messages listlengths 1 1 | ground_truth stringclasses 61
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, -7, 10, 8, -12, -10, -10],\n [1, 7, 9, -8, 4, 2, -7],\n [1, 1, 12, 4, -5, -5, 6],\n [-4, -2, 0, 0, 11, 6, 8],\n [6, -8, 3, -4, 7, 9, -10],\n [6, -8, -5, 1, 11, -10, 11],\n [0, -2, -5, 6, -3, 5, 5]]\n\nPresent the answer in LaTex... | 31 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[12, -6, 3, -7, 3, 3, 10],\n [11, -12, 11, 6, -10, -7, -9],\n [-9, -9, -3, -4, -5, 6, 4],\n [4, -12, 7, 1, 9, 7, -2],\n [-10, 11, -5, 9, 12, -3, 4],\n [-5, 9, -12, 7, 8, -6, 11],\n... | 39 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-9, -3, -9, 9, -4, 9, -12],\n [-8, -4, -8, -7, 6, -5, -3],\n [-2, 0, 7, -9, -2, -1, -8],\n [-3, 12, 11, -6, 8, -4, -4],\n [-3, -3, -11, -9, -5, 1, 4],\n [0, 8, 11, 5, 5, 0, -5],\n [-1, 12, 10, 11, 8, -12, 7]]\n\nPresent the answer in... | 36 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -10, -1, 6, 12, 0, -3],\n [2, 7, -11, 6, -10, 1, -6],\n [-5, -2, 9, 7, -7, -2, 4],\n [-3, 11, 4, 8, -11, -7, 12],\n [-8, -9, -11, -1, -10, -7, 11],\n [1, -5, 8, 8, 1, -10, 3],\n [2, -6, 2, 0, -7, ... | 31 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-9, 9, 9, 1, 2, -1, 6],\n [9, -3, -7, 12, -4, -11, -9],\n [-4, 2, 0, 7, -5, 6, 6],\n [12, 3, -2, -3, -5, -12, -3],\n [5, -10, -2, 5, -10, -5, 1],\n [-7, 2, 1, -6, -3, 2, -3],\n [9, 4, 6, 4, -1, 2,... | 26 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[12, -4, -8, -9, -1, 3, -4],\n [12, -10, 8, -10, 5, 4, -3],\n [-11, 11, -2, 11, -10, 10, 10],\n [-11, -4, 6, -11, 6, -11, 2],\n [11, 8, -10, -8, -2, 11, -6],\n [-7... | 30 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 12, 2, -12, 7, -10, 10],\n [-8, -8, -9, 4, 8, 7, 1],\n [-5, -11, -5, -12, -9, 6, -8],\n [-8, 8, 7, 11, 6, -1, 7],\n [-12, -6, 4, -11, -2, -6, 4],\n [-10, 9, -7, 9, -2, 5, 5],\n [9, -3, -8, 10,... | 126 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, 2, 8, 7, 10, -9, 8],\n [8, -12, 2, 4, 6, 1, 6],\n [5, -11, -7, 0, 4, -7, 8],\n [9, -8, -6, -12, 0, 6, 9],\n [-12, 0, -2, -6, 7, -10, 12],\n [-12, -5, 4, 0, 1, -8, 11],\n [9, 10, 11, -7, 9, -7,... | 119 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 0, 5, 10, -9, 4, -8],\n [-10, -9, 10, -8, 1, 2, 7],\n [4, -7, -3, 9, 10, 3, 4],\n [1, 7, -1, -4, 2, -1, 1],\n [9, 5, 7, -7, -9, 10, -1],\n [0, 6, 9, 0, -1, 7, -10],\n [-10, 1, 5, ... | 99 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -4, -9, 2, 6, 3, -5],\n [4, 8, -12, -6, 8, 5, -1],\n [3, -12, 2, -6, 4, -10, -2],\n [-7, -7, 2, -6, -2, 4, 10],\n [5, 9, 11, 8, 6, -5, 11],\n [7, -... | 29 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[8, -12, 7, -1, 4, 2, -11],\n [5, 3, -9, -5, -11, 1, 12],\n [2, -4, -11, 4, -3, -4, -11],\n [11, 6, 4, -2, 4, -3, 5],\n [10, -7, 3, 5, 7, 5, -12],\n [-10, 2, 7, -3, 8, -8, 2],\n [10, 1, 2, -3, 11, -4, -1]]\n\nPresent the answer in LaT... | 32 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -8, 12, 11, -3, 12, -5],\n [9, 7, 12, 3, -1, -4, -3],\n [3, -3, -4, -10, 6, -2, -7],\n [-7, 2, 2, 0, 9, -8, 1],\n [8, -11, 10, -1, 7, 1, 6],\n [11, 7, 2, 7, 11, 4, 12],\n [1, 10, ... | 118 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -3, -5, -7, 12, 2, -1],\n [12, 12, -7, -1, 2, -1, -4],\n [6, 8, -11, 0, 0, -5, 0],\n [-9, -7, -7, 8, -1, -1, 4],\n [-6, 2, 11, 4, -3, 10, 7],\n [-7, -4, 2, 3, 8, -5, 3],\n [-8, 5, 7, 1, -11, 10, 10]]\n\nPresent the answer in LaTe... | 32 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-10, 1, -6, 2, 4, -12, -4],\n [9, 1, 3, 8, 0, -7, 9],\n [-12, 8, 12, -9, -10, 4, -11],\n [6, 7, 10, 9, -5, 12, 2],\n [-7, 10, 7, -11, 12, 12, 2],\n [7, -1, -10, -3, 1, 9, 1],\n [-10, -12,... | 35 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -9, -9, 0, -4, -6, 3],\n [5, -10, 7, 7, -3, 11, 9],\n [3, -10, -2, 12, -3, 3, -5],\n [-4, 2, 8, -10, -9, 0, -1],\n [8, -4, 12, 1, 6, -6, 3],\n [9, 7, -8, -3, 5, -2, -6],\n [1, 7, 5, -... | 27 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-11, 10, -12, 10, -3, 8, -12],\n [-7, -6, 4, -4, -6, 4, -10],\n [3, -8, 7, 5, -12, -9, 10],\n [-2, 7, -4, -5, -5, -8, -1],\n [-12, 2, 12, 5, -7, -3, 1],\n [8, -5, -10, 9, 9, 6, -1],\n [-1, 2, -6,... | 118 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 0, -9, 11, -4, 8, 5],\n [2, 2, -7, -2, -5, 8, 4],\n [11, 12, 4, 11, 5, -9, 2],\n [-11, -11, -3, -10, -5, 7, -6],\n [-1, 6, 2, 1, 3, 1, -10],\n [5, 9, -7, 4, 10... | 35 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -5, 3, 11, -10, 0, -9],\n [5, -11, 7, 9, 8, 2, 4],\n [-3, -12, -7, -10, 6, -6, 0],\n [0, 4, -12, 1, -10, 1, 11],\n [-12, 3, -3, 0, -9, -4, 1],\n [-9, -3, -5, 10, -10, 10, -6],\n [-... | 111 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 7, 5, 2, 5, 11, 10],\n [-1, 10, 8, -5, -11, -11, -8],\n [-12, 9, -9, -7, 10, 0, 6],\n [-2, 0, -5, -6, 0, -12, -7],\n [-6, 3, 2, 7, -11, 12, 10],\n [3, 4, 11, 2, -10, -9, -1],\n [-8, 4, -7, -3, 9, 5, -3]]\n\nPrese... | 34 | 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, 7, 2, -9, 12],\n [3, 9, 11, -5, -6, 6, 4],\n [8, 0, 2, -11, -3, 0, 5],\n [10, -2, 0, 6, 11, 12, 11],\n [9, -8, -10, 6, 10, 0, -8],\n [-1, 1, -7, 9, -4, 4, -5],\n [0, -... | 25 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 2, 1, -2, -2, -4, -7],\n [2, -1, -7, -12, 12, 3, 7],\n [2, -11, 4, -10, -10, -8, 4],\n [10, 4, 7, -7, -12, -6, 2],\n [-6, 6, 7, 9, -2, 10, 1],\n [0, 7, 12, -4,... | 29 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, -11, 2, 4, 3, 8, -5],\n [-3, -3, 5, -3, -4, 11, 6],\n [-12, -9, 11, -10, -3, -1, 5],\n [10, 7, -7, 8, -11, -3, -11],\n [-4, -3, -11, -5, 11, 4, 4],\n [-9, 5, -1, 4, -4, 6, 1],\n [1, 4, -11, -5, -8, -6, 9]]\n\nPresent the answer i... | 33 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, 4, 9, -6, 7, -5],\n [-5, 10, -2, 2, 5, -7, 9],\n [-1, 2, 10, -7, 5, 11, 7],\n [-4, -5, 1, 6, 6, -5, -11],\n [12, -9, -7, -10, -10, 6, -2],\n [-3, -1, 1, 5, 11, -4, 2],\n [11, -10, 10, -2, -3, 5, -9]]\n\nPresent the answer i... | 103 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -7, 8, 0, 12, 7, -8],\n [7, 1, 0, 1, -5, 3, 0],\n [11, 2, 6, -12, 9, -11, 5],\n [6, -5, -10, 10, 1, -4, -5],\n [4, 10, 10, 11, 3, -3, 8],\n [-3, 12, 12, 11, -7, 9, 4],\n [3, 2, 9, ... | 121 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -9, 8, 8, 3, 8, -9],\n [-12, 11, 6, -11, -4, 10, 12],\n [0, 5, 3, 3, 12, -3, -4],\n [-2, 12, -9, -3, -10, -7, -10],\n [-4, -10, 5, -5, 9, -5, 2],\n [0, -6, 6, -5, -3, 4, -12],\n [0, 0, 11, 3, ... | 25 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-8, -11, -2, -4, -7, -5, -4],\n [-4, -5, -1, -5, -10, 0, 6],\n [-11, 4, 3, -9, 5, 1, -11],\n [0, 8, 7, 4, 2, 12, 7],\n [-8, -6, 5, 11, -2, 5, -8],\n [0, 5, -11, 7, -9, 0, 11],\n [3, -7, -5, 3, 0, ... | 26 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, -4, 5, 4, -5, 2, -4],\n [4, 10, -11, -7, -8, 4, -11],\n [5, -3, -3, -7, -1, 4, 0],\n [7, 3, -3, 8, -11, -11, 10],\n [-6, -7, -12, -1, 0, -1, 6],\n [-4, -3, 4, 5, -5, -6, -4],\n [-3, -1, 2, 2, -9, -9, 10]]\n\nPresent the answ... | 102 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-12, -1, 12, -11, 2, 4, -6],\n [-7, -1, 6, -12, 8, 1, -9],\n [-8, -12, -12, 8, -7, -8, -11],\n [12, 8, -8, -4, 6, 8, 2],\n [0, -1, -8, -11, -9, 5, 8],\n [-3, 0, -1, -11, 2, 1, 12],\n [-3,... | 32 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, 8, 9, 1, -12, 0, -5],\n [5, 9, -4, 0, -10, 5, -3],\n [-8, 12, -7, -5, 11, -6, 8],\n [5, 1, 2, -3, 8, -1, -6],\n [-6, -2, 0, 2, 5, -6, -7],\n [10, -2, -5, 7, -12, -5, -5],\n [6, -10, -8, -10, 2, 1, 8]]\n\nPresent t... | 32 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 11, 4, 5, -11, -1, 3],\n [-9, 12, -11, 1, -2, 0, 12],\n [-6, -3, 11, -12, 8, 12, -9],\n [5, -7, -11, -10, 1, -5, 3],\n [6, 5, -7, 1, -10, 3, -12],\n [-1, 1, 6, 9, 6, -4, -6],\n... | 31 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-9, 12, 4, -1, -7, 5, -5],\n [8, 2, -10, -11, 11, 10, -4],\n [-5, -9, -11, 1, -11, -11, 9],\n [-6, -1, -7, 5, -9, 6, 0],\n [7, 8, 10, 12, -11, -5, 6],\n [-4, -9, 3, 6, -3, -7, 3],\n [... | 113 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 6, -1, 0, 12, -9, 12],\n [-3, 8, -6, -8, 4, 5, -2],\n [2, 8, 9, -6, 5, 12, -7],\n [5, 3, -11, 6, -12, 12, -2],\n [7, -8, 3, 10, -12, 6, 1],\n [-10, -11, 11, -8, 4, 5, -12],\n [2, 9, -4, 10, -8, 0, 6]]\n\nPrese... | 114 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[11, -3, 7, 12, 8, 1, 9],\n [8, -1, -2, 10, -6, 4, 5],\n [-6, 11, 7, -7, -2, -1, 3],\n [6, 10, 6, -2, 3, 10, -1],\n [-5, -10, -11, -7, 3, 7, 11],\n [2, 1, -11, 7, ... | 30 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 10, -7, -1, -10, -1, 10],\n [-12, -4, 7, 9, -7, -2, -10],\n [-9, -3, 6, -7, -12, -5, -5],\n [12, -7, 4, 6, -12, 2, 0],\n [8, -10, -11, -10, -4, 3, 11],\n [0, 6, 5, 8, -1, -1, -12],\n [7, -5, ... | 116 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 4, -3, -9, 9, -6, -6],\n [-5, 11, 11, -5, 3, -1, 2],\n [-5, 9, -4, -10, 9, 8, 3],\n [2, 11, -9, 7, 3, -3, -2],\n [-8, -2, 0, 2, -7, 3, 2],\n [-2, 7, -11, -11, -1, 3, 6],\n [-11, 4... | 106 | 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, 0, 3, -4, 11, -9, 11],\n [3, 10, -2, -6, 4, 9, 0],\n [-9, 1, -3, -3, -3, -1, -11],\n [10, -4, -8, -5, 8, 1, -6],\n [-6, -4, -10, 1, 4, 5, -1],\n [9... | 25 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, 5, 10, 11, 11, 3, 2],\n [-5, 2, 12, -12, 4, 2, 1],\n [1, -3, -11, -7, 4, -8, -8],\n [2, 2, 7, -2, -8, -12, -2],\n [-2, -7, 10, -5, -11, 2, 10],\n [9, -4, 2, -5, 3, 1, 2],\n [7, 0, -4, -12, -7, -5, 7]]\n\nPres... | 110 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 5, 4, 8, 3, 0, 9],\n [-9, -9, 8, 1, -8, 3, 1],\n [1, 1, 12, 11, 12, 1, 6],\n [-10, 4, 1, -3, 0, 9, -9],\n [-2, 2, 2, 11, -11, -2, -11],\n [10, -8, 0, -12, -6, -6, -3],\n [-7, 7... | 26 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, 3, -11, 6, -7, -12, -2],\n [5, -3, 5, -12, 6, 3, -6],\n [2, -12, 10, 8, -4, -11, 4],\n [12, 11, -3, -7, -8, -5, -5],\n [-8, -1, -6, 0, 0, 4, -9],\n [5, -3, -10, -1, -12, -2, 5],\n [0... | 28 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-10, -10, -7, -3, 11, 9, 5],\n [5, 1, 3, -6, -12, 4, 10],\n [12, -8, -12, 8, 4, -3, -1],\n [12, 7, 12, -11, 10, 3, 2],\n [0, 5, 7, 9, 1, 5, -11],\n [-11, -10, -8, 12, 3, 9, 2],\n [-1, -4,... | 35 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -5, 3, -10, -11, 3, 6],\n [-4, 3, 9, -9, -3, 6, 0],\n [5, 2, -9, -4, -9, 3, 8],\n [2, 11, -11, 1, -10, 9, 10],\n [-9, -12, 10, -4, 4, 1, 4],\n [-12, -3, 10, 3, 12, 6, 11],\n [... | 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[[-6, 6, -6, -8, -5, 8, 3],\n [3, 6, 12, 2, -6, -8, 10],\n [-2, -3, 12, 8, 10, -4, -12],\n [7, -12, -5, -10, -11, -9, 6],\n [-2, -8, 11, -3, 11, 10, -5]... | 30 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[7, -12, -2, -2, -5, 9, -10],\n [6, -1, -7, 10, -5, -8, -3],\n [9, 3, -1, 4, -7, -4, -3],\n [7, 1, 1, 4, 12, 3, -9],\n [-11, 3, -12, -10, 10, -2, 3],\n [5, 2, -4, -1, 5, -8, 11],\n [-5, -10, -11, 12, ... | 30 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -12, 9, 0, 10, 7, 4],\n [-10, -4, -8, -7, -9, 4, 8],\n [8, 8, 3, 3, 9, -2, -11],\n [4, 2, 5, -3, -7, 8, 3],\n [-8, -1, -7, 1, 10, 3, 12],\n [-6, -11, -7, -4, -... | 29 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -8, -11, -2, -12, 0, -8],\n [5, 1, 0, -6, -5, 5, -6],\n [7, 4, 3, -2, 6, -12, 8],\n [-5, -12, -4, 6, 8, -4, 8],\n [12, -3, 11, 10, -2, -12, 7],\n [12, -5, 7, -1, -12, -3, -9],\n [2, 6, -7, -8, -8, 5, -10]]\n\nPresent the answe... | 105 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[9, -11, -9, 5, -4, 6, -3],\n [9, 2, -12, -2, 1, -3, 6],\n [11, 8, 3, -5, -11, 10, 12],\n [-6, 6, -6, 2, -5, 1, -12],\n [0, -10, 8, -7, 6, 2, -9],\n [8, -10, -9, -... | 29 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-12, 1, 9, 10, 0, 12, -1],\n [-10, 5, 8, 0, 2, -3, -12],\n [-7, -4, -3, 2, -4, 10, 1],\n [-2, -6, 11, -11, 1, -7, -8],\n [-8, 6, 6, -7, -3, 10, 1],\n [4, -10, -12... | 29 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, 1, -3, -11, -8, -12, 12],\n [-3, 12, 9, -4, -10, 2, -9],\n [0, -7, 7, 4, 10, -8, 2],\n [-5, 12, -8, 11, 0, -12, -12],\n [-6, 9, -8, 1, 2, 8, 12],\n [4, 11, 5, -6, 9, 5, 6],\n [7, -6, -5, 0, 5, 11... | 29 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 10, -12, 9, -5, 8, -1],\n [-11, 2, 8, 11, 5, 4, 2],\n [7, 7, -4, -10, 7, 6, 5],\n [7, -5, -12, 11, 11, 2, 6],\n [-3, -1, -7, 0, -9, 0, 4],\n [-12, -8, 11, 4, 5, -6, 3],\n [-5, -1, 1, 6, -2, -... | 103 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -12, -4, -11, 1, 0, 3],\n [-11, -9, -1, 3, -3, -10, -9],\n [-7, 10, -8, 5, -10, -3, -2],\n [6, 1, 8, -2, 8, -9, 11],\n [9, -7, 4, 9, 6, 0, 9],\n [-3, -2, -7, -11, -12, -2, 3],\n [-10, -8, 2, 2, -9, 10, -9]]\n... | 117 | 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, -6, 12, 4, 2, -8, 0],\n [-9, 9, 4, 9, 4, 1, 1],\n [4, -5, -11, 0, 9, 3, 3],\n [-7, 9, 11, -9, -10, -7, -9],\n [5, -7, -8, -4, -2, -7, 3],\n [6, -2... | 28 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -4, 6, 2, 6, -11, -3],\n [6, 4, 7, 11, 8, -11, 6],\n [4, 5, 4, -11, 6, -12, -2],\n [12, -3, -8, 3, 11, -8, 11],\n [10, -1, -9, 10, -7, 6, -4],\n [-1, 2, 3, 0, 12, 8, 11],\n [-6, 12, 10, 7, -9, -2, -5]]\n\nPresent... | 32 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, 12, -3, -6, -6, -9, -10],\n [11, -6, -9, 0, 7, 4, -6],\n [4, -9, -2, -10, -2, -10, -1],\n [-12, -9, 1, -12, 1, 0, 0],\n [11, 2, 4, -1, 9, 10, 1],\n [-1, 5, -9, 1, 6, 0, 12],\n [10, 5, -2, -7,... | 117 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 2, -2, -7, 1, -10, 6],\n [7, 12, -2, 11, 4, 4, 10],\n [-10, 1, -6, 12, 6, -10, -11],\n [4, -4, 9, -7, 11, 8, -4],\n [-8, -11, 9, 2, -4, 6, -3],\n [-9, -3, -5, 9, 0, -6, -6],\n [-9, 2, -1, 3, -... | 107 | 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, -6, -9, 0, 6, -6, -3],\n [12, -1, -10, 12, 11, -1, 6],\n [2, -5, -1, 7, -7, -3, -11],\n [11, 0, 12, -6, -5, 10, 3],\n [-2, -9, 4, 3, 6, 10, -2],\n... | 25 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -2, 11, -4, 4, -9, 7],\n [6, -6, -12, -4, 0, 11, -11],\n [-11, 11, 2, 4, 0, -6, -4],\n [-1, -10, 10, 9, 2, -6, 10],\n [-12, 1, 6, 3, -3, -12, -8],\n [-10, 4, 5, 8, 6, 9, 12],\n [9,... | 109 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, -2, -5, 9, -3, 10],\n [-12, -1, -4, -8, -4, 3, 5],\n [-5, 10, -2, 7, 6, -9, 7],\n [-3, 11, 0, 7, 1, 8, -11],\n [-9, -6, 6, 4, 3, 0, 11],\n [11, 9, 10, 5, 8, -1, 10],\n [12, -12, 2, -10, -7, 1, 10]]\n\nPres... | 115 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-7, -12, 7, -7, -5, 2, 1],\n [3, 7, 10, 3, 6, 11, -12],\n [-9, 11, -3, 7, 5, -11, -9],\n [2, -9, 3, 2, 5, -6, 2],\n [9, -2, 6, -5, 11, -12, -10],\n [-8, 5, -1, -1, 8, 6, -4],\n [-2, 4... | 113 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, 6, -10, 8, 10, -8, -2],\n [11, -8, -6, -7, 0, -11, 6],\n [-2, 7, -8, -4, -7, 4, 6],\n [10, -5, -6, -8, 2, -3, 11],\n [3, -4, -6, -2, -4, 4, -4],\n [-10, 9, -5, 6, 7, 3, -6],\n [-6... | 107 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, 7, 3, -6, -9, -1],\n [4, -12, 4, -11, -7, -1, -2],\n [8, -2, 5, -5, 12, -6, 1],\n [3, -1, -4, 7, 10, 8, 3],\n [8, 6, 3, -4, 0, -8, 9],\n [6, -3, -6, -4, 12... | 26 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-7, -1, 11, 0, -5, 3, -11],\n [9, -6, -1, -6, 6, 1, -4],\n [5, -2, 3, 6, -2, 5, -2],\n [12, -9, 5, 6, 0, -9, -3],\n [9, -8, -10, 3, -5, 11, -6],\n [6, 1, 2, 4, 8, -12, -7],\n [10, 2, ... | 103 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 7, 1, 5, 9, -5, -11],\n [-4, -6, 5, 3, 8, -8, 10],\n [2, -8, -2, 9, 1, 12, 6],\n [-10, 11, -3, -7, -10, -11, 0],\n [5, -11, 2, -8, 2, 8, 4],\n [-11, 5, 2, 7, 10, -10, -8],\n [-2, -4, -8, 12, -12, 12, 1]]\n\nPrese... | 36 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-8, -5, 8, 1, 3, -7, -5],\n [-11, 6, -4, -8, -8, 12, 6],\n [-9, 3, 3, 3, -6, 5, 11],\n [8, -12, -10, 12, 8, -5, -12],\n [-6, -6, -5, 6, 4, -2, 2],\n [-4, 4, -2, -... | 37 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-8, 7, 8, 9, 9, -8, -2],\n [-1, 9, -4, 8, 0, 9, 7],\n [-10, 0, 9, -2, -2, 8, 7],\n [8, -6, 4, 3, 1, -12, -2],\n [0, -12, -11, -4, 0, -8, -4],\n [0, -8, 2, -6, 1, ... | 26 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 11, -10, -9, -12, -11, 0],\n [-4, -1, -3, -3, 5, -1, 9],\n [3, 10, -7, 11, 12, 11, 8],\n [11, -3, 2, -4, 11, -11, 5],\n [-1, -10, -6, -4, -5, 12, -7],\n [-12, 1, 3, 3, -9, -7, 2],\n [9, -5, -12, 0, 5, 5, 0]]\n\nPresent the answer... | 33 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, 1, -2, -6, 5, 8, 9],\n [-9, 4, 6, 1, -3, 12, -7],\n [5, 12, -9, -2, 0, -5, -3],\n [10, -2, -10, 2, -5, 7, 5],\n [8, -12, 11, -5, -10, -12, 7],\n [12, 3, -4, 4, 3, 10, -7],\n [10, -6, 11, 3, -5, -3, 1]]\n\nPresent the answer in... | 115 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -11, -1, 7, 7, 0, 2],\n [-1, 0, -5, 3, -10, 0, -1],\n [6, -11, -12, -5, -4, 12, -5],\n [8, 4, -4, -7, 2, 10, 11],\n [0, 8, 9, -1, 0, -6, 10],\n [5, 1, -2, 1, 4, 11, 8],\n [-11, 6, 3, 9, -3, 9... | 102 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[8, -8, -6, 0, 3, -8, 3],\n [2, -4, 9, 10, -1, -5, 0],\n [-8, 1, 3, -2, 7, -1, 2],\n [11, -1, -4, -12, -10, -1, 7],\n [0, 10, -7, -3, -3, 3, -12],\n [3, -9, -7, 6,... | 24 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -11, 7, -9, -12, -6, 10],\n [-2, -3, -12, -2, 11, -3, 1],\n [1, -6, 10, -2, 9, -9, 11],\n [-11, -6, 6, 1, 6, -6, -1],\n [-10, 2, -8, -5, 1, -9, -6],\n [-6, 5, 1, -5, -1, -3, 1],\n [-4,... | 30 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -2, -1, -10, -7, -2, 0],\n [-2, -5, -3, -11, 11, 1, 3],\n [4, -2, -11, 11, 10, -8, 3],\n [3, -11, 3, 12, -8, -5, 7],\n [1, 12, -3, 10, -11, -10, 5],\n [8, -11, 8, -4, -11, 12, -6],\n [-6, 1, -8... | 31 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-7, 1, 5, 4, -4, 0, 3],\n [8, -3, -3, -9, -1, -5, 2],\n [8, 10, 6, 2, -5, -5, 6],\n [-4, 11, 4, -5, -1, 2, -9],\n [-7, 3, 12, -8, 10, 0, 2],\n [4, 12, 9, 7, 9, -8, 6],\n [-6, -10, 0, 1, 3, 0, -11]... | 26 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 7, -6, -8, 1, -4, -3],\n [-6, 1, 12, 1, 12, -11, 4],\n [7, -9, 0, 5, -10, 6, -8],\n [-12, -4, 11, -5, -10, -11, -12],\n [-1, 9, 0, -3, 4, -2, -8],\n [12, -4, 0, 7, 10, -2, 10],\n [... | 110 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, 12, -8, -7, 6, -12, 3],\n [5, 11, 0, -12, -3, -6, -8],\n [0, 9, 3, 11, 7, 9, 1],\n [-2, 6, 10, -11, -5, 0, -6],\n [-1, -5, 3, 5, 6, -9, 12],\n [-1, 3, 8, 9, 4... | 30 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -11, -11, 8, 10, -6, -9],\n [0, 7, -2, -10, -11, 3, -10],\n [11, 2, 4, 3, 7, -6, 3],\n [-8, -11, -12, 9, 0, 3, -8],\n [-10, 2, 3, -2, 12, 6, 5],\n [8, -4, -5, 9, 6, 9, -8],\n [4, -8, 1, -6, -4, 4, -10]]\n\nPresent the answer in La... | 33 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 9, 0, 3, 8, -3, 5],\n [-10, -1, 3, 5, 4, -6, 6],\n [10, 10, -5, 4, 8, 12, -6],\n [-12, -5, 6, 7, 7, -3, -1],\n [11, -12, 11, 12, 12, 8, -9],\n [-9, -4, 2, 11, 2, -6, -1],\n [-10, 7, -4, 1, 0, 11,... | 31 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, 6, 3, -1, -3, -11, 5],\n [0, 11, -7, -1, 9, -9, -12],\n [-2, 10, -5, -11, -11, 3, -12],\n [-9, -7, 8, 7, 1, 7, 2],\n [-6, -6, 5, 10, -11, 7, 2],\n [-12, 8, 4, 7, 12, 0, -1],\n [11, 9, 2, 11, -8, -6, -5]]\n\nPresent the answer in... | 32 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, 1, -9, 8, 1, -3, 9],\n [3, -2, 9, 12, 1, 1, -11],\n [9, 0, -10, 5, 9, -9, 8],\n [8, 6, 3, -9, 6, 10, 2],\n [-12, 3, 2, 3, 9, 7, -12],\n [4, -8, -8, -6, 0, -1, -9],\n [12, -9, 10, 8, 8, -7, 11]]\n\nPresent the... | 124 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 8, 6, -7, -1, 1, 5],\n [-1, 11, 11, 2, 6, -5, -4],\n [-8, -8, -7, 10, -10, -8, -12],\n [-2, 8, 7, -12, -6, 2, 4],\n [-5, -11, 0, -1, -8, 0, -7],\n [12, 2, 10, 9, 8, 9, -2],\n [... | 36 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[11, -6, -5, -12, 12, -12, -10],\n [-5, -2, -12, 1, -12, -7, 8],\n [-7, -10, -3, -1, -3, 9, -11],\n [11, 9, 0, 3, 0, -9, -9],\n [-2, 10, 1, -10, 6, 9, 12],\n [-12, -8, 4, -12, 6, 6, -9],\n [6, -7,... | 133 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -2, 4, 10, -12, -4, 1],\n [2, 11, -12, -11, 5, 5, -7],\n [7, -5, -12, 2, -3, -9, -3],\n [-2, -8, -4, -8, -2, -10, -9],\n [-3, -6, -12, -7, -5, 4, 11],\n [-6, -12, -4, -2, 6, -11, 10],\n [-2, -10, 4, -3, -10, 9, -10]]\n\nPresen... | 120 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[8, 12, -6, -11, -12, -6, 7],\n [-2, 10, -7, 10, -9, 6, 8],\n [6, 1, -10, -9, -5, 5, -9],\n [-2, 3, -10, -6, -11, -12, -12],\n [-7, 6, -6, 11, -8, 8, 5],\n [11, 0, -12, -3, -4, 4, -12],\n [-12, -6, -9, 10, 8, -1, 3]]\n\nPresent th... | 124 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 10, -3, 1, -6, -9, -11],\n [11, 5, 3, -4, -8, -4, 12],\n [-5, 11, 7, 3, 7, 5, -9],\n [3, -9, -7, -10, 5, 2, -5],\n [5, 11, 10, -10, -7, 9, 8],\n [11, 2, -1, -8, -6, 9, 2],\n [-6, 0, 12, -10, 10, 0, -10]]\n\nPresent the answer ... | 119 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-11, 10, -9, 4, -7, -2, -7],\n [9, -11, 4, -10, -1, 1, -11],\n [9, 9, -8, -3, -3, 8, -4],\n [8, 0, -3, -7, -2, -9, 1],\n [4, 7, -11, -3, -10, -6, -6],\n [-12, -5, 10, -12, -5, 1, 1],\n [-11, -5, 6... | 31 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, 2, -2, 1, -2, -11, -11],\n [-1, 2, 4, 1, 12, 3, -5],\n [11, 4, -8, -1, -7, 5, -8],\n [-7, -4, 2, -3, 4, 6, -1],\n [-4, 2, 1, -12, 4, -12, 10],\n [8, 9, 0, -5, 0, 3, -11],\n [0, 5, -10, 0, 6, 0, 6]]\n\nPresent the ... | 29 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 6, 5, 12, -7, 6, 12],\n [-9, -9, 11, -6, -6, 10, 3],\n [3, -8, 2, 10, -9, 11, 12],\n [0, 6, -6, -1, -4, 4, -11],\n [3, -6, 5, -6, -12, -10, 8],\n [-2, 9, 2, 12, 12, -10, 11],\n [0, -9, 10, 9, -5, 9, -9]]\n\nP... | 129 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, -2, -9, 0, -4, -4],\n [10, 8, 6, -10, 12, 12, -1],\n [-2, 7, -2, 4, 8, 1, 3],\n [11, -3, -9, -3, 7, -1, -4],\n [2, -4, -6, 11, -1, 7, 11],\n [1, 9, 3, 6, 10, -10, -2],\n [1... | 27 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-10, -3, 0, -4, -7, 2, 3],\n [-8, 8, 0, 6, -11, -7, -12],\n [2, 2, 1, -6, -8, 7, 12],\n [3, 4, -2, 2, 7, 3, -10],\n [-7, 8, 10, 0, -12, 8, 1],\n [-11, -11, 2, 5, -4, -10, -9],\n [2, -8, 7, 7, -8, -3, 3]]\n\nPresent t... | 30 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[12, -1, 12, 1, 9, -2, 6],\n [-7, -3, 7, -10, 9, 2, -2],\n [9, -11, 12, 11, -7, 4, 5],\n [-9, 10, -4, -3, 8, -11, -2],\n [-2, -2, -12, 1, -12, 8, 10],\n [12, -4, 11, -12, 8, 9, 9],... | 36 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[7, 1, -8, 2, 2, 12, 3],\n [3, -9, 12, -4, -12, -8, -4],\n [7, -8, -9, 3, -11, 3, 5],\n [-11, 3, -12, 3, -10, 2, -2],\n [-3, 4, -9, 4, -9, 6, 12],\n [-12, 1, 11, -... | 32 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-7, -6, -7, 12, -1, -4, 5],\n [-11, 12, 4, 8, -12, 10, -4],\n [-7, -11, -7, -4, -10, 3, 12],\n [11, 2, -1, 10, -5, -7, -10],\n [10, -9, -3, 1, 8, 11, 2],\n [-6, -6, -5, -3, 6, 6, -11],\n [2, -12, -3,... | 32 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 11, -7, -7, -12, -1, 10],\n [10, -3, 12, 1, 2, 10, 11],\n [-9, 12, -12, -5, -10, 1, 4],\n [-11, 2, -7, -8, 1, 6, -4],\n [-5, -10, 5, -5, 3, 2, 8],\n [2, 3, 12... | 32 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, 3, -4, -2, -7, 4, -1],\n [9, -5, 3, -8, 8, -12, 4],\n [11, 8, -5, -3, 5, 2, 7],\n [0, -3, -4, 0, -10, 9, 10],\n [-10, -12, -11, -2, 1, -3, -6],\n [10, -12, -6, 2, -2, -7, 9],\n [-6, -6, -12, -3, 8, 2, -5]]\n\... | 112 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[11, 6, -10, 10, 2, -9, -7],\n [12, -3, 5, 3, 5, -7, 6],\n [4, 5, 0, -6, 7, -1, -11],\n [-1, -1, 11, -9, -9, 5, 3],\n [1, 4, 4, -10, -7, 10, 0],\n [-4, 8, -4, -5, ... | 28 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 1, -1, -7, 7, 0, 3],\n [-4, -11, 9, -10, -3, 7, -11],\n [11, -3, -5, 4, 9, -12, -7],\n [-6, 2, 5, -4, -5, 12, -3],\n [-9, 7, -5, -12, -5, 10, -1],\n [10, 12, 2, 0, 3, 10, 5],\n [-12, 4, 3, 10, -8, 7, 8]]\n\nPr... | 108 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -7, -1, -3, 9, 4, -11],\n [6, 7, -7, 0, -4, -1, 5],\n [-5, 12, 5, 12, 10, 12, 9],\n [-11, -5, -3, -4, 11, 5, -5],\n [6, -10, -4, 0, -4, 12, 7],\n [-1, 10, 0, -5, 2, 0, 8],\n [0, 4, 2, 12, 9, 6, -10]]\n\nPresent the answer in LaTe... | 30 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -3, 4, -5, 5, -1, 4],\n [10, -2, -4, 9, 11, 11, 12],\n [10, 12, 2, -4, -1, -2, 4],\n [-7, -5, -3, 12, 2, -9, 5],\n [-2, -4, -4, -5, -10, 8, 5],\n [1, -10, 4, -... | 25 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 7, -8, -2, -11, 9, 3],\n [-9, -8, -6, -7, 11, 9, -3],\n [1, -5, 1, 1, 7, 10, -10],\n [-12, -4, -4, 9, -11, 3, -5],\n [-7, 10, 0, -12, 6, 2, -12],\n [-3, -12, -1, -2, 4, -9, 10],\n [-6, -1, 0, -8,... | 30 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 1, 12, 9, 1, -3, -9],\n [-10, 12, 10, 1, -7, 10, 2],\n [-5, -8, -10, -10, 0, -11, 11],\n [-12, -1, -5, 6, -4, 1, 5],\n [-3, -4, -7, -12, -8, -3, 12],\n [0, 9, 10, -9, -12, 8, -11],\n [11, -9, 4, -3, 10, -1, -11]]... | 37 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-10, 1, 12, 2, 0, -4, -11],\n [6, 3, -2, -1, 12, -12, -11],\n [3, -11, 6, -3, 6, -3, 3],\n [0, 3, 5, 11, -5, 11, 5],\n [0, 12, -6, 8, 10, 11, 12],\n [5, -7, -4, -... | 29 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, -3, 5, -10, 8, -10, -8],\n [3, 7, 0, -2, 0, 6, -7],\n [11, 0, -9, 12, 9, -8, 6],\n [-8, 8, 1, -9, -1, -7, 6],\n [-3, -12, 10, 10, 3, -9, -4],\n [5, 4, 2, 6, -... | 34 | MATH |
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