sunyiyou/math_arithmetic_matrix_svd_level_1

messages listlengths 1 1	ground_truth stringclasses 24 values	dataset stringclasses 1 value
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, 2, -3],\n [-2, -2, -1, -3],\n [1, -2, 2, 0],\n [-3, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	16	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, 0, 1],\n [1, -3, 3, 1],\n [-2, 3, 3, 3],\n [-1, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 3, 0, -1],\n [-4, -2, -3, -2],\n [-3, 3, 2, -3],\n [-4, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -1, 3, 4],\n [1, 2, 1, -2],\n [2, -1, -3, 1],\n [0, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, 0, -3],\n [0, 4, -3, 4],\n [1, -1, 2, -1],\n [2, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -2, 2, 0],\n [4, -4, 4, -2],\n [3, 3, -3, 4],\n [4, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	10	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, -3, -2],\n [-3, 1, -3, -3],\n [1, -1, -3, 0],\n [4, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	17	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 2, -2, 2],\n [-2, 4, -1, 4],\n [3, 4, -3, 1],\n [3, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 0, -4, -3],\n [-4, -1, -3, 1],\n [-1, 4, 2, 4],\n [3, -4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	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, 3, -4, 2],\n [-3, 1, -3, -3],\n [1, -1, -3, 4],\n [0, 4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 2, 3, -2],\n [2, -4, 1, -2],\n [0, 3, 2, 2],\n [3, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	17	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, 1, -3],\n [-3, 3, 1, -1],\n [-1, 3, 4, 2],\n [-2, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	17	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, -2, 2],\n [-2, 3, 2, 1],\n [-2, 1, -3, -2],\n [4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	16	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, -4, 2],\n [0, 1, -2, 3],\n [-4, 3, 4, -3],\n [0, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	21	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, 1, 0, 0],\n [4, 4, -3, 2],\n [-2, -1, -3, 2],\n [3, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 2, 3, 3],\n [-2, 4, 4, -2],\n [2, 0, -1, -3],\n [2, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	16	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -1, 2],\n [-3, 4, -4, -1],\n [4, -1, 1, -3],\n [-2, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 1, 0, -4],\n [3, 3, -2, -3],\n [-3, -4, -2, 1],\n [-3, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, -3, -1],\n [0, 3, -1, 4],\n [-1, 2, 0, 0],\n [3, 3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -1, -1, -1],\n [-1, 3, -4, -4],\n [3, -2, 0, -4],\n [3, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -3, 2, -2],\n [-4, 1, 0, 3],\n [2, 4, 3, 2],\n [0, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -3, -2, -1],\n [-4, -2, -4, 2],\n [0, 3, -1, 4],\n [1, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -3, -2, 2],\n [0, -3, 1, 3],\n [3, -4, 1, -1],\n [3, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, 0, -2],\n [-2, 4, 3, 3],\n [0, 4, 2, -2],\n [-4, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, 1, -3],\n [1, 4, -3, 0],\n [3, -3, -1, 2],\n [-3, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 2, 4, -1],\n [-1, 3, 1, 2],\n [3, 2, 0, -4],\n [-3, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	17	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -2, 4, -1],\n [-1, -1, 1, 3],\n [1, -2, -1, 1],\n [0, -3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	13	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -4, 4, -2],\n [0, 3, 4, 1],\n [-2, -4, -1, 2],\n [-4, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -1, 1, 0],\n [0, -1, 4, 3],\n [2, 4, 1, 2],\n [-1, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -4, 0, -4],\n [3, 2, 0, 0],\n [4, -3, -4, 1],\n [0, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 2, -2, 4],\n [3, -2, 3, -4],\n [-1, -2, -3, -1],\n [3, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 3, 4, -2],\n [2, -4, 3, 0],\n [-2, 3, -2, 2],\n [0, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	17	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 4, -4, 0],\n [-2, 3, 4, 0],\n [-3, -2, -2, -2],\n [0, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, -2, 1],\n [-3, -4, -4, 4],\n [-3, -2, 3, 1],\n [1, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 1, -3, 3],\n [-3, -3, -1, -4],\n [0, -1, 4, 2],\n [-2, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, 2, -1],\n [3, -4, -3, 4],\n [-1, 1, 0, -2],\n [2, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -3, 0, 1],\n [0, -1, 3, 3],\n [3, 0, 2, 1],\n [1, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -1, 1, -2],\n [-3, 2, -4, 3],\n [3, -1, -4, 2],\n [-1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	16	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, 1, -1],\n [4, -2, -1, 1],\n [-2, 1, 1, 1],\n [-3, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 4, -3, -1],\n [2, 1, 4, -4],\n [2, 4, 0, -3],\n [3, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 3, 4, -2],\n [2, 3, -1, 4],\n [-4, -2, 0, 1],\n [-3, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, 4, -3],\n [-2, -1, 2, 2],\n [-2, 1, 1, -3],\n [4, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 0, 4, -4],\n [2, 1, 0, -3],\n [-4, 4, -3, -1],\n [3, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	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[[-3, -3, 0, -3],\n [-2, -3, 0, -2],\n [4, 1, 0, 0],\n [-4, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -2, 3, 0],\n [4, -2, 0, -4],\n [2, 3, -4, 0],\n [-3, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, -2, 4],\n [1, -3, 3, -3],\n [2, 3, -2, 4],\n [-1, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, 1, -4],\n [4, 1, 2, 3],\n [-4, -2, 1, -4],\n [4, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 4, 4, 2],\n [4, 0, -4, -2],\n [1, -1, 0, -2],\n [-2, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 1, -3, -1],\n [3, 1, -2, -1],\n [3, -2, 0, -1],\n [-2, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 4, -4, 2],\n [-3, -4, 2, -2],\n [4, 3, -1, 3],\n [2, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, 1, 4],\n [4, 0, 3, -2],\n [-4, 2, -4, 0],\n [-3, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, 4, 1],\n [4, 1, 4, 0],\n [0, 4, 1, -1],\n [-1, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 0, 4, 0],\n [2, -2, 3, 0],\n [0, 3, -3, -2],\n [-1, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, -3, -4],\n [4, -4, -1, -4],\n [3, -4, -2, 2],\n [4, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	23	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, 3, -1],\n [-1, -2, 1, 2],\n [1, 1, 2, -2],\n [-2, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	14	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -2, 4, 1],\n [4, -1, -4, -3],\n [4, 1, -4, -4],\n [3, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -4, 1, 3],\n [-1, 1, -4, 1],\n [4, -3, 3, 1],\n [-4, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	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, 3, 0, 3],\n [-1, -1, 3, 2],\n [-1, -1, 3, -3],\n [-3, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 2, -1, -1],\n [3, -3, -1, 1],\n [1, -2, -1, 1],\n [-2, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, 0, 2],\n [-2, 2, 2, 0],\n [-3, 3, 3, -3],\n [1, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 0, -4, 4],\n [0, 3, -4, 3],\n [2, 4, -3, 1],\n [2, -4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -4, 4, 1],\n [-2, -1, 1, 1],\n [-4, -2, 4, 3],\n [4, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	16	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, 1, -4],\n [4, -4, -4, -3],\n [-1, -2, -1, -2],\n [1, -3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	17	MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 2, -2],\n [0, 2, -1, 4],\n [-3, -1, -2, 1],\n [-1, 4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 1, -1, -2],\n [3, 4, -1, 2],\n [-2, -4, -4, 0],\n [4, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 4, -1, 2],\n [-4, 4, -2, -3],\n [-4, -2, 1, 4],\n [2, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -1, 1, -2],\n [-3, 3, 2, 1],\n [-4, -1, 0, -2],\n [-1, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, 1, -3],\n [2, -4, 0, 3],\n [-2, -4, 2, 2],\n [3, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -4, 3, -4],\n [-3, 1, 1, 1],\n [3, -1, 1, -2],\n [-4, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -3, -3, 0],\n [-4, -4, 1, -4],\n [3, 1, 2, -1],\n [0, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -1, -3, -4],\n [-3, 3, 2, -2],\n [-4, 1, -1, 3],\n [-4, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	19	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -4, -3, -3],\n [-1, -2, 1, 0],\n [4, 1, -2, 4],\n [1, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -4, -1, 1],\n [-3, 3, -3, -3],\n [4, 3, 3, 2],\n [3, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	20	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, 3, -1],\n [-4, -4, 0, 4],\n [-2, -4, -3, -3],\n [-2, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -4, -1, -4],\n [-4, 2, 3, -4],\n [2, -4, -2, 2],\n [0, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -4, 1, 0],\n [4, 0, 1, -3],\n [-2, -1, -2, -2],\n [-1, -1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, 3, -4],\n [3, 0, 4, -4],\n [1, 4, -2, 1],\n [0, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 3, -3],\n [-1, -1, -2, -4],\n [-3, 2, -3, -2],\n [0, -3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	20	MATH
[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -4, -4, 4],\n [-1, -1, -3, 1],\n [2, 0, -4, -4],\n [-1, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 2, 4, 4],\n [-3, 0, 2, -3],\n [-2, 4, 3, 4],\n [0, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	19	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 2, -3, -1],\n [-4, 0, 0, 3],\n [0, -1, 3, -2],\n [1, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -3, 3, 2],\n [-4, -2, 1, 3],\n [-1, 2, 3, -1],\n [-3, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 1, -3, 1],\n [-1, -3, 3, 1],\n [2, 2, -2, 3],\n [-4, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, 4, -3],\n [-2, 3, -1, -4],\n [4, -2, 4, 1],\n [4, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	22	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, 2, 3],\n [3, -2, 2, -1],\n [0, 4, -2, 2],\n [0, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 2, 0],\n [-1, -2, 4, 1],\n [-4, 1, -1, -1],\n [3, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	16	MATH
[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, -2, -4],\n [-1, 4, -3, 2],\n [4, -3, 3, 1],\n [4, -4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -4, -2, -4],\n [3, 3, -4, 2],\n [-4, 3, 2, 1],\n [-4, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	19	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -4, 1, 2],\n [-2, 1, -2, 0],\n [1, 1, -4, 4],\n [3, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	17	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, 0, -3],\n [0, 1, 1, -2],\n [0, -2, 2, 1],\n [0, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, 4, 2],\n [-4, 1, -4, 3],\n [-2, -2, 4, -4],\n [1, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	19	MATH
[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 0, 2, 2],\n [3, 3, 0, 3],\n [3, -4, 3, 4],\n [-3, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, 1, 3],\n [1, 2, 4, -4],\n [2, 1, 3, 4],\n [-4, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 3, 3, -1],\n [4, 1, -2, 2],\n [-3, -3, -4, 4],\n [1, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	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, 4, -3, 2],\n [3, 1, 3, -1],\n [-1, 1, -3, -1],\n [2, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, -4, 0],\n [-2, 0, 4, 1],\n [-4, 2, -4, -1],\n [1, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 0, 2],\n [2, 4, 1, 3],\n [-2, 2, -3, 4],\n [-4, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	18	MATH
[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -1, 1, -2],\n [3, -1, 3, 4],\n [-2, 4, 2, -4],\n [-3, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	19	MATH
[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, -4, -2],\n [2, 0, 4, -4],\n [4, 0, -4, 0],\n [-4, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 1, 1, 2],\n [0, 0, -2, 3],\n [2, -4, 0, -4],\n [3, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, 2, -3],\n [-2, -2, -1, -3],\n [1, -2, 2, 0],\n [-3, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

16

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, 0, 1],\n [1, -3, 3, 1],\n [-2, 3, 3, 3],\n [-1, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 3, 0, -1],\n [-4, -2, -3, -2],\n [-3, 3, 2, -3],\n [-4, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -1, 3, 4],\n [1, 2, 1, -2],\n [2, -1, -3, 1],\n [0, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, 0, -3],\n [0, 4, -3, 4],\n [1, -1, 2, -1],\n [2, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -2, 2, 0],\n [4, -4, 4, -2],\n [3, 3, -3, 4],\n [4, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

10

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, -3, -2],\n [-3, 1, -3, -3],\n [1, -1, -3, 0],\n [4, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

17

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 2, -2, 2],\n [-2, 4, -1, 4],\n [3, 4, -3, 1],\n [3, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 0, -4, -3],\n [-4, -1, -3, 1],\n [-1, 4, 2, 4],\n [3, -4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

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, 3, -4, 2],\n [-3, 1, -3, -3],\n [1, -1, -3, 4],\n [0, 4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 2, 3, -2],\n [2, -4, 1, -2],\n [0, 3, 2, 2],\n [3, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

17

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, 1, -3],\n [-3, 3, 1, -1],\n [-1, 3, 4, 2],\n [-2, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

17

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, -2, 2],\n [-2, 3, 2, 1],\n [-2, 1, -3, -2],\n [4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

16

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, -4, 2],\n [0, 1, -2, 3],\n [-4, 3, 4, -3],\n [0, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

21

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, 1, 0, 0],\n [4, 4, -3, 2],\n [-2, -1, -3, 2],\n [3, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 2, 3, 3],\n [-2, 4, 4, -2],\n [2, 0, -1, -3],\n [2, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

16

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -1, 2],\n [-3, 4, -4, -1],\n [4, -1, 1, -3],\n [-2, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 1, 0, -4],\n [3, 3, -2, -3],\n [-3, -4, -2, 1],\n [-3, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, -3, -1],\n [0, 3, -1, 4],\n [-1, 2, 0, 0],\n [3, 3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -1, -1, -1],\n [-1, 3, -4, -4],\n [3, -2, 0, -4],\n [3, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -3, 2, -2],\n [-4, 1, 0, 3],\n [2, 4, 3, 2],\n [0, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -3, -2, -1],\n [-4, -2, -4, 2],\n [0, 3, -1, 4],\n [1, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -3, -2, 2],\n [0, -3, 1, 3],\n [3, -4, 1, -1],\n [3, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, 0, -2],\n [-2, 4, 3, 3],\n [0, 4, 2, -2],\n [-4, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, 1, -3],\n [1, 4, -3, 0],\n [3, -3, -1, 2],\n [-3, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 2, 4, -1],\n [-1, 3, 1, 2],\n [3, 2, 0, -4],\n [-3, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

17

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -2, 4, -1],\n [-1, -1, 1, 3],\n [1, -2, -1, 1],\n [0, -3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

13

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -4, 4, -2],\n [0, 3, 4, 1],\n [-2, -4, -1, 2],\n [-4, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -1, 1, 0],\n [0, -1, 4, 3],\n [2, 4, 1, 2],\n [-1, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -4, 0, -4],\n [3, 2, 0, 0],\n [4, -3, -4, 1],\n [0, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 2, -2, 4],\n [3, -2, 3, -4],\n [-1, -2, -3, -1],\n [3, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 3, 4, -2],\n [2, -4, 3, 0],\n [-2, 3, -2, 2],\n [0, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

17

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 4, -4, 0],\n [-2, 3, 4, 0],\n [-3, -2, -2, -2],\n [0, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, -2, 1],\n [-3, -4, -4, 4],\n [-3, -2, 3, 1],\n [1, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 1, -3, 3],\n [-3, -3, -1, -4],\n [0, -1, 4, 2],\n [-2, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, 2, -1],\n [3, -4, -3, 4],\n [-1, 1, 0, -2],\n [2, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -3, 0, 1],\n [0, -1, 3, 3],\n [3, 0, 2, 1],\n [1, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -1, 1, -2],\n [-3, 2, -4, 3],\n [3, -1, -4, 2],\n [-1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

16

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, 1, -1],\n [4, -2, -1, 1],\n [-2, 1, 1, 1],\n [-3, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 4, -3, -1],\n [2, 1, 4, -4],\n [2, 4, 0, -3],\n [3, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 3, 4, -2],\n [2, 3, -1, 4],\n [-4, -2, 0, 1],\n [-3, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, 4, -3],\n [-2, -1, 2, 2],\n [-2, 1, 1, -3],\n [4, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 0, 4, -4],\n [2, 1, 0, -3],\n [-4, 4, -3, -1],\n [3, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

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[[-3, -3, 0, -3],\n [-2, -3, 0, -2],\n [4, 1, 0, 0],\n [-4, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -2, 3, 0],\n [4, -2, 0, -4],\n [2, 3, -4, 0],\n [-3, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, -2, 4],\n [1, -3, 3, -3],\n [2, 3, -2, 4],\n [-1, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, 1, -4],\n [4, 1, 2, 3],\n [-4, -2, 1, -4],\n [4, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 4, 4, 2],\n [4, 0, -4, -2],\n [1, -1, 0, -2],\n [-2, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 1, -3, -1],\n [3, 1, -2, -1],\n [3, -2, 0, -1],\n [-2, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 4, -4, 2],\n [-3, -4, 2, -2],\n [4, 3, -1, 3],\n [2, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, 1, 4],\n [4, 0, 3, -2],\n [-4, 2, -4, 0],\n [-3, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, 4, 1],\n [4, 1, 4, 0],\n [0, 4, 1, -1],\n [-1, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 0, 4, 0],\n [2, -2, 3, 0],\n [0, 3, -3, -2],\n [-1, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, -3, -4],\n [4, -4, -1, -4],\n [3, -4, -2, 2],\n [4, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

23

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, 3, -1],\n [-1, -2, 1, 2],\n [1, 1, 2, -2],\n [-2, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

14

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -2, 4, 1],\n [4, -1, -4, -3],\n [4, 1, -4, -4],\n [3, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -4, 1, 3],\n [-1, 1, -4, 1],\n [4, -3, 3, 1],\n [-4, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

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, 3, 0, 3],\n [-1, -1, 3, 2],\n [-1, -1, 3, -3],\n [-3, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 2, -1, -1],\n [3, -3, -1, 1],\n [1, -2, -1, 1],\n [-2, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, 0, 2],\n [-2, 2, 2, 0],\n [-3, 3, 3, -3],\n [1, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 0, -4, 4],\n [0, 3, -4, 3],\n [2, 4, -3, 1],\n [2, -4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -4, 4, 1],\n [-2, -1, 1, 1],\n [-4, -2, 4, 3],\n [4, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

16

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, 1, -4],\n [4, -4, -4, -3],\n [-1, -2, -1, -2],\n [1, -3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

17

MATH

[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 2, -2],\n [0, 2, -1, 4],\n [-3, -1, -2, 1],\n [-1, 4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 1, -1, -2],\n [3, 4, -1, 2],\n [-2, -4, -4, 0],\n [4, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 4, -1, 2],\n [-4, 4, -2, -3],\n [-4, -2, 1, 4],\n [2, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -1, 1, -2],\n [-3, 3, 2, 1],\n [-4, -1, 0, -2],\n [-1, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

4

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, 1, -3],\n [2, -4, 0, 3],\n [-2, -4, 2, 2],\n [3, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -4, 3, -4],\n [-3, 1, 1, 1],\n [3, -1, 1, -2],\n [-4, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -3, -3, 0],\n [-4, -4, 1, -4],\n [3, 1, 2, -1],\n [0, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -1, -3, -4],\n [-3, 3, 2, -2],\n [-4, 1, -1, 3],\n [-4, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

19

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -4, -3, -3],\n [-1, -2, 1, 0],\n [4, 1, -2, 4],\n [1, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -4, -1, 1],\n [-3, 3, -3, -3],\n [4, 3, 3, 2],\n [3, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

20

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, 3, -1],\n [-4, -4, 0, 4],\n [-2, -4, -3, -3],\n [-2, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -4, -1, -4],\n [-4, 2, 3, -4],\n [2, -4, -2, 2],\n [0, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -4, 1, 0],\n [4, 0, 1, -3],\n [-2, -1, -2, -2],\n [-1, -1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, 3, -4],\n [3, 0, 4, -4],\n [1, 4, -2, 1],\n [0, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 3, -3],\n [-1, -1, -2, -4],\n [-3, 2, -3, -2],\n [0, -3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

20

MATH

[ { "content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -4, -4, 4],\n [-1, -1, -3, 1],\n [2, 0, -4, -4],\n [-1, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 2, 4, 4],\n [-3, 0, 2, -3],\n [-2, 4, 3, 4],\n [0, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

19

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 2, -3, -1],\n [-4, 0, 0, 3],\n [0, -1, 3, -2],\n [1, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -3, 3, 2],\n [-4, -2, 1, 3],\n [-1, 2, 3, -1],\n [-3, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 1, -3, 1],\n [-1, -3, 3, 1],\n [2, 2, -2, 3],\n [-4, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, 4, -3],\n [-2, 3, -1, -4],\n [4, -2, 4, 1],\n [4, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

22

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, 2, 3],\n [3, -2, 2, -1],\n [0, 4, -2, 2],\n [0, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 2, 0],\n [-1, -2, 4, 1],\n [-4, 1, -1, -1],\n [3, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

16

MATH

[ { "content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, -2, -4],\n [-1, 4, -3, 2],\n [4, -3, 3, 1],\n [4, -4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -4, -2, -4],\n [3, 3, -4, 2],\n [-4, 3, 2, 1],\n [-4, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

19

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -4, 1, 2],\n [-2, 1, -2, 0],\n [1, 1, -4, 4],\n [3, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

17

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, 0, -3],\n [0, 1, 1, -2],\n [0, -2, 2, 1],\n [0, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, 4, 2],\n [-4, 1, -4, 3],\n [-2, -2, 4, -4],\n [1, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

19

MATH

[ { "content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 0, 2, 2],\n [3, 3, 0, 3],\n [3, -4, 3, 4],\n [-3, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, 1, 3],\n [1, 2, 4, -4],\n [2, 1, 3, 4],\n [-4, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 3, 3, -1],\n [4, 1, -2, 2],\n [-3, -3, -4, 4],\n [1, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

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, 4, -3, 2],\n [3, 1, 3, -1],\n [-1, 1, -3, -1],\n [2, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, -4, 0],\n [-2, 0, 4, 1],\n [-4, 2, -4, -1],\n [1, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 0, 2],\n [2, 4, 1, 3],\n [-2, 2, -3, 4],\n [-4, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

18

MATH

[ { "content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -1, 1, -2],\n [3, -1, 3, 4],\n [-2, 4, 2, -4],\n [-3, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

19

MATH

[ { "content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, -4, -2],\n [2, 0, 4, -4],\n [4, 0, -4, 0],\n [-4, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 1, 1, 2],\n [0, 0, -2, 3],\n [2, -4, 0, -4],\n [3, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH