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[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-8, -12, -5, -6, 2, -2, 5],\n [1, -4, -8, 10, -9, -1, -12],\n [11, 0, -12, -10, 9, -5, 11],\n [5, 12, 3, 7, 7, 3, -11],\n [4, -3, -6, -3, 6, 7, -4],\n [9, 4, -4, -4, -8, 11, -6],\n [-2, -5, 12, 1, -11, -3, 8]]\n\nPresent the answ...
114
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[11, 3, 3, 6, -2, -7, -7],\n [-6, 3, 0, -10, 11, 11, -4],\n [11, -10, -7, 12, 4, -10, -11],\n [-1, 11, -7, -3, -2, 3, 3],\n [11, 5, 9, 10, 11, -4, 8],\n [6, -11, 11, -12, 3, 9, 5],\n [...
124
MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -5, -8, 7, -4, 2, 8],\n [1, -9, 11, 11, -5, 7, 4],\n [-11, 7, 3, -3, -11, -2, -3],\n [6, 12, 12, 1, -2, -4, -6],\n [2, 7, 4, -10, 2, 1, -5],\n [-9, -3, -11, 1, -5, 10, -3],\n [12, 5, 2, -8, 9, 0, 5]]\n\nPresent t...
31
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, 0, 1, -3, -9, 2, -5],\n [2, 1, 8, -4, 7, -10, 2],\n [11, 4, 12, 3, -9, -2, 12],\n [-5, -10, 6, 1, -4, -10, -9],\n [12, -9, -2, 6, 3, 10, 9],\n [4, -3, 11, 4, 3, 7, 9],\n [-7, -6, 1, -2, -1, 1, -...
33
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, 7, 9, 10, 2, -12, 12],\n [11, 10, -4, -10, -9, 3, -6],\n [9, 1, 3, 5, 3, 3, -11],\n [-3, -6, 12, 2, -4, -6, 11],\n [3, -10, 4, 10, -5, -11, 12],\n [7, 12, -10, -5, -11, 6, 4],\n [-8, 7, 4, -3, -4...
40
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -11, 10, -1, -1, 3, 12],\n [9, 11, -1, 8, 5, 0, 2],\n [3, -9, -1, 4, -12, 9, 5],\n [9, 3, -12, -3, 6, 3, 1],\n [12, -11, 11, -7, 9, 10, -8],\n [-1, -9, 9, 11, -9, -8, -6],\n [-7, 0, -9, 0, -9, -3, 7]]\n\nPresent the answer in LaT...
31
MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-12, 8, -5, -6, -8, -10, 2],\n [4, 10, 0, 2, 6, 7, 1],\n [8, 0, -1, 11, 10, -4, -10],\n [-2, -3, -12, 4, 0, 1, -12],\n [-11, -11, -6, -4, 11, -9, -11],\n [6, -8, -4, 11, 0, -1, 6],\n [-4, -3, 6, -3, -1, 1, -5]]\n\nPresent the ans...
112
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 4, 7, -9, -7, -1, 5],\n [-6, -8, -3, -7, 1, -7, 1],\n [-1, 9, -1, -5, -3, 3, 7],\n [-5, -4, 0, 7, 4, 6, 4],\n [-6, -12, 7, 1, 4, 0, -11],\n [1, -12, -8, -6, 6, 1, 11],\n [1, 2, -8, -8, 8, 11, -11]...
26
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 11, -4, -3, 5, -9, -5],\n [5, 7, 4, 3, 5, -6, -12],\n [-12, 5, -9, 10, 7, 8, 7],\n [-9, 12, -7, -10, -7, 0, 10],\n [-6, 11, -9, -12, -7, 11, -8],\n [0, 6, -9, 11, -7, 0, -8],\n [0, 12, -3, -10, 10, 12, 0]]\n\n...
129
MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -9, -3, -10, 4, -4, -12],\n [5, -4, 8, 7, 12, -4, -11],\n [6, 3, -10, 3, 8, 0, -10],\n [-3, 9, 5, -7, -7, 5, -7],\n [-7, 9, 0, 1, 8, -6, 0],\n [2, -1, 8, -12,...
23
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -11, -3, -11, 8, -1, -8],\n [-1, 10, -12, -11, 3, 9, -11],\n [3, 7, 3, -7, 0, -1, 10],\n [-3, -8, -5, -7, -8, 7, 9],\n [-7, 9, 4, -7, 4, -8, 10],\n...
25
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -3, -3, 10, -10, -12, -10],\n [12, -8, -6, -10, -9, 4, -10],\n [10, -9, -11, 1, -8, 8, -11],\n [2, -2, 9, -3, 7, -12, 6],\n [1, 12, 10, 9, 1, -12, 12],\n [-4, 4, 1, 0, 0, -7, -6],\n [-11, -5, ...
115
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 9, 10, -7, -2, -10, 3],\n [-8, 11, 9, -11, 2, 3, -6],\n [3, 11, -9, 3, 4, -11, 3],\n [-9, -6, 5, -7, 5, -6, -11],\n [6, -4, -9, 1, -8, 12, -6],\n [-5, 2, 6, -2, 7, 10, -9],\n [5, 1, -7, 12, 3,...
118
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -12, -12, 6, 8, 12, -3],\n [5, -1, 4, -12, -5, -3, -3],\n [5, -4, 12, -11, -10, -11, -7],\n [10, -1, 9, 6, 2, 6, -1],\n [5, 3, -11, -2, -1, -8, 11...
32
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-8, -8, 5, -7, 8, 5, -3],\n [2, 11, 9, -2, 6, 12, 0],\n [7, -10, 3, -6, -1, 2, -5],\n [10, 4, -12, 8, -5, 1, -3],\n [6, -5, 6, -9, -3, 10, -10],\n [-9...
33
MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -7, -10, 7, 11, -9, -5],\n [7, -4, 9, -12, 0, -11, 10],\n [-3, 10, 6, 4, 11, 0, 1],\n [-2, -3, -6, -3, 11, -12, 1],\n [-10, 0, -11, 4, 8, -10, 2],\n [-5, -7, -4, 12, -2, 9, -11],\n [-4, 5, 6, 9, 5, -8, 5]]\n\nPres...
32
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -9, 2, -2, 6, -8, -7],\n [0, 10, -3, 11, 12, 1, -9],\n [7, 10, -1, 2, -3, -2, -4],\n [-2, -11, 0, 9, -5, 8, 8],\n [-5, -12, -7, 0, -4, -7, 2],\n [10, 3, -9, 4, -4, -1, 9],\n [6, 7, -1...
29
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, -8, 8, -10, -11, -5, -3],\n [2, -4, -3, -2, -4, 1, -8],\n [-4, -9, -11, 6, -12, 8, -12],\n [-1, -2, -12, 1, -2, -6, -11],\n [2, -5, 9, 7, 12, 2, -5],\n [-3, 6, -10, 7, 1, -4, -4],\...
105
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 10, -9, 3, 7, -7, -4],\n [10, -8, 8, 11, -7, 4, 4],\n [12, 11, 9, 0, 4, 1, -11],\n [6, -10, -11, -11, 9, -6, -9],\n [4, -7, -6, 7, -7, -4, 7],\n [...
31
MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[7, 2, 4, 6, 0, 9, 8],\n [-3, 4, -8, 5, 4, -9, 9],\n [-6, 12, -8, -5, -5, -2, -4],\n [6, 6, -4, 10, 7, 4, 3],\n [-6, 9, -10, 8, 6, -5, -8],\n [-7, -11, 11, 12, 6, 0, -7],\n [-7, -11, 11, -8, -2, -2, 11]]\n\nPresent the answer in L...
108
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 0, -5, 2, -1, -10, 8],\n [10, -8, -7, -11, -5, -8, 9],\n [4, -11, -2, -9, -2, -4, -7],\n [11, -11, 2, -8, -1, 0, 4],\n [-9, -3, -12, -2, 3, -2, -4],\n [-11, -6, 6, 5, 7, -6, 10...
32
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[10, -8, 12, 10, -6, 6, 4],\n [3, 8, 11, 8, 6, 12, 5],\n [6, -9, -12, -9, -9, -4, -5],\n [-11, 10, -7, 10, -2, -9, 1],\n [8, 9, -4, -11, 12, -12, -9],\n [-1, -8, -4, 9, -9, 3, -11],\n [3, ...
38
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-12, 2, 11, -9, 5, 4, -6],\n [5, 0, 7, 7, -3, -12, -11],\n [4, 9, -10, 4, -1, 11, -1],\n [7, -3, -6, -3, 5, 9, -7],\n [-6, 4, -1, 4, 5, 1, -2],\n [-11, 8, -12, -2, -11, 3, 9],\n [-10,...
115
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-12, -8, -12, -2, 8, -4, -8],\n [-11, 0, 5, 12, -1, 1, -8],\n [11, -3, 7, -11, -9, -1, -2],\n [-9, -2, -4, -3, -7, 2, -3],\n [9, 8, -7, -12, 8, 9, 11],\n [7, 8, -9, 10, 9, 1, 7],\n [9, 7, -5, -2, 2, 6, -5]]\n\nPr...
113
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 5, 9, 11, 4, -7, 12],\n [2, 0, 5, -2, 0, -12, 5],\n [-8, -7, -12, -6, -9, -4, 2],\n [-7, 12, 4, 7, 5, 9, -9],\n [-4, 1, -10, -12, -2, -12, -1],\n [12, -4, -8, 2, 5, -4, 0],\n [0, 11, 0, -3, -3...
110
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[9, -8, 7, -6, 7, -3, -3],\n [12, 8, 11, 0, 2, -7, 7],\n [-1, 6, -2, -7, -12, -11, 10],\n [2, -9, -8, 2, -2, -3, 4],\n [-11, 7, 11, -3, 7, -10, 6],\n [-8, -10, -5, -8, -1, 1, -6],\n [-2, -5, -8, -5, -1, 2, 6]]\n\nPresent the answer in...
30
MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 1, -6, -5, -6, 5, 11],\n [-7, 6, -9, 10, -10, 4, 9],\n [6, 2, -7, -1, 6, -7, -2],\n [7, 7, -3, 3, 5, 1, -9],\n [-1, 7, 10, 8, -5, -6, -4],\n [11, 12, 4, -3, -1...
30
MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[7, 8, 1, 8, 0, -9, 7],\n [7, -2, 5, -12, -1, 5, -6],\n [-1, -12, 9, -9, 5, 2, -10],\n [-6, -7, 2, 2, -7, -5, -5],\n [9, -12, 0, 10, 11, 8, 0],\n [-2, -9, -6, -1, 0, 9, -1],\n [3, -7, 1, 6, 3, -9, ...
28
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 11, -10, 9, -3, 4, 6],\n [-3, -1, 10, -6, 5, 6, 2],\n [-6, -1, 9, -6, -3, 12, 11],\n [9, 7, -3, 12, 10, -8, 5],\n [-4, 3, -6, 12, 12, -3, -8],\n [-6, -8, 2, 6, -3, -5, 11],\n [-4, -2, 9, -11, -10, 0, -2]]\n\nPresent the answer in...
36
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 2, -7, -12, 1, 5, 11],\n [-2, -5, 9, -10, 1, -11, 3],\n [-7, -12, 1, -3, -7, -4, -6],\n [12, -11, -2, 1, -8, -4, -6],\n [12, 1, 3, 9, 3, -6, -3],\n [8, -7, 4, -12, -11, 1, -9],\n [-4, 10, -7, 4, ...
32
MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[8, -4, 3, -10, -9, 11, -10],\n [0, 6, 12, 8, -12, 10, 10],\n [-7, 9, -10, -10, 3, -3, 12],\n [4, -6, 0, -2, -3, -6, 11],\n [-7, 11, -12, 4, 12, -1, -9],\n [-10, -7, 3, 0, -4, -2, 7],\n [12, 8, 0, ...
32
MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, 1, 9, -4, 12, 11],\n [4, -7, -9, -9, 6, -1, 12],\n [-11, 4, 2, -3, -10, 7, -9],\n [9, -12, -12, 5, -9, 10, 9],\n [2, 12, 10, 8, 9, -3, 12],\n [4, 12, 9, -1, 7, -1, 3],\n [-8, 3, 4, 10, 2, 0, -5]]\n\nPresent the answer in L...
116
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[8, -11, -5, -3, -6, -3, 12],\n [-9, -2, -4, -9, -10, -2, -10],\n [5, 6, 1, 11, -2, 11, -11],\n [-11, -11, -3, 10, 2, 9, -1],\n [-2, 4, 5, 1, 4, 2, -1],\n [3, 10, -7, -11, -11, 3, -11],\n [-5, -6, -12...
31
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -9, 4, -2, -2, 7, -2],\n [2, 1, 4, -11, 5, 3, -1],\n [-3, 3, -10, -5, 9, 9, 12],\n [11, -11, 9, -12, 1, 12, -9],\n [-9, -4, -10, -8, -12, 9, 6],\n [-12, -3, 9, -1, -3, -11, 3],...
31
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, -10, -4, 5, 6, -6, -9],\n [-7, 6, -12, 3, -2, 9, -9],\n [5, 10, -8, 9, -7, 12, -11],\n [-1, 9, -4, 7, -1, 0, 9],\n [10, 4, -8, 7, 0, 0, -3],\n [2, 2, 5, 5, -11, 10, -2],\n [0, -2, -9, 2, 9, 10, 12]]\n\nPresen...
115
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, 3, -3, -1, 0, -4],\n [8, 0, -7, -7, -2, 6, -2],\n [-3, 10, 2, 0, 10, -5, -8],\n [-11, 3, 0, 6, -4, 2, -7],\n [-5, 11, 1, -8, 4, 9, -6],\n [-4, ...
28
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -3, -11, -6, 2, 6, -3],\n [11, 7, 1, -9, 12, -2, -10],\n [10, 4, -6, -2, 5, 1, 1],\n [-7, -4, 9, -10, 4, -1, -9],\n [7, 3, 11, -3, -6, -3, -6],\n [10, 5, -4, 9, 5, 4, -2],\n [-12, 4, -9, -9, 1, -4, 0]]\n\nPre...
101
MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -12, -10, 6, -5, 5, -7],\n [7, -7, -8, -1, -4, -4, 4],\n [6, 4, 9, 3, -1, -10, 1],\n [4, 9, 3, 8, -1, 11, -11],\n [-5, -1, 8, 3, -5, 3, -3],\n [7, 2, -9, 2, -9, -2, -7],\n [-9, -4, -4, -10, 10,...
28
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -11, -10, 8, -1, 3, -8],\n [-3, 2, 1, 1, 10, 0, 3],\n [-5, -5, 4, 4, -10, -12, 4],\n [11, 3, 4, 12, -11, 12, 1],\n [-6, 12, 6, -12, 4, -3, -7],\n [-6, 12, -7, -8, -11, 5, 11],\n [4, 11, 10, -6, 8...
32
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -6, 3, -1, 2, 2, -2],\n [-11, -10, 6, 7, 12, 2, 3],\n [-12, 2, -1, -6, -6, -2, 7],\n [-2, 4, -10, 3, -8, -11, 10],\n [-6, -3, -8, 2, -1, -3, 9],\n [4, 7, 7, -2, -5, 2, -11],\n [4, 10, -7, 8, 0, -5, -2]]\n\nPr...
93
MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 0, 5, 5, 12, 4, 9],\n [0, -10, 8, 11, -6, -1, -9],\n [11, -2, 1, 5, -6, -8, 3],\n [-2, 9, -10, 3, -2, -3, 10],\n [10, -11, 3, 4, -3, 5, -1],\n [-5, -10, 7, 11,...
34
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[11, -4, 1, -2, -11, 8, -11],\n [-8, -6, 9, -9, 1, -11, 10],\n [-1, -3, 12, -12, 6, 10, 3],\n [2, 1, -4, 8, 10, 2, -6],\n [-9, 8, 5, -5, -1, 2, 2],\n [4, -11, -1, -10, -6, -7, 1],\...
30
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 10, -11, -1, 11, 9, -1],\n [6, 6, 8, -10, -7, -11, 11],\n [0, -4, 0, 10, 1, 6, -2],\n [1, 3, -3, 7, 3, -11, 12],\n [3, 1, 8, 5, -7, -6, 0],\n [-11, 2, 4, 0, -6, -12, -10],\n [7, 5, -6, 8, 4, -1, 3]]\n\nPresen...
104
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[11, -3, 10, 3, 7, 5, 2],\n [10, -2, 5, -7, -12, 10, -6],\n [-1, 7, -9, -3, 8, -11, -4],\n [-3, 7, -2, 12, 1, -10, 12],\n [-12, -6, -9, -6, 3, -3, 2],\n [3, -7, -9, -9, 11, 10, -9],\n [9, 9, 4, 0, -11...
35
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[9, -12, -5, 5, 8, -9, -8],\n [-8, 2, -3, -5, -6, -1, 12],\n [-2, 0, 2, 4, 9, 9, 5],\n [-5, -7, -2, -4, -8, -6, 9],\n [2, 8, 9, -9, 6, 0, -12],\n [-12, 9, 1, -4, 11, -1, 5],\n [-4, -5,...
112
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, 0, 12, -3, -5, -6, 11],\n [-1, 4, 12, -1, 3, -3, 12],\n [-1, -2, 12, 1, 9, 7, 0],\n [-11, 7, -6, -12, 12, -10, 7],\n [-1, -8, -1, -10, 7, -8, -12],\n [3, -4, -3, -3, 0, 3, 7],\n [12, -9, 1, 4, -...
31
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-10, -8, 3, 6, 6, 4, 5],\n [5, 12, 10, -5, 5, -4, 6],\n [-3, -11, 4, 12, 11, 0, -2],\n [3, 7, -6, -10, 3, 6, 7],\n [3, -11, 1, 7, -3, 6, 11],\n [-2, 5, -2, -4, 6, 7, -3],\n [-10, ...
29
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[7, 11, -7, -11, 6, -6, -2],\n [-2, -9, 7, 3, -8, 11, -6],\n [12, 3, 2, -8, -12, 7, 9],\n [9, -4, 8, -8, 9, -7, -10],\n [-7, -5, -7, 3, 3, 8, -10],\n [4, 8, -7, -7, 9, 6, 7],\n [2,...
32
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, 2, -1, 2, 1, -6, 4],\n [-8, 7, -3, 6, 5, 12, 11],\n [-3, -11, -7, -10, 6, -8, -6],\n [-6, -3, -12, -2, 10, -6, -7],\n [-7, 0, 3, 0, -11, 6, 6],\n [6, 5, 12, -7, -11, 6, -7],\n ...
30
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 12, 9, 5, 4, 6, 6],\n [11, 8, 4, -9, -6, -8, 3],\n [-7, 1, 7, -11, 12, 5, 5],\n [0, 5, 4, 0, -1, -10, 9],\n [-6, -12, -8, 8, -12, -9, -12],\n [0, 1, 2, 4, -1, -6, 10],\n [6, 10, -10, 5, -9, -10, ...
35
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[10, -1, 4, -7, 2, -11, -5],\n [1, -8, -10, -3, -6, -2, 2],\n [-11, -8, -2, -5, 0, -2, 4],\n [2, -12, 6, 3, 6, 0, 10],\n [9, 10, -9, -2, 5, 5, -3],\n [4, 0, 12, 1, -6, -3, -10],\n [-11...
109
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, 9, -7, 1, -6, 9, -11],\n [-2, 8, -10, -4, -5, -2, 5],\n [-12, 2, -9, -9, -3, -2, 5],\n [10, 2, -10, -6, -6, 4, 9],\n [7, 11, 3, 3, -5, -10, 7],\n ...
28
MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-7, 11, 12, -1, 10, 7, 7],\n [9, 1, 7, -6, -5, -5, -5],\n [-11, 1, -3, 5, 5, 5, 3],\n [7, -8, 7, -8, 7, 10, -3],\n [4, 0, 4, 5, 0, 4, 2],\n [-1, -3, 0, -2, -10, 9...
28
MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, -6, -11, -12, 10, 12],\n [5, -1, -6, 6, 9, -10, -3],\n [-2, -8, -11, -5, 1, -5, 10],\n [-7, -12, 11, -12, -5, -2, 5],\n [11, -3, -1, 7, 10, 3, -8],\n [3, 11, -1, -7, -8, -12, 6],\n [-3, 12, 1, 12, 8, -10, -7]]\n\nPresent ...
115
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, 4, 5, -1, -8, -4, -1],\n [7, -4, -10, -12, 9, 2, -3],\n [1, -6, -9, -8, 7, 3, -10],\n [4, 0, -7, -8, 3, -2, 4],\n [-8, -7, -3, 8, -12, 8, -3],\n [4, -10, -11, 4, -9, -11, -8],...
32
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -11, -12, 8, 9, 3, 9],\n [5, 3, 10, 9, 11, -7, 12],\n [-3, -11, -6, 8, 4, -10, 7],\n [-1, -11, -6, 4, 6, -1, -4],\n [1, -11, 8, -9, 6, 8, 3],\n [9, 4, -11, 4, 6, -5, 11],\n [7, -7, -1, 12, 10, 5, -11]]\n\nPresent the answer in LaT...
36
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 11, -3, 12, -10, 12, -1],\n [3, -1, -5, -8, -2, -3, -10],\n [10, -4, -1, -7, 6, 3, 8],\n [10, 11, 1, -9, 5, -3, 5],\n [-1, 6, -5, -12, 1, 10, -7],\n [1, -11, -4, -1, -8, -11, 6...
25
MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-7, -5, 6, 6, 11, 11, 11],\n [4, 11, 11, 5, -1, -4, 10],\n [11, 3, 5, 3, 3, -9, 10],\n [9, -6, -12, 11, 10, 7, -12],\n [-5, 10, -5, -3, -12, 8, 12],\n [8, 1, 1, -3, 6, 12, 3],\n [-4, 7, 3, 7, -5, ...
33
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[8, -7, 2, 6, 1, 2, -7],\n [11, -3, 1, 3, 0, -2, 12],\n [-10, -5, -10, -11, 8, 1, 7],\n [8, 9, 2, -10, -12, 2, 7],\n [9, -11, 5, -12, -4, -10, -11],\n ...
29
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-10, 2, -7, -12, 5, 10, -2],\n [-10, 0, 4, 5, 1, 12, -6],\n [-6, 1, 11, 2, -1, -1, -5],\n [3, -4, -11, 1, 11, 11, 3],\n [-8, -8, 7, 8, 5, 5, -8],\n [-...
31
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 2, 4, -2, -11, 8, 5],\n [12, -9, -4, 4, 4, 4, 3],\n [7, 12, -5, 10, 2, -12, 6],\n [12, 2, -4, -8, 3, 0, 3],\n [9, -2, 0, -7, 7, 4, -8],\n [4, -12, -8, -8, -6, 3, 5],\n [-7, -11, 0, -3, 8, 7, ...
106
MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, -11, -5, 11, 9, 6, 7],\n [4, 3, 12, -3, -8, 1, 11],\n [6, -9, 7, 3, 11, 2, -4],\n [-10, 10, -4, 5, -9, 6, 11],\n [-9, -4, -12, -12, 7, 6, -10],\n [-3, -1, 5, 1, -3, -3, 5],\n [11, -12, 2, -5, -10, 5, -4]]\n\nPrese...
32
MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 8, 2, -8, 0, 9, 7],\n [-6, 3, -6, 12, 9, 3, 0],\n [4, -4, -1, 0, -4, -8, -6],\n [-12, -9, -9, 3, -8, 9, -9],\n [-7, 10, -10, 12, -5, 4, 5],\n [5, 12, -1, 12, 12, -12, 10],\n [-1, -2, 0, -10, 12...
32
MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 12, 0, -3, 4, -10, 0],\n [9, -7, 1, -3, 7, 3, 5],\n [0, -3, -7, -3, -8, -7, -6],\n [-2, 3, 12, -1, -1, 10, 7],\n [-8, 3, -7, -4, -8, 8, 10],\n [3, 5, 6, -1, -11, -3, -1],\n [1, 5, 6, -7, -8, 3, 1]]\n\nPresent the ...
25
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 8, -11, -11, -1, -12, 6],\n [3, -6, 8, -6, 3, 12, -7],\n [5, -12, -12, 12, 1, -7, -7],\n [-9, -1, 5, -3, -10, -10, -5],\n [9, 10, 12, -12, 5, 2, 12],\n [8, 7, 4, 12, -2, 0, 12],\n [7, 12, -3, ...
132
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[7, 3, 3, 8, -10, -11, -7],\n [-2, -10, -12, -2, 0, -8, 5],\n [2, 5, 2, 7, 7, 7, -6],\n [4, -5, 0, 3, 12, -3, 1],\n [-7, 7, 9, -6, -7, 4, 8],\n [11, -5, -1, 12, -9, -3, -7],\n [-6, 8, -5, -10, -5, 2, 8]]\n\nPresent the answer in LaTex...
32
MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-12, 0, 9, 5, 2, -6, 2],\n [12, -10, 1, 7, -9, -9, -10],\n [-8, 12, -2, -5, -11, 3, 12],\n [-3, 5, -6, -8, -6, 8, -7],\n [11, -12, -2, 0, -1, -12, 8],\n [2, -12, -10, 2, -4, 1, 10],\n [9, 11, -5, 9, -9, 7, 7]]\n\nPre...
34
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-7, -12, 5, -7, 1, -2, 4],\n [-4, 9, -6, 1, 4, -5, 3],\n [-1, -1, -8, -8, 1, -7, -6],\n [10, 8, 4, -4, 9, 0, -4],\n [3, -9, -11, 0, 0, 6, -1],\n [-9, -3, 3, 11, 6, -5, -7],\n [-9,...
25
MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-10, -3, 2, 7, 8, 4, 10],\n [11, -7, 12, -10, 5, -8, 0],\n [12, -12, 4, -10, 6, 8, 7],\n [9, -1, -5, -5, 2, -2, 7],\n [-12, 3, 1, -6, -7, 8, -9],\n [9, -5, 9, 6, 12, -10, -9],\n [0, 8, -11, -2, 3, -3, 2]]\n\nPresent ...
35
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -11, -7, 1, -11, -3, 4],\n [-5, 3, 1, -3, 0, -12, -3],\n [9, -1, 4, 11, 1, -8, 6],\n [-8, 2, 0, 4, -12, 1, -9],\n [12, -4, 4, -10, 0, -1, 3],\n [-9, 5, 10, -10, 4, -12, 6],\n [9, -9, 4, -6, -11, -1, -8]]\n\nP...
114
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, 10, -5, 0, 1, -2],\n [-7, 3, 10, 12, 9, 12, 2],\n [3, 0, -1, 5, 5, 1, -11],\n [9, -11, -10, 11, -5, -2, -1],\n [-9, -4, 11, 4, 11, 3, 4],\n [2, 7, 9, -6, -3, -9, 11],\n [11...
24
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[7, 5, 2, 10, 6, 0, -1],\n [6, 6, 7, -11, 8, -10, -3],\n [-8, -1, -6, -4, -11, 12, -3],\n [-7, -1, -7, -10, -3, -4, 7],\n [-8, -10, -8, -5, -5, 1, 11],\n [9, 4, -2, 3, -7, -2, -3],\n [10, -4, 11, 11, ...
35
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, 2, -11, 9, -11, -3, 7],\n [2, -3, 6, 9, 0, 11, -2],\n [9, -11, 8, 0, 9, 12, 9],\n [8, -12, -8, 8, 9, -6, 0],\n [0, 7, 10, 8, -7, 7, -1],\n [-5, -4, 5, -2, 7, -2, 11],\n [11, 2, -4, -10, 4, 12, 4]]\n\nPresent the answer in LaTex ...
33
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-10, 6, -4, 4, 10, 5, 10],\n [2, -12, -3, -5, -3, -11, 6],\n [1, -5, 6, -12, 3, 12, 11],\n [2, 7, 11, -8, -10, 4, -3],\n [-8, -2, -7, -9, -6, 6, -6],\n [1, 4, 10, 4, 0, -12, -11],\n [5, -9, 0, -12, -...
34
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -9, 12, -4, 4, 8, 10],\n [7, 8, -11, -10, 10, 2, -6],\n [-9, -1, -12, 4, -9, -9, 9],\n [10, 12, -4, 8, -3, 6, 6],\n [2, 9, 4, -6, -10, -8, 3],\n [10, -6, 3, -4, -12, -10, 12],\...
29
MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 12, 7, -7, 12, -2, -8],\n [-1, -12, 6, -2, 2, 12, 3],\n [-10, -2, -2, -3, -11, 7, -8],\n [10, 10, 12, -5, 0, 2, -11],\n [-1, 11, -5, 8, 6, 12, 10],\n [-12, -5, -3, 0, -8, 9, -4],\n [-3, 1, 11, -2...
31
MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 7, 4, -8, -6, 4, 7],\n [9, -2, -1, 12, 11, -11, 6],\n [-8, -2, 10, 6, -6, 8, 9],\n [-7, -2, 1, -9, -5, -4, -11],\n [12, -2, 7, 9, -6, -9, 11],\n [1, 11, -12, 11, -1, 6, -8],\n [-5, -2, 9, -9, 2, 7, -1]]\n\nPresent...
33
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[7, 9, 10, 8, -3, 11, 3],\n [10, -5, 7, -5, -7, -10, -5],\n [10, -3, -8, -2, -9, 4, -10],\n [5, -5, 11, -1, 8, 3, 1],\n [8, 3, -9, -12, -12, 9, 2],\n [...
30
MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, 5, 8, -4, -7, 7],\n [-10, -5, -10, -12, 7, 0, 8],\n [-8, 3, 8, 11, 3, 11, -1],\n [0, -9, -4, 3, -12, -8, 8],\n [-8, 11, 12, 6, -4, -5, 6],\n [5, 2, -9, 2, 0, 5, 7],\n [-8, 5, -5, -12, 6, 10, 4]]\n\nPresent ...
113
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-11, 6, 3, 5, -11, -7, -6],\n [-7, -7, -4, -5, 11, 9, 8],\n [-4, -1, 5, 10, -7, 10, -9],\n [12, -6, 5, 7, -8, 5, -3],\n [-5, -12, 2, -10, 2, 1, -12],\n [8, -5, -6, -4, 5, -1, -5],...
30
MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, -8, 8, 0, -4, 0, -4],\n [11, 11, 3, -1, -11, 6, 3],\n [11, 0, -8, 10, 11, -7, 8],\n [11, 4, 4, 4, -10, 0, -1],\n [-7, 9, 8, 0, 1, -6, -8],\n [1, 5, -9, -12, -...
29
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[12, 4, 2, -9, -7, 11, 9],\n [-7, -3, -9, -4, 3, -6, 1],\n [-7, -12, 5, -1, 9, 2, -12],\n [2, 2, 3, 8, -12, -10, -1],\n [-6, -8, -12, -12, 2, -5, -2],\n [1, 12, 10, 0, 6, -1, 9],\n...
33
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[12, -4, -10, -4, -1, -10, 7],\n [4, 8, -1, 12, 5, -9, -3],\n [5, -5, -4, 6, 0, 12, -7],\n [9, -6, 8, -7, -2, 4, 6],\n [12, -1, 8, 8, 11, 0, 5],\n [-6, 12, 10, -8, 3, 9, -9],\n [10, -12, -9, -10, -9, -12, -1]]\n\nPresent the answer in...
36
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -11, -4, -6, 0, 9, -11],\n [-12, 5, -6, 5, 6, -5, 10],\n [-1, -2, -4, -9, -6, 4, -2],\n [-11, 10, 5, 9, -1, -4, -2],\n [-8, -6, -12, 11, 12, -8, -7],\n [0, -2, -5, 7, -11, 2, -3],\...
119
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, -10, -2, -2, 3, -10, -4],\n [-10, 6, -2, 1, -11, -6, -3],\n [-3, 7, -12, -7, 8, 1, -11],\n [-7, -12, -10, -9, 0, -10, 2],\n [0, 9, -2, -9, 4, -8, 8],\n [12, 11, -5, 8, 11, -3, ...
30
MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[9, 7, 6, -7, -3, 0, 12],\n [-11, -3, -3, -8, 9, -9, 10],\n [-11, -6, 5, 4, -2, 8, 5],\n [-5, -1, 11, -12, 7, 12, 8],\n [-1, -7, -10, -8, 1, -1, 0],\n [0, 4, 11, 2, -7, -1, -11],\n [-9, 7, 12, 12, ...
32
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -7, 11, 4, 4, -2, 10],\n [-6, -11, 6, -11, 9, 0, 11],\n [11, 3, 4, -2, -4, 11, -4],\n [1, 0, 12, -2, -1, 9, -10],\n [-12, -5, 6, 0, -6, 0, -7],\n [...
28
MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[12, 0, -8, 1, -2, 12, 1],\n [12, -6, 11, 4, -9, -3, -3],\n [2, 7, -1, -4, -10, 2, -1],\n [2, -12, 2, -2, -8, -6, -1],\n [7, 12, -7, 9, -10, -3, 8],\n [9, -9, 0, 6...
31
MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, 6, 3, -12, 7, 7, -3],\n [-11, 1, -5, -7, -10, 3, 4],\n [-1, 6, 11, 7, -10, 0, 3],\n [-2, 7, 3, 7, -11, -9, 12],\n [-9, 4, -12, -12, -8, 9, -1],\n [-7, -7, 12, 4, 9, 0, -5],\n [...
30
MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 8, 5, -11, -2, 10, 7],\n [4, 8, 5, 2, -6, 3, 12],\n [-12, 5, 9, -5, -6, 12, -11],\n [-1, 3, -4, 7, -2, 2, -10],\n [10, 8, 0, 8, 0, -11, -7],\n [-7, -1, -9, -8...
29
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, 7, -1, 7, -5, 6],\n [8, 3, 8, 5, -4, -9, -4],\n [12, -11, -4, -4, 5, -2, 0],\n [-7, -4, 3, -9, -11, -6, 2],\n [12, -7, -2, 7, 4, -9, 6],\n [-6, -2, 0, 8, -10, 1, -11],\n [5, -8, 0, 0, 11, 11, 1]]\n\nPresent the answer in LaTex...
31
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 8, 0, 5, 0, -9, 10],\n [9, -3, 10, -8, 5, -5, 1],\n [-11, -5, 3, -6, -10, -9, -6],\n [-9, -4, 10, 4, 4, 7, 1],\n [1, 12, 0, -9, 0, 8, 4],\n [2, 5, -2, -9, 7, -2, -3],\n [9, 0, 9, -5, ...
25
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-12, 2, 9, -9, 7, -12, 12],\n [-1, -2, 6, 2, 8, -3, -12],\n [11, -10, 1, 2, -12, -3, 9],\n [-12, 2, -10, 8, 7, 10, 9],\n [-1, 6, 3, -5, 11, 1, 5],\n [10, -12, -11, 11, -1, 4, -11],\n [4, 8, -6, -...
122
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, 2, -6, -10, 12, -3, -10],\n [1, 9, -10, -12, -12, 6, -9],\n [-11, 12, -2, 11, -1, 0, 3],\n [3, 6, 10, 7, 8, 7, -4],\n [3, -6, 0, -9, 0, -5, -11],\n [-6, -2, 4, 11, 1, 0, 2],\n [9, 8, ...
31
MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -4, 5, -8, -2, -11, 4],\n [10, 7, 8, -9, 9, 5, 11],\n [7, -5, 6, -1, -2, 3, -8],\n [-10, -1, 2, 3, 0, -6, 2],\n [-10, -1, -5, 12, -1, 5, -10],\n [-1, 10, 8, 10, -11, 1, 1],\n [-9, 4, 2, 3, -8, 11, 4]]\n\nPresent the answer in LaTe...
31
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, -6, 10, 2, 4, -1, -2],\n [6, -2, -11, 2, -8, 5, 8],\n [8, 3, -9, 10, -3, 9, -11],\n [2, -9, 3, -6, 12, 12, -1],\n [-10, 4, -4, -5, 10, -7, 2],\n [-3, 10, 12, -7, 2, 1, 6],\n [0, 1, -10, -9, 1...
116
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, 1, -5, -2, -3, 5],\n [-9, -9, -1, 5, -5, -10, 5],\n [-6, -12, 9, 0, -10, -10, 2],\n [8, 6, -9, 0, 0, 2, 6],\n [3, -6, -10, 7, -11, 5, 12],\n [-2, -12, 3, 4, 3, -3, 4],\n [-10, 5, 6, 1, 8,...
101
MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -2, 4, -7, 6, 0, -6],\n [9, -2, -6, 0, 0, 8, -12],\n [6, 6, 10, 2, 1, -10, 8],\n [7, -9, -6, -12, 10, 11, 6],\n [-10, 7, 2, 0, 9, 1, -6],\n [-12, 0, -9, -1, -6, -11, 4],\n [-12, 1, 9, 8, -12, ...
36
MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 12, -4, 9, -10, -12, 6],\n [-11, 8, 11, -8, 4, 6, -8],\n [10, 8, 1, -3, 8, -6, -5],\n [-5, -6, 0, 1, 6, -2, -11],\n [4, -7, -4, 6, -8, -4, 12],\n [-6, -9, 5, 5, 7, 4, -9],\n [9, 3...
119
MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-11, -9, 7, 7, 4, 7, 8],\n [12, 6, -10, -8, -3, -7, -10],\n [4, -3, 11, -1, -12, 5, 6],\n [9, 7, -9, 2, -4, -7, -1],\n [5, 10, 2, 6, -4, 9, 11],\n [0, 3, 0, -12, 5, 9, -10],\n [4, 9, -8, 12, -7, ...
109
MATH