -12, 33, 16, 35, 22, -14, 23, 8, 1],\n [0, 21, 21, 4, -16, -19, 16, -32, 27, 14, 14, -20],\n [0, 0, -18, 14, -6, 13, -15, -14, 11, -11, 20, 28],\n [0, 0, 0, -32, -24, -19, 0, -20, -13, -27, 19, 28],\n [0, 0, 0, 0, -6, -25, 15, -17, -23, 21, -33, 2],\n [0, 0, 0, 0, 0, -23, 24, -22, 8, 34, -8, -13],\n [0, 0, 0, 0, 0, 0, 22, 35, -21, 32, -30, -34],\n [0, 0, 0, 0, 0, 0, 0, 27, -19, 18, -15, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, 26, -21, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -26, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-32, 20, -10, 24, -4, -28, 7, 14, 1, 10, 24, -6],\n [20, 28, -8, -11, -16, 19, -10, 2, -4, -2, -14, 1],\n [-10, -8, -20, -7, -18, 34, 8, -6, -9, -15, -4, -6],\n [24, -11, -7, -18, -20, -16, 20, -10, 17, 18, 4, 6],\n [-4, -16, -18, -20, -24, 4, 3, -20, -17, -8, 2, 2],\n [-28, 19, 34, -16, 4, -23, 6, 0, -8, 21, -16, -14],\n [7, -10, 8, 20, 3, 6, -3, 3, 16, 6, 28, 4],\n [14, 2, -6, -10, -20, 0, 3, -31, 3, 0, -21, -4],\n [1, -4, -9, 17, -17, -8, 16, 3, -23, -8, 23, -4],\n [10, -2, -15, 18, -8, 21, 6, 0, -8, 31, -9, -9],\n [24, -14, -4, 4, 2, -16, 28, -21, 23, -9, 9, 10],\n [-6, 1, -6, 6, 2, -14, 4, -4, -4, -9, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-2, 22, -29, -11, 21, -24, -5, -9, -2, -2, 1, 22],\n [0, -10, 9, 9, -4, 33, 35, -13, 29, 3, 31, 9],\n [0, 0, 34, 18, -9, 0, -31, 31, 15, -4, -15, -19],\n [0, 0, 0, 23, -26, -31, 19, -10, -32, -9, 22, -33],\n [0, 0, 0, 0, 9, -23, -30, -1, 17, 32, 6, -32],\n [0, 0, 0, 0, 0, 15, -19, 0, 13, -20, 8, -14],\n [0, 0, 0, 0, 0, 0, 6, -15, -34, -31, -19, -12],\n [0, 0, 0, 0, 0, 0, 0, 25, -28, -24, -22, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 14, 6, 35, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 0, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[6, -27, -5, -34, -12, 7, 34, 7, 15, 10, -35, 31],\n [0, 27, 26, 25, 4, -7, -1, -25, -25, 27, 33, 20],\n [0, 0, 3, 6, 17, -15, -6, -35, -12, -30, -30, 33],\n [0, 0, 0, 12, 7, -1, -31, -5, -5, -28, -30, 17],\n [0, 0, 0, 0, -32, -4, 17, 31, 27, 24, -3, -14],\n [0, 0, 0, 0, 0, 15, -6, -1, -11, -8, -10, -28],\n [0, 0, 0, 0, 0, 0, -27, -22, -16, -32, -12, -8],\n [0, 0, 0, 0, 0, 0, 0, 2, -2, 11, -4, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -4, -13, 13, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 1, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, 34, -12, 25, 26, 4, 8, -6, 22, -4, 7, -16],\n [34, -15, 29, -5, 24, 14, -27, -25, -2, -10, 10, -18],\n [-12, 29, 22, -10, 12, -15, 14, -28, 16, -8, -8, -11],\n [25, -5, -10, -19, 6, 20, -2, -4, 8, -28, -2, 29],\n [26, 24, 12, 6, 20, 11, -7, -22, -2, -12, -22, 3],\n [4, 14, -15, 20, 11, -13, -4, -5, -18, 0, 6, -8],\n [8, -27, 14, -2, -7, -4, -2, -3, 10, 10, 16, -18],\n [-6, -25, -28, -4, -22, -5, -3, 19, -4, 14, 10, -11],\n [22, -2, 16, 8, -2, -18, 10, -4, -19, 1, -8, -29],\n [-4, -10, -8, -28, -12, 0, 10, 14, 1, 26, -8, -6],\n [7, 10, -8, -2, -22, 6, 16, 10, -8, -8, 7, 30],\n [-16, -18, -11, 29, 3, -8, -18, -11, -29, -6, 30, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
527
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[32, 15, -4, -32, 4, -4, -9, -11, 4, -2, -5, -7],\n [15, -7, 5, -20, -9, -29, 11, -14, -6, -22, -4, -22],\n [-4, 5, 29, 0, -9, 22, -31, 0, 6, 11, 8, 26],\n [-32, -20, 0, -12, 8, -22, -6, -17, -6, -26, 2, 16],\n [4, -9, -9, 8, 8, -14, 18, 4, -24, -14, -15, 26],\n [-4, -29, 22, -22, -14, -14, 22, 18, 9, -18, -15, -12],\n [-9, 11, -31, -6, 18, 22, 23, -17, -8, 12, 1, 14],\n [-11, -14, 0, -17, 4, 18, -17, -10, 11, 2, -4, -28],\n [4, -6, 6, -6, -24, 9, -8, 11, 15, 4, -22, -13],\n [-2, -22, 11, -26, -14, -18, 12, 2, 4, -32, -1, -12],\n [-5, -4, 8, 2, -15, -15, 1, -4, -22, -1, 11, -2],\n [-7, -22, 26, 16, 26, -12, 14, -28, -13, -12, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
526
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[15, 2, 10, 24, -7, -4, 10, 0, 0, -8, 14, 0],\n [2, -18, -7, -4, -14, 1, 4, -9, 8, -16, 22, 24],\n [10, -7, -1, -8, -26, -6, 2, 0, -12, 8, 22, -8],\n [24, -4, -8, 33, -8, 22, -8, -2, 16, 3, -12, -4],\n [-7, -14, -26, -8, -7, 1, -8, 7, 4, 3, 5, -14],\n [-4, 1, -6, 22, 1, 10, -25, 2, 4, -15, -22, 0],\n [10, 4, 2, -8, -8, -25, 18, -4, -16, 27, -13, 22],\n [0, -9, 0, -2, 7, 2, -4, 2, -16, 18, 20, 11],\n [0, 8, -12, 16, 4, 4, -16, -16, -9, -18, 20, 6],\n [-8, -16, 8, 3, 3, -15, 27, 18, -18, 22, 6, 1],\n [14, 22, 22, -12, 5, -22, -13, 20, 20, 6, -10, -8],\n [0, 24, -8, -4, -14, 0, 22, 11, 6, 1, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
468
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[32, 10, 0, 22, 1, -2, 14, 27, 4, 6, -24, 8],\n [10, 29, -4, 5, -4, 2, -3, 18, 0, -4, 20, -16],\n [0, -4, -28, -6, 4, -4, -3, 20, -16, -7, 2, -29],\n [22, 5, -6, 12, -11, -32, -2, 33, -2, -7, 0, 12],\n [1, -4, 4, -11, 9, 7, -6, 26, 2, 0, 5, -10],\n [-2, 2, -4, -32, 7, -22, 4, 9, -14, 7, -30, -8],\n [14, -3, -3, -2, -6, 4, -33, 16, -28, -5, 12, -11],\n [27, 18, 20, 33, 26, 9, 16, -13, -22, 0, -6, -6],\n [4, 0, -16, -2, 2, -14, -28, -22, 22, 0, -1, -16],\n [6, -4, -7, -7, 0, 7, -5, 0, 0, 13, -10, -12],\n [-24, 20, 2, 0, 5, -30, 12, -6, -1, -10, 35, -18],\n [8, -16, -29, 12, -10, -8, -11, -6, -16, -12, -18, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
517
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-20, -30, 27, -13, 8, -35, 21, -9, -11, 26, -18, -6],\n [0, 11, -14, 6, -2, 27, -32, -5, 15, 14, -22, -28],\n [0, 0, -25, -7, 19, 3, -23, 28, 13, -17, 31, 16],\n [0, 0, 0, -31, 26, -19, 17, 1, -17, -26, 8, 13],\n [0, 0, 0, 0, 19, -23, -16, 7, 5, 12, 20, 32],\n [0, 0, 0, 0, 0, 3, 22, 25, -17, 33, -14, -1],\n [0, 0, 0, 0, 0, 0, 9, 22, -16, 15, -29, -12],\n [0, 0, 0, 0, 0, 0, 0, 32, 33, 4, 11, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 21, 5, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -10, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[10, 22, -4, -7, 4, -16, -10, 13, 3, -21, 26, -12],\n [22, -21, 8, 15, -7, -2, -1, 8, 11, -24, -2, 0],\n [-4, 8, -16, -6, 4, 0, -4, 35, 4, -1, 14, -6],\n [-7, 15, -6, -8, -16, -2, -8, 26, -24, -10, -6, -2],\n [4, -7, 4, -16, -14, 20, -1, -26, 10, -16, -14, 0],\n [-16, -2, 0, -2, 20, 24, 12, 28, -7, 5, 23, 26],\n [-10, -1, -4, -8, -1, 12, -14, 2, 2, 22, 6, 17],\n [13, 8, 35, 26, -26, 28, 2, 2, -22, -7, 6, 6],\n [3, 11, 4, -24, 10, -7, 2, -22, 29, 6, 2, 12],\n [-21, -24, -1, -10, -16, 5, 22, -7, 6, -9, -6, 8],\n [26, -2, 14, -6, -14, 23, 6, 6, 2, -6, -7, 12],\n [-12, 0, -6, -2, 0, 26, 17, 6, 12, 8, 12, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
503
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[25, -23, -8, 8, -8, -28, 6, -31, 26, 2, -4, 19],\n [-23, 16, 16, 18, -2, 18, -18, 0, 26, 11, 14, -20],\n [-8, 16, 28, 26, 14, -2, -4, 2, -8, 4, 12, -28],\n [8, 18, 26, -25, 17, 10, 28, 28, -12, -26, -22, 1],\n [-8, -2, 14, 17, -30, 8, 2, -2, 20, 4, 20, -13],\n [-28, 18, -2, 10, 8, 32, -10, -22, 12, -13, -7, -3],\n [6, -18, -4, 28, 2, -10, 18, 6, 13, -32, -4, -14],\n [-31, 0, 2, 28, -2, -22, 6, -12, -8, -16, -8, 12],\n [26, 26, -8, -12, 20, 12, 13, -8, -31, 18, -9, 10],\n [2, 11, 4, -26, 4, -13, -32, -16, 18, 20, -9, 2],\n [-4, 14, 12, -22, 20, -7, -4, -8, -9, -9, 31, -19],\n [19, -20, -28, 1, -13, -3, -14, 12, 10, 2, -19, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
580
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[32, -20, -8, -12, -22, -2, -4, -9, 0, 26, 6, -20],\n [-20, -13, -33, -4, 1, -21, 12, -26, -4, 14, 14, 8],\n [-8, -33, -28, -24, 2, -1, -12, -7, -7, 24, 1, -15],\n [-12, -4, -24, -27, -8, 10, -22, -10, -5, -24, 8, 2],\n [-22, 1, 2, -8, -32, -4, -1, 2, -26, 16, 26, 22],\n [-2, -21, -1, 10, -4, -21, 10, 22, 7, 11, 27, 18],\n [-4, 12, -12, -22, -1, 10, 18, 1, -20, -2, 28, 14],\n [-9, -26, -7, -10, 2, 22, 1, 22, 24, -6, 12, -8],\n [0, -4, -7, -5, -26, 7, -20, 24, 8, -23, 6, -20],\n [26, 14, 24, -24, 16, 11, -2, -6, -23, 9, 6, 2],\n [6, 14, 1, 8, 26, 27, 28, 12, 6, 6, -33, 7],\n [-20, 8, -15, 2, 22, 18, 14, -8, -20, 2, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-2, 0, -27, 4, -32, 1, -18, -12, -23, 0, -32, 1],\n [0, 3, 8, 8, 8, 21, 24, 9, -30, -18, 0, -4],\n [-27, 8, 26, -12, -6, -3, -10, -8, 32, 3, 16, 2],\n [4, 8, -12, -18, 9, 12, 2, 3, 6, -13, -12, -8],\n [-32, 8, -6, 9, -9, 4, 11, -21, 19, 20, 30, 8],\n [1, 21, -3, 12, 4, 31, -28, 5, -8, 0, 16, -6],\n [-18, 24, -10, 2, 11, -28, 18, -18, 12, 31, -26, -20],\n [-12, 9, -8, 3, -21, 5, -18, -35, -10, 2, 9, -2],\n [-23, -30, 32, 6, 19, -8, 12, -10, -29, -12, 30, 14],\n [0, -18, 3, -13, 20, 0, 31, 2, -12, -2, -25, 10],\n [-32, 0, 16, -12, 30, 16, -26, 9, 30, -25, 0, -23],\n [1, -4, 2, -8, 8, -6, -20, -2, 14, 10, -23, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
574
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[33, 22, -16, 12, 6, -4, 16, 8, 14, -20, 9, -2],\n [22, 22, -19, 11, -1, -4, -6, 12, 19, 16, 20, 1],\n [-16, -19, -30, 22, 7, -4, 10, -16, 4, 18, -23, -1],\n [12, 11, 22, 22, -4, 6, -17, 0, -30, -10, 32, -8],\n [6, -1, 7, -4, -31, 12, -14, 13, -4, 22, -6, -16],\n [-4, -4, -4, 6, 12, 25, -16, 0, -4, 12, 2, -12],\n [16, -6, 10, -17, -14, -16, -12, -12, -13, -11, 12, -20],\n [8, 12, -16, 0, 13, 0, -12, 35, 13, -13, 6, -12],\n [14, 19, 4, -30, -4, -4, -13, 13, -13, -11, 18, 4],\n [-20, 16, 18, -10, 22, 12, -11, -13, -11, -32, 1, 6],\n [9, 20, -23, 32, -6, 2, 12, 6, 18, 1, -16, 14],\n [-2, 1, -1, -8, -16, -12, -20, -12, 4, 6, 14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
97
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[32, 2, -3, 19, 0, 0, 16, -14, 8, 16, -6, 24],\n [2, -12, 25, 8, 4, 13, -9, -4, 10, 13, 16, -8],\n [-3, 25, 8, -8, -2, 10, 27, 0, -10, 12, 13, -2],\n [19, 8, -8, -12, 32, 0, -26, 28, 14, 2, -17, 2],\n [0, 4, -2, 32, -34, -4, 6, 2, 4, 5, -9, 2],\n [0, 13, 10, 0, -4, 33, -4, 24, -18, 12, 25, -4],\n [16, -9, 27, -26, 6, -4, -27, -1, 11, -15, 16, -14],\n [-14, -4, 0, 28, 2, 24, -1, -25, -8, -11, -12, 0],\n [8, 10, -10, 14, 4, -18, 11, -8, -25, 32, 4, -18],\n [16, 13, 12, 2, 5, 12, -15, -11, 32, -15, 4, -5],\n [-6, 16, 13, -17, -9, 25, 16, -12, 4, 4, 15, -6],\n [24, -8, -2, 2, 2, -4, -14, 0, -18, -5, -6, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, -22, -23, -10, 7, 7, 30, -8, -35, -24, 14, 17],\n [0, 19, -1, 25, -10, -5, 21, -24, -31, -29, -20, 16],\n [0, 0, -13, -11, -25, 27, 21, 18, -26, 14, -35, 34],\n [0, 0, 0, -12, -31, -29, -33, -23, 18, 27, -30, 11],\n [0, 0, 0, 0, -14, -1, -8, 6, -24, -35, -13, -8],\n [0, 0, 0, 0, 0, -26, -31, -22, -12, 27, -8, -15],\n [0, 0, 0, 0, 0, 0, 18, -34, -22, -22, 8, 4],\n [0, 0, 0, 0, 0, 0, 0, 34, -12, 12, 3, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -10, -22, 13, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -29, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
227
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-16, -35, 28, -35, 25, -35, 10, 24, 7, 8, 2, -34],\n [0, -13, -27, -28, 14, 26, -13, 23, -26, -24, 26, -6],\n [0, 0, 5, -29, 16, 9, 2, 0, 22, 10, 31, 29],\n [0, 0, 0, 6, 13, 13, -29, -27, 35, -9, -15, -1],\n [0, 0, 0, 0, 0, 12, 10, -4, -29, -24, 19, -13],\n [0, 0, 0, 0, 0, 35, 15, 22, -9, -29, 14, -12],\n [0, 0, 0, 0, 0, 0, 27, -29, 24, 1, -15, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, 0, -2, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 17, 12, 11, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 34, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-31, 4, 21, 9, -14, -16, 22, -15, 15, 6, 3, 2],\n [4, 17, -6, -2, 23, -2, 8, -2, 29, -22, -8, 8],\n [21, -6, 9, -30, -4, 3, -21, -16, -10, 7, -5, -6],\n [9, -2, -30, 31, -31, 8, -18, 12, 28, -4, 4, 16],\n [-14, 23, -4, -31, 0, 8, 8, 17, 10, -11, 4, 0],\n [-16, -2, 3, 8, 8, 8, 14, -2, -1, -7, -28, -25],\n [22, 8, -21, -18, 8, 14, -21, -12, -16, -4, -16, -7],\n [-15, -2, -16, 12, 17, -2, -12, 26, 4, 2, -5, -8],\n [15, 29, -10, 28, 10, -1, -16, 4, -10, 2, -12, -10],\n [6, -22, 7, -4, -11, -7, -4, 2, 2, -1, -24, 4],\n [3, -8, -5, 4, 4, -28, -16, -5, -12, -24, -13, 20],\n [2, 8, -6, 16, 0, -25, -7, -8, -10, 4, 20, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
525
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-2, 6, -4, 16, 10, 19, 6, 17, 6, 12, 16, 9],\n [6, -35, 17, -18, -7, 4, 8, -6, -18, 21, 6, 15],\n [-4, 17, -20, -18, -18, -22, 5, -8, 26, -16, 4, -21],\n [16, -18, -18, -1, -23, 2, 26, 5, 6, 2, 13, 0],\n [10, -7, -18, -23, -2, 6, 22, 7, -4, 14, 26, 25],\n [19, 4, -22, 2, 6, -28, -8, 1, -13, -8, -4, -32],\n [6, 8, 5, 26, 22, -8, -18, 14, -14, 15, 0, -13],\n [17, -6, -8, 5, 7, 1, 14, -12, 7, -14, 4, 9],\n [6, -18, 26, 6, -4, -13, -14, 7, 8, 5, 18, -16],\n [12, 21, -16, 2, 14, -8, 15, -14, 5, 35, -3, 0],\n [16, 6, 4, 13, 26, -4, 0, 4, 18, -3, 20, -4],\n [9, 15, -21, 0, 25, -32, -13, 9, -16, 0, -4, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
479
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-12, -14, -26, 30, 2, 0, -20, 8, -4, 32, -22, -4],\n [-14, -10, 1, 0, -22, 12, -9, 0, 19, -10, 2, -20],\n [-26, 1, -31, 26, -10, -4, 10, -11, -12, 6, -4, -18],\n [30, 0, 26, -28, -13, -12, -12, 14, -5, 12, -16, -6],\n [2, -22, -10, -13, 11, 6, -20, 8, -22, 16, 2, 2],\n [0, 12, -4, -12, 6, 0, -15, 15, -10, -9, -4, 12],\n [-20, -9, 10, -12, -20, -15, -20, -4, -28, -19, -6, -30],\n [8, 0, -11, 14, 8, 15, -4, 8, -8, 12, 18, 12],\n [-4, 19, -12, -5, -22, -10, -28, -8, -7, -10, -4, -8],\n [32, -10, 6, 12, 16, -9, -19, 12, -10, 9, -1, 28],\n [-22, 2, -4, -16, 2, -4, -6, 18, -4, -1, -33, 20],\n [-4, -20, -18, -6, 2, 12, -30, 12, -8, 28, 20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-2, 20, -2, -10, 35, 9, -15, 7, 3, -23, 6, 9],\n [0, -19, 27, -29, 19, -32, -5, 20, -32, 4, 11, 14],\n [0, 0, 2, -27, 25, -15, -27, -11, 0, 7, -8, 28],\n [0, 0, 0, -28, -22, -21, 3, -11, 27, 23, -7, -33],\n [0, 0, 0, 0, -17, -23, -17, 30, 29, -33, -12, 2],\n [0, 0, 0, 0, 0, 9, 11, -10, -27, 12, -5, 19],\n [0, 0, 0, 0, 0, 0, 34, 35, 30, -34, 33, -23],\n [0, 0, 0, 0, 0, 0, 0, -28, 2, -30, -34, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, 7, -31, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 8, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-23, 27, -21, 4, 2, 19, 8, 30, 30, 7, 2, -7],\n [0, -30, -27, -14, 10, -5, -15, 2, 16, -17, -26, 10],\n [0, 0, 26, 10, -1, 7, -6, 27, -6, -7, 30, -14],\n [0, 0, 0, -10, -5, -34, 3, -24, 8, 7, 31, 2],\n [0, 0, 0, 0, 23, -17, -16, 7, 22, 18, 4, -9],\n [0, 0, 0, 0, 0, 14, 30, -33, 3, -29, 32, 19],\n [0, 0, 0, 0, 0, 0, -15, -16, -32, -17, -7, 35],\n [0, 0, 0, 0, 0, 0, 0, -25, -6, 21, -26, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, -10, -27, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 0, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-35, -13, -14, -13, 20, -8, -10, -5, -18, -6, -16, 8],\n [-13, -12, -4, 18, 14, -2, 8, 16, 12, 4, -22, -4],\n [-14, -4, -12, -2, -1, -24, 32, 20, -20, 5, 10, 4],\n [-13, 18, -2, -18, -15, 12, -8, 22, 22, -24, 16, 16],\n [20, 14, -1, -15, 13, 2, 6, 10, -4, -6, -12, 6],\n [-8, -2, -24, 12, 2, -35, -7, 0, 6, -14, -28, -9],\n [-10, 8, 32, -8, 6, -7, 10, 4, 13, -2, 4, 28],\n [-5, 16, 20, 22, 10, 0, 4, -7, 11, 32, -17, 2],\n [-18, 12, -20, 22, -4, 6, 13, 11, -16, 16, -18, -3],\n [-6, 4, 5, -24, -6, -14, -2, 32, 16, 15, 4, -11],\n [-16, -22, 10, 16, -12, -28, 4, -17, -18, 4, 19, -6],\n [8, -4, 4, 16, 6, -9, 28, 2, -3, -11, -6, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-23, 14, -21, 2, -17, -29, 0, -12, 6, 24, -8, 18],\n [14, 26, -18, -9, -8, 5, 16, 13, -4, 20, -8, 14],\n [-21, -18, -34, 2, 2, -12, 5, -6, -2, -6, 3, 10],\n [2, -9, 2, 2, -10, 22, 5, -26, 7, 2, -2, 10],\n [-17, -8, 2, -10, -23, 10, 9, -24, -3, -8, -6, 30],\n [-29, 5, -12, 22, 10, 3, 16, 5, -3, 12, 8, -23],\n [0, 16, 5, 5, 9, 16, 27, -18, 0, -14, 8, 9],\n [-12, 13, -6, -26, -24, 5, -18, -26, -8, -27, -14, -22],\n [6, -4, -2, 7, -3, -3, 0, -8, 15, 7, -20, 12],\n [24, 20, -6, 2, -8, 12, -14, -27, 7, -4, 24, 26],\n [-8, -8, 3, -2, -6, 8, 8, -14, -20, 24, -2, -11],\n [18, 14, 10, 10, 30, -23, 9, -22, 12, 26, -11, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, -4, 2, 26, 7, 16, -8, -24, -16, -6, 32, -14],\n [-4, 34, 28, -8, -10, -1, -18, 10, 20, 0, 17, 12],\n [2, 28, 30, 14, 1, 4, -8, -10, -12, -14, -21, 3],\n [26, -8, 14, -27, 22, -17, -32, -4, -30, -19, -6, -32],\n [7, -10, 1, 22, 8, -28, 1, 0, -12, -16, -19, 20],\n [16, -1, 4, -17, -28, 2, 20, -28, 6, -24, -8, -18],\n [-8, -18, -8, -32, 1, 20, 21, -3, -2, -10, -2, -6],\n [-24, 10, -10, -4, 0, -28, -3, 29, 8, -8, -13, 3],\n [-16, 20, -12, -30, -12, 6, -2, 8, 22, 1, -18, 20],\n [-6, 0, -14, -19, -16, -24, -10, -8, 1, -34, 19, -10],\n [32, 17, -21, -6, -19, -8, -2, -13, -18, 19, -25, 24],\n [-14, 12, 3, -32, 20, -18, -6, 3, 20, -10, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
595
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-11, 18, -12, 22, -2, 6, 18, -14, 4, -18, 22, 9],\n [18, 21, -6, -4, -24, 2, -21, -11, -2, 4, -16, -14],\n [-12, -6, 19, 12, 18, 6, 4, -8, -18, 27, -28, -26],\n [22, -4, 12, -1, 10, -25, -7, 0, 24, 2, 7, -16],\n [-2, -24, 18, 10, 15, -28, 29, 2, 30, -14, -6, -6],\n [6, 2, 6, -25, -28, 16, -4, 11, -18, -32, -4, -14],\n [18, -21, 4, -7, 29, -4, -20, -18, 14, 5, 4, 2],\n [-14, -11, -8, 0, 2, 11, -18, -7, -14, 20, 24, 12],\n [4, -2, -18, 24, 30, -18, 14, -14, -22, 20, 3, 6],\n [-18, 4, 27, 2, -14, -32, 5, 20, 20, -22, -8, 16],\n [22, -16, -28, 7, -6, -4, 4, 24, 3, -8, -33, -16],\n [9, -14, -26, -16, -6, -14, 2, 12, 6, 16, -16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
564
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-14, 10, -24, -4, -10, 10, 16, 6, 18, 20, 0, -8],\n [10, -24, 12, 6, -6, 18, 4, 20, 27, -8, -10, 12],\n [-24, 12, -19, 4, 16, 12, 2, 17, 18, 0, 12, -17],\n [-4, 6, 4, 6, -16, 16, -2, -20, 25, -11, 9, -1],\n [-10, -6, 16, -16, -34, 13, 23, -6, 6, -29, 6, 8],\n [10, 18, 12, 16, 13, 28, 21, 18, -24, -30, 7, -18],\n [16, 4, 2, -2, 23, 21, 20, -15, 28, 9, -16, 7],\n [6, 20, 17, -20, -6, 18, -15, 24, 4, 7, 24, -5],\n [18, 27, 18, 25, 6, -24, 28, 4, -23, -13, -6, -8],\n [20, -8, 0, -11, -29, -30, 9, 7, -13, 10, 10, -32],\n [0, -10, 12, 9, 6, 7, -16, 24, -6, 10, 35, -12],\n [-8, 12, -17, -1, 8, -18, 7, -5, -8, -32, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
579
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-17, -14, 6, -10, 10, -10, -20, 10, -34, -7, -14, -12],\n [-14, 21, -4, -2, 16, 8, -2, -4, -4, -18, 20, -34],\n [6, -4, -1, 30, 30, -8, -5, 20, -10, 2, -4, 14],\n [-10, -2, 30, -2, -8, 14, 11, 6, 22, 12, -19, -4],\n [10, 16, 30, -8, -19, -11, -14, 12, 21, -1, 3, 11],\n [-10, 8, -8, 14, -11, -2, -8, -13, -5, -3, 8, -1],\n [-20, -2, -5, 11, -14, -8, 30, -19, 14, 29, 2, 4],\n [10, -4, 20, 6, 12, -13, -19, 16, 4, -10, 20, -16],\n [-34, -4, -10, 22, 21, -5, 14, 4, -17, 1, -6, 4],\n [-7, -18, 2, 12, -1, -3, 29, -10, 1, 33, 22, 0],\n [-14, 20, -4, -19, 3, 8, 2, 20, -6, 22, 25, -6],\n [-12, -34, 14, -4, 11, -1, 4, -16, 4, 0, -6, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH