messages listlengths 1 1 | ground_truth stringclasses 112
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[[0, -16, -22, 2, -4, -21, -11, 19, 2, 9],\n [20, -5, 8, 21, -14, -2, 16, -16, -10, -3],\n [-10, 5, 14, 2, 22, 3, 21, 10, 17, 17],\n [4, -8, -20, 6, 8, 17, -5, 1, 16, 21],\n [-15, 6, 14... | 373 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-22, -20, 0, 22, 17, -1, 21, -8, 18, -7],\n [4, 9, 11, 19, -11, -5, -5, -19, 11, 16],\n [-4, 20, 22, 8, 8, 19, -3, -3, 9, -3],\n [-7, -4, 8, -10, -3, 20, -11, 3, 12, 18],\n [-13, -11, 1, -14, -18, 8,... | 67 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, 17, -19, 9, 13, -19, -6, 19, 10],\n [-1, -5, 4, -8, 2, -13, -7, -19, 8, 9],\n [1, -5, 9, 5, -12, -15, -22, -21, -2, -4],\n [19, 7, 17, 2, -14, 19, 5, 14, 9, 18],\n [-12, -2, 1, -22, -7, 1, -13, 9, 5, 10],\n [15, -1, -22, ... | 333 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -11, 13, -22, 19, 16, -7, -17, 10, 20],\n [-10, 22, -14, 12, 5, 11, 9, -22, 16, 2],\n [-13, -21, -19, 2, -7, 17, 21, -18, 0, -3],\n [-20, -22, 2, -7, 18, -18, 13, -17, -11, 0],\n [15, -18, -21, -20, 18, -16, 3, -11, 22, -22],\n [... | 78 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 15, -6, -3, 19, 19, 18, 3, 5, 22],\n [-15, 20, -16, -16, 6, -20, -7, -10, -5, 21],\n [-10, 8, -20, 7, -20, 3, -21, 16, 11, 15],\n [-10, -12, 14, -16, 20, 4, -... | 68 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -8, -15, 13, 9, 16, 16, -1, -18, -13],\n [8, 14, 0, 9, 1, -19, 20, 15, -8, -12],\n [2, 3, 16, 14, 13, 10, 21, -3, 11, 22],\n [-11, 13, -19, -10, -20, -6, -16, 22, -9, 9],\n [3, 8, 8, -7, -22, 11, 3, 7, 18, -18],\n [1, -13, 15, 12,... | 68 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, -6, 6, 21, -4, 17, 6, -11, -15, 20],\n [20, 8, -8, 11, 3, 12, 6, 10, 10, 13],\n [-2, 7, -4, 9, -22, 10, 3, 19, 22, 4],\n [5, -3, -15, 3, 8, -18, -12, -2, -15, 3],\n [-11, 20, -10, -13, 6, -15, 19, 15, -22, -14],\n [-19, 10, 19, -... | 71 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-11, 16, -20, 1, -21, -19, 0, 0, -15, 19],\n [21, -11, -14, -12, 22, 8, -22, 12, 20, -8],\n [-16, 5, -17, -3, 1, 19, 13, 15, -11, -20],\n [5, -11, -7, 21, -8, 8, -2, -5, -17, -6],... | 70 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -8, -20, 0, 22, -11, 9, 5, 11, -22],\n [-13, 4, -11, 22, 13, 10, -19, -2, -3, -6],\n [11, -9, -13, -3, 12, -8, 16, 4, -8, -4],\n [3, -11, 1, 13, 10, -18, -14, 17, -9, 13],\n [2, -16, 11, 20, -... | 332 | 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, 22, 4, 1, -11, -22, -9, 9, -20, -13],\n [3, 8, -13, -22, 9, -4, -22, 3, -18, 3],\n [15, -22, 7, -11, 13, 13, 1, 19, 2, -15],\n [-11, 4, -11, 9, 12... | 74 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, 17, -22, -11, -6, 2, 6, 19, 5, -4],\n [18, -13, -12, -13, 7, -16, -18, 5, -3, 9],\n [-11, -18, 7, 10, -13, 16, 4, -11, -21, 7],\n [18, -18, 14, -9, 3, -15, 8, -20, 5, -9],\n [-12, 6, 17, -11, ... | 63 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 19, -18, 9, 6, 6, 19, -20, -19, 21],\n [2, -1, 19, -12, -15, 4, 21, -1, -20, 4],\n [-12, 4, -16, 4, -12, 2, 16, -7, -2, 3],\n [4, 22, -6, 8, -9, 0, -21, 3, 3,... | 72 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -17, 7, -11, 12, -12, -19, -10, -22, 15],\n [6, -9, -2, 18, 8, 18, -16, -8, 19, -14],\n [6, 1, -8, -2, 18, 1, -16, 1, 0, 2],\n [-15, 11, 12, -1, 11, 5, -22, 21, 14, 7],\n [2, -21, 5, 5, 0, 15, 1, 12, -15, 13]... | 321 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, 17, 18, 22, 4, 11, -11, -11, -8, -3],\n [-13, 3, -6, -13, -12, -6, -12, -8, -19, 2],\n [13, 8, 6, 8, -14, -22, -20, -19, -4, 18],\n [-1, -15, 2, -19, 22, -9, -18, 6, -2, -8],\n [0... | 361 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[19, -12, 10, -2, 16, 1, 21, -3, -14, 8],\n [5, 15, -18, 14, 18, 11, -13, 9, 14, -6],\n [13, 13, -10, -3, 15, -4, -1, -7, -17, -12],\n [-13, 8, -5, 9, 18, 19, 1, -7, 6, 16],\n [2, 17, 2, 17, 22, -4... | 65 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[7, 5, -2, -5, 18, 1, 3, 13, 20, -7],\n [9, -21, -14, -5, 22, -4, 15, -11, -10, 12],\n [-13, -1, -13, 12, 22, -7, 13, -12, -6, 2],\n [-22, -11, -20, -14, -4, -4, -3, -12, 1, -1],\n... | 78 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 7, -6, -10, 15, -16, -14, -2, 7, 14],\n [14, -1, 8, -19, -13, 7, 7, 18, -16, -8],\n [-4, -13, 16, 4, -20, 12, -5, 1, -10, 21],\n [-6, -6, -12, -6, -4, -16, -4, 11, 6, 7],\n [19, 6, 15, -15, -19, 5, -12, -5, -2... | 304 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -21, -3, 0, 10, -15, 14, 19, 7, 8],\n [18, -5, 8, 3, 1, -18, -12, 1, -22, -11],\n [15, 0, 21, 2, -11, -20, 1, 3, -8, 8],\n [20, 19, -2, -2, -2, 2, -11, 14, -5, -13],\n [-17, 6... | 66 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-18, -14, -10, 17, 6, -5, 7, -13, -4, -14],\n [-2, -22, 18, 3, -9, 16, 6, 20, -16, 1],\n [4, 19, -21, -21, -7, -11, 17, 3, -13, -8],\n [2, -19, 3, 0, 14, 19, -19, -22, -22, 16],\n [-20, -... | 66 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[12, 12, -18, 15, -17, 6, 0, 22, 14, 9],\n [-22, 11, 21, 5, -16, 14, 6, -4, 21, -4],\n [-3, -8, 1, 18, -15, -16, -4, 5, -11, 3],\n [12, -19, 11, -16, 4, -20, 10, -11, -4, -6],\n [-5, -20, -10, 9, -18, 2, -1, -15, -7, 9],\n [-18, 13, 2... | 61 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[14, -13, 6, 11, 1, 4, -14, -14, -13, -11],\n [-8, -20, 5, -14, 16, 7, 0, 7, -7, 13],\n [7, 14, -7, 5, -3, -9, 22, 6, 14, -4],\n [-6, -22, 6, 6, 1, -4, 20, -13, 13, -6],\n [-6, 9, -7, 0, -7, 9, -2... | 311 | 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, -13, -22, -22, 15, 4, 2, 3, 16, -13],\n [13, -15, 10, 6, 11, 4, 19, -19, -18, 19],\n [-12, -22, -10, -3, 11, 10, -9, -11, -12, -22],\n [-15, -5, -... | 72 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-18, 2, 20, 17, -6, 2, 19, 10, -18, -8],\n [19, -8, -22, 20, -5, -17, 11, -21, -6, -18],\n [-3, -9, -11, -19, 18, -13, 16, 7, 14, 3],\n [22, -19, -17, -8, 22, 22, -5, -6, 10, 13],\n [20, 2, 5, -10, 9, -4, 8, -8, ... | 365 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-7, -17, 16, 22, 6, 3, -14, -4, -16, 2],\n [1, 16, 14, 11, 6, 11, -3, -18, 21, 13],\n [7, -3, -12, -2, -3, -17, 22, 3, 0, -18],\n [2, 6, -19, 4, -13, 11, 4, -15, ... | 65 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 18, 5, -4, -22, 11, 15, 1, 18, 1],\n [-5, -22, -13, -19, -9, -2, 3, 15, -18, -8],\n [1, -13, 12, -6, 9, -14, 8, 18, -8, -20],\n [17, 12, -10, -1, -16, -3, 14, 3, -4, 7],\n [11, 12, 5, 12, 11, -7, 9, -6, 1, -18],\n... | 69 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-14, -16, 21, -14, 21, -12, -20, -10, -18, 9],\n [-1, 20, 3, -20, 18, -15, 1, 17, -10, -12],\n [15, 22, 20, -9, -18, -10, 1, -7, 6, -4],\n [-6, 8, 6, 9, -6, -16, ... | 66 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, -5, -19, 14, 17, -19, -6, -6, 11, -4],\n [-1, 16, 20, -22, -5, 16, 5, -10, 12, -14],\n [-6, 11, -8, -14, 16, -4, -12, 1, -2, -5],\n [3, -19, -21, -6, -22, -10, -13, -6, -2, 20],\n [-1... | 77 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 18, -5, -1, 18, 14, 3, -11, -17, -6],\n [-9, -13, 3, -20, 19, -8, -7, 15, -9, 13],\n [-10, 4, -15, 0, 18, -12, -18, -18, 2, -5],\n [1, -14, 20, -12, -9, 19, -14, -18, 4, -12],\n [5, ... | 67 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[8, 8, 16, -2, -16, 9, -11, 0, 20, 20],\n [17, -17, 9, 15, -8, 3, -3, -11, 18, 22],\n [3, 7, 6, 7, -10, 18, 20, -1, 20, 18],\n [-6, 0, 2, -17, 14, 3, -2, 12, -17, -1],\n [-6, -12, -19, 21, -13, -6, 15, -5, -4, -1],\n [-8, 21, -4, ... | 320 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -12, 7, 5, 0, -8, -12, 20, -2, 22],\n [16, 8, -8, -6, 2, 1, 22, 13, 10, 21],\n [-19, -22, 15, -12, -2, 2, 5, -17, -17, -1],\n [-8, 10, -6, -11, 8, 12, 11, 9, 0... | 64 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 19, -8, 21, -18, 19, 10, 7, -7, 13],\n [14, 18, 15, 1, 2, 4, -18, -2, 20, 12],\n [-17, -14, 22, 4, -22, 7, -8, 9, -3, -19],\n [11, 15, -3, 5, 16, 2, -12, -15, 11, 4],\n [21, -1, -15, 10, 16, -14, -1, -14, 8, 11],... | 72 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-13, -5, 11, -9, -13, 15, 9, -20, -15, -14],\n [-12, -7, 11, 1, 8, -18, 10, 7, 7, -8],\n [16, -7, 3, -11, -4, 12, -3, -2, 14, -8],\n [-7, -7, 0, 21, -19, 6, 14, 1, -15, 21],\n [-1... | 71 | 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, 16, 22, 22, 5, 20, -18, -7, 5, -21],\n [19, -13, -4, -3, 15, 22, 12, 18, -13, 13],\n [-7, 3, 8, 19, -22, 0, 19, 4, -4, -7],\n [15, -15, -7, -11, -1... | 73 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-20, 16, 14, 11, 5, -9, 5, 7, 7, 4],\n [-21, 14, -10, 16, 19, 5, -3, 16, -5, 11],\n [22, -6, 15, 0, 8, -14, 12, 2, 16, 7],\n [-18, 5, -16, 19, 19, 19, 15, -4, 2, -5],\n [3, 22, -3... | 63 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-21, -10, 20, 20, -14, -2, 18, 21, -22, -3],\n [-18, -11, 20, -2, 16, 0, -15, -1, 3, -4],\n [-8, 14, 18, -2, -10, -16, 2, 10, -20, 16],\n [9, 18, 13, 17, 0, -21, 9, -17, -16, -2],\n [10, -7, -20, 3, 2, -8, -1, 20, 14, -3],\n [6, ... | 345 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, 7, 20, 15, 21, -11, 8, 21, 14],\n [15, -16, -16, 12, 4, 3, 17, 20, -4, -1],\n [-22, 11, 9, 6, -1, -3, 5, 22, 5, -15],\n [-2, -5, 19, -8, -13, 4, -5, -3, 15, 10],\n [7, -20, -22, -13, -22, ... | 63 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -20, 1, 11, -15, 1, -7, -17, -2, 9],\n [16, -1, -14, -5, -11, -17, 4, 21, 16, -22],\n [-8, -9, -10, -2, 18, -17, -3, -19, 17, -4],\n [20, 17, -13, -18, -21, 8, 21, -3, -17, 20],\n [-4, -5, 7, -16, -6, -19, -20, 2, 7, 13],\n [... | 384 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, 20, -4, -7, 3, 10, -8, 14, -3, -18],\n [17, 1, -17, -11, -19, 20, -10, -2, -18, -10],\n [-21, 21, -17, 6, 0, 12, -13, -3, 2, 13],\n [-13, 4, -16, -2, -1, -5, -22, 2, -2, 7],\n [9, 12, -9, 16, 19, 2, 6, 17, 9, -12],\n [5, -18, 12,... | 70 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-18, 4, 16, 10, 17, 15, -19, 20, 15, -21],\n [-4, -5, -12, 12, -12, 10, -21, -22, 10, -10],\n [4, -22, 19, 6, 22, 17, -1, 16, -3, 21],\n [17, 22, -21, 18, -6, 18, -18, 3, -10, 11],\n [7, 21, 18, -21, -11, -1, 15, -10, 2, 17],\n [16, ... | 75 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, -22, 12, 18, 3, -19, 8, -18, 0, 11],\n [-8, -20, -4, 20, 16, 16, 4, -1, -8, 17],\n [19, -8, 9, 8, 16, -6, -10, 15, 14, -7],\n [5, 11, 9, 1, 14, -18, 21, 0, -2, -22],\n [-10, 21, -... | 365 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -17, 8, 13, -12, -5, 11, -20, 18, 15],\n [13, -6, 7, 7, 20, 8, 9, -4, -14, -7],\n [15, -4, 7, 13, -12, -8, 1, 18, -2, 20],\n [-13, 19, 2, 9, 10, 1, -2, 3, -6, -4],\n [-20, -10, -21, 18, 22, 9, 10, 9, 19, 2],\... | 351 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-18, 16, 11, 15, 20, -21, 22, 10, 4, -20],\n [-21, 5, 7, 18, 0, 10, -9, -9, -10, -19],\n [-4, 1, 13, -17, -11, -14, -10, 1, -8, 7],\n [9, 9, 11, 12, -5, -4, -8, -1, 2, 1],\n [-17, 13, -13, -11, -18, -3, 14, -5, 17, 10],\n [18, -1... | 354 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[20, -2, -4, 11, 7, -3, -5, -2, 13, -16],\n [-18, -14, 22, -5, -22, 13, 22, -9, -15, 14],\n [-3, 8, -16, 18, 15, 21, 20, -8, 12, -6],\n [4, -2, 17, 21,... | 79 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-16, 0, 0, 1, 8, -1, 4, 15, -18, -5],\n [-15, 12, -6, -11, 16, -1, -17, 7, -21, -18],\n [-21, 12, -18, 8, -6, 4, 8, -13, -11, -5],\n [-10, -15, 12, 21, -19, -16, -2, 22, 21, -8],\n [11, -1, -22, -17, -22, -4, 4, -13,... | 74 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, 0, -6, 5, -5, 18, -12, 11, -8, -22],\n [10, -14, 21, -6, -8, -19, 14, -17, -17, -4],\n [0, 7, -22, -14, -1, -22, 13, 2, -7, 3],\n [5, -18, -1, -9, -14, -9, -7, 7, 9, -17],\n [-6, -22, -5, -12... | 338 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[14, 21, -22, 2, 2, -22, -20, 16, -2, 20],\n [2, -2, -20, 17, 6, 12, -1, 0, -10, 11],\n [0, 12, -4, -8, -8, 3, 16, -20, -6, 7],\n [5, 11, -7, 20, 18, -12, 1, 0, 2,... | 70 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-15, 22, -7, 6, 11, 6, 12, -13, -22, -18],\n [-20, 16, -9, 4, 6, -22, -5, -20, 3, -2],\n [1, 22, -3, 6, -5, -20, 10, -5, 14, -2],\n [21, -4, 0, -3, 1, -4, 3, 10, 9, 12],\n [2, 10, 1, ... | 333 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[12, -7, -17, -7, -15, -3, 8, -3, -14, 7],\n [-10, 3, -21, 18, 22, 1, -10, -7, -5, -7],\n [-21, -22, -13, 2, -9, -6, -5, -16, -2, 6],\n [4, -19, -11, -1, 17, 11, 3, 5, -4, 8],\n [-9, 0, -6, 0, -6, -15, 15, -13, 7, -16... | 68 | 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, 16, -22, 17, -7, -3, 1, -8, -13, -11],\n [14, 12, 4, -10, 7, -20, 12, -11, 6, 7],\n [-1, -6, 4, -1, -16, -12, -7, 13, -1, 17],\n [14, -20, 12, 15, ... | 61 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-11, 20, 11, 2, -9, -14, 7, -11, -13, 1],\n [11, -11, 3, 9, 12, -10, -4, -10, -1, 0],\n [-22, -15, 22, 16, 11, -10, 21, 18, -13, -20],\n [5, 4, -2, -12, 1, -11, -16, 19, 9, -13],\n [5, 3, 6, 4, -... | 351 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, -10, 7, 17, -6, -14, 16, -1, -8],\n [6, -7, -3, 2, 17, 1, -7, -7, 2, -22],\n [10, -16, 15, 22, 5, 16, 5, 9, 1, -15],\n [21, 9, 5, -20, -16, -17, 6, 22, -9, 22],\n [17, -4, ... | 72 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -19, 16, -1, 6, 19, 14, -10, -8, 12],\n [2, -20, -11, -9, 17, 9, -19, 6, 8, 9],\n [1, -12, 7, -4, 13, -17, -21, 16, -4, 17],\n [-5, 18, 13, -3, 14, -22, 0, 15, -3, -19],\n [15, -18, -17, 3, -22, -8, -7, 0, 18, -1],\n [-18, 20, -1... | 79 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[19, -19, 7, 5, -2, -11, -10, -10, 4, 5],\n [-5, 14, -7, -2, -13, -9, 5, 6, -12, 7],\n [17, 4, -20, -22, 9, 16, -2, -21, -13, 8],\n [-5, -16, -18, 6, -19, -20, -10, -20, -15, -19],\n [19, 12, -11, 1, ... | 75 | 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, 2, 11, 4, 12, -2, 16, -20, 2, -19],\n [-8, -20, -12, 5, -20, -5, -14, -8, 17, -15],\n [17, -9, 15, -10, 16, -13, 21, 7, -18, -1],\n [12, -18, -11, ... | 72 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 20, 13, 2, -3, 15, 10, 10, 15, -22],\n [10, 15, 1, -14, 8, 15, 5, 0, 7, -5],\n [3, 10, -7, 6, -7, 10, 16, 15, 0, 3],\n [-6, 15, 22, 1, 20, -4, 19, 4, -21, -15],\n [-8, 18, -10, 4, -1, -22, -18, 6, -8, 7],\n [-17, -17, 0, -18, -1, ... | 74 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -7, -22, 12, 6, 15, -10, 17, -11, 0],\n [-7, -9, -7, -17, 13, 1, 4, 2, 17, 13],\n [6, 8, -20, -10, -19, -12, -8, -21, -8, -17],\n [-10, 12, 21, 21, 17, -10, -11, -7, 20, 18],\n [-3, 17, -10, 11, -4, 22, 4, 6, -4, 20],\n [4, -2... | 350 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[14, -13, -14, 10, -10, -3, 21, -12, 18, 6],\n [-10, 21, -9, -14, 19, 15, -4, 19, -15, -5],\n [11, 13, -14, -7, -18, -8, 1, 21, 20, 16],\n [2, -7, 19, -1, -7, 10, -18, -16, -5, -17],\n [-11, 21, 10, 11, -2, -5, -9, 19... | 66 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, -22, 19, -18, -21, -1, 9, 18, -16, -2],\n [-6, -3, -22, 9, 17, 9, -3, -13, -17, 18],\n [10, -13, 2, 1, 8, 6, -11, 20, 14, 19],\n [-14, 6, -20, -19, -2, -17, -21, 14, -3, 22],\n [10, -9, -3, 2... | 75 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, 22, 14, -15, 11, -4, 13, 11, 13, -17],\n [-22, 22, 7, -8, -14, 6, -21, 7, -19, -4],\n [-3, -18, -14, -3, -7, -3, -3, 3, 16, 10],\n [-11, -2, 0, -3, 0, -17, 22, -11, 12, -15],\n [4, -7, 9, 6, -16, -7, 6, 2, 20,... | 320 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[22, 3, -6, 15, -20, 10, 7, -8, -15, 7],\n [0, -11, 16, -15, -14, -15, 15, 10, 10, 22],\n [-12, 0, 20, 20, 2, -8, -13, -3, -7, 12],\n [11, -2, 17, -22, 2, -9, -4, -15, 18, -8],\n [21, -5, -22, 10, -22, 11, -19, -6, -2... | 77 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, 19, -10, 14, 7, -8, 12, -20, 6, 1],\n [22, 0, -14, -21, -8, 9, -5, 6, 17, -20],\n [10, -16, 7, 4, 15, 6, 8, -22, 18, 20],\n [4, 4, 6, -18, -20, 6, 18, 16, -10, 10],\n [-3, -20, -17, 20, -6, -19, 10, 10, -17, 18]... | 72 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[20, -17, 19, 19, 22, -6, 13, -5, 10, -5],\n [-16, 6, -18, -7, 8, -18, -13, 6, 6, -7],\n [-19, -22, -15, 5, -22, 5, -20, -21, 2, 14],\n [-12, -5, 19, 16, 17, -3, -6, -16, -6, -19],\n [13, 7, -22, 12, -11, -6, -7, 5, 9... | 72 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[12, 15, 15, 13, -19, 22, -13, 9, -13, 20],\n [22, -13, -12, 16, -14, -10, 19, -5, 14, -12],\n [5, -17, 10, -9, 6, 16, -8, -18, -1, 8],\n [-4, -5, -17,... | 72 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -11, -15, 17, -1, 16, 16, 21, -7, 11],\n [-7, -9, -17, -13, 1, 4, -14, -7, -21, 8],\n [-4, -12, -1, 6, 8, -15, -13, -17, 8, 12],\n [17, 6, -2, 18, -18, -18, 1, -8, 5, 11],\n [-10, 21, 9, -1, 6... | 67 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-16, 13, -22, 7, -5, 19, 16, 3, -12, -22],\n [15, -18, -1, -10, -6, -16, 15, -16, -11, 15],\n [0, -15, -8, 7, -14, 22, -2, 21, -9, -15],\n [13, -14, 3, -3, 15, -17, 11, 0, 16, 10],\n [-2, 18, 3, -... | 79 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-13, -5, -14, 22, 3, 19, -14, 13, -8, 1],\n [17, -21, -19, 15, 8, -3, 16, 22, 3, -18],\n [-19, -1, -17, 14, 8, -18, -16, -18, -19, 4],\n [-14, 14, -21, -4, 16, -6, -6, 17, 1, -10],\n [5, 22, 19, -9, 0, 0, -13, 15, -6... | 64 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[18, -11, 9, 20, 10, 8, 10, -3, 18, 14],\n [14, 17, -9, 13, -11, 3, 11, -17, -10, -1],\n [12, -4, 14, 0, 9, 21, -12, -19, -11, 16],\n [7, -13, 1, 0, -2... | 78 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[19, 22, 4, -1, -20, 15, 1, 10, 12, 17],\n [6, -15, -12, -7, 10, -12, 6, 22, 1, -21],\n [-18, 1, 21, -16, 8, 7, -17, -18, -8, 4],\n [12, -14, 0, -6, 0, 16, 6, 16, 22, -12],\n [-10, -11, -2... | 69 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[14, -12, -12, 10, -21, 10, -20, -3, 10, 3],\n [11, -9, 6, -21, -15, 4, -15, -16, -12, 16],\n [7, 16, -2, -2, -16, -3, -9, -3, -18, 8],\n [-11, -11, -21, 3, -19, 7, 11, 14, -3, -21],\n [22, 12, -8, -9, 13, 7, 21, 4, -... | 67 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[19, 14, 11, 18, -17, 13, -9, 18, 1, 10],\n [19, -4, 6, -17, -20, -5, -2, 6, 19, 13],\n [8, -15, 9, -7, -1, -21, -8, 17, -6, -10],\n [12, 2, -13, 22, -12, 10, -9, 11, -1, 21],\n [-19, 21, 3, -22, -... | 65 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[19, 0, -1, 7, 4, 11, -12, 6, 14, -17],\n [-7, -3, -13, 15, 14, -13, 21, 2, -1, 9],\n [-6, 3, -7, -13, -6, -21, -21, 6, -19, 7],\n [-11, 11, -9, 1, 1, -5, 2, 2, 18... | 59 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[21, 4, 15, 16, -6, -14, 9, 0, 21, -9],\n [-12, -19, 15, -7, 13, 2, -18, -13, -18, 18],\n [-5, 0, 15, -9, 0, 12, 10, 15, -22, -17],\n [-2, 4, -18, 4, 2... | 63 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[14, -18, -9, -9, -7, 16, 20, -19, 14, -9],\n [18, 0, -14, 1, -12, 5, -4, -4, -11, 11],\n [-11, -20, 7, 12, -8, 20, -1, -14, 5, 6],\n [16, 16, 16, -6, -19, -19, -16, -21, 14, -13],\n [-5, 5, 12, 12, 7, -2, 2, -10,... | 329 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -14, -15, -8, 11, -19, 4, 15, -10, 9],\n [12, 13, -13, 0, 0, -19, 21, -18, -19, 7],\n [18, 10, 17, -10, -5, 9, 10, -16, -9, 17],\n [-9, -13, 18, 16, 14, -5, -4, 17, 19, 20],\n... | 78 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-15, 22, 2, -12, -11, 22, -15, -13, 12, 15],\n [-2, -5, -5, 3, -3, 2, 8, -5, -7, 22],\n [20, -5, -9, -16, 15, 6, 0, 19, 11, -6],\n [22, -5, -4, -21, 6, -21, -5, 16, 19, 13],\n [13, -2, 10, -21, -13, -8, -11, -20, -19, -14],\n [19... | 362 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[17, -4, -17, 18, -6, 0, 17, -14, 14, 15],\n [-2, -2, 4, -12, 16, 7, 5, -3, 22, 15],\n [-19, -5, 6, 13, 4, -22, 12, -18, -17, 13],\n [-18, 21, 9, 16, 22, 8, 17, 22... | 79 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, -9, 10, 6, 1, -17, 3, 16, 21, -20],\n [17, 9, 3, -20, -11, -9, -4, -19, -11, 12],\n [0, -20, -20, 16, 19, -7, -10, -4, 5, 15],\n [-14, -6, -16, -15, 14, -11, 5, -21, 5, 2],\n [4, 12, -8, 12,... | 358 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -16, 5, -18, -10, -21, -3, -11, 4, -16],\n [11, -2, -5, -13, 15, 16, 21, -2, -7, -3],\n [17, 1, -2, 21, 8, -13, -3, -9, -4, 7],\n [-7, -1, -3, -17, 22, 20, 10, 18, -4, -18],\n [-16, 11... | 72 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-20, -10, 11, -6, -22, -9, -22, 1, -12, -20],\n [-10, -1, 18, 18, 7, 2, -16, 2, 16, 2],\n [-21, 11, -1, -22, -5, -7, -13, 8, -10, 11],\n [11, 19, -11, 14, 17, -6, 18, -8, -10, -15],\n [-6, -12, 17, -... | 70 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, -22, -19, 3, 4, 17, -7, 7, 15, 10],\n [-7, 10, -3, 8, 4, 9, -1, 13, 4, 2],\n [-21, 15, 0, -11, 14, 14, -2, 19, -12, -2],\n [14, -19, 3, -3, -16, 15, 4, -6, 9, -13],\n [-12, -5, -21, 12, -17, -... | 317 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, -21, 3, -14, -6, 12, -20, -17, 20, 0],\n [12, -8, -15, 9, 11, -12, -20, 6, -13, -5],\n [-5, -11, 4, -4, 18, 10, 2, 21, -21, -21],\n [-18, -1, 10, 21, -18, 5, -9, 17, 20, -13],\n [18, -8, -13, -19, 20, -5, -6, 8, 10, 2],\n [-... | 364 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[13, 18, 15, 11, -20, 0, 20, -6, 6, -22],\n [-20, -9, -12, 7, -2, -7, -14, -21, 3, 19],\n [-20, -8, -11, -4, 18, -9, -8, 0, -12, 20],\n [-20, 20, -22, -19, -2, 2, -3, -13, -5, 10],\n [12, 2, -20, -10, 12, 2, -5, 7, 17, 7],\n [1, 3... | 361 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, 6, 11, -7, -1, -15, -11, 11, -7, -14],\n [4, 12, -12, -4, 8, -8, 4, 10, -16, 0],\n [13, -1, -22, 4, -12, -11, -2, -15, -10, 14],\n [10, -21, -14, -10, 3, 22, -14, -8, -16, 20],\n [14, -14, -9, 7, -3, 0, -8, ... | 332 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, 10, -18, 17, -19, -16, -7, 14, -12, -18],\n [6, 2, -20, 9, 7, -3, 7, -20, 21, -8],\n [18, -9, 17, -13, -6, -8, 6, 11, 12, -14],\n [-6, -21, 3, 15, 20, 5, 7, 20, -14, 5],\n [-... | 69 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[7, -22, -17, -9, -20, 16, -8, 8, -4, -1],\n [-16, 4, 12, 20, -18, 12, 13, 14, 0, 13],\n [-19, -21, 14, 12, -19, -19, -17, -6, -19, -1],\n [-2, -11, -16, 5, -10, 20, 20, 10, 17, -10],\n [-19, 2, -3, 15, 12, -14, 7, 16, 0, -12],\n ... | 366 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 6, -7, 17, 15, -3, 22, -7, -2, -5],\n [18, 8, -21, 1, -17, -6, 3, 14, -21, 3],\n [21, 14, -22, -21, 10, -12, 7, 11, 4, 20],\n [11, -16, 16, 16, -21, 7, -20, -21, 7, 14],\n [6, 12, ... | 351 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[7, 21, -19, 18, 15, -15, -15, -2, 17, -15],\n [6, -8, -9, 15, -13, 4, 17, 4, 19, 17],\n [12, 13, -12, -10, 12, -2, 14, 21, -11, 2],\n [5, 21, -5, -13, 16, -20, -18, -11, -9, 22],\n [18, 9, 19, 10, -17, 7, -17, 8, -21, 3],\n [9, -... | 348 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -6, 3, -4, 10, -16, 8, 16, -8, -21],\n [22, -21, -6, 11, 2, -12, 21, -14, -16, -12],\n [-19, 14, 3, 11, -7, 18, 7, -7, -17, 10],\n [-8, -3, -11, 1, 17, 9, 18, 10, -11, -8],\n [-15,... | 342 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 1, -10, 16, -18, -8, 1, -12, -6, -15],\n [19, 1, 15, 4, 19, -16, 1, 4, 14, 22],\n [-20, -1, 15, -1, 17, 6, -13, -6, 19, -16],\n [20, 12, 17, -20, -10, -17, -6, -21, 16, 15],\n [10, 19, 0, 10, ... | 371 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-19, -22, -15, -21, -6, 18, 20, 0, -2, 6],\n [-18, 9, -2, -14, -16, -5, -8, 2, -7, -3],\n [22, 14, 11, -18, 10, -22, -16, 19, -19, -19],\n [22, -10, 12, 20, -5, 20, -12, -10, 20, 8],\n [16, 19, -17, 15, -12, -2, 3, -8, 1, -5],\n [-15... | 82 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -3, 21, -10, 14, -4, -18, 13, 1, 11],\n [-15, -19, 21, 15, -15, -14, 18, 18, 8, 8],\n [17, -16, 2, -10, -18, -5, -16, 15, 19, -8],\n [22, 10, 8, -14, -4, -17, 13, 9, 5, 15],\n [-13, ... | 69 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-13, -6, -14, 19, -8, -19, -2, -16, -15, -3],\n [-16, -17, -14, -9, 13, 6, -20, 22, 8, 1],\n [1, 13, 12, 2, 16, -2, -8, 11, -14, -20],\n [-13, -8, -7, -10, 21, 21, -22, 10, -15, -7],\n [12, -9, 1... | 335 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-19, 3, 22, -20, 13, -16, -13, 22, -19, -16],\n [-1, 7, -1, 6, -12, -7, 21, -17, 14, -10],\n [10, -15, -12, 10, 10, 21, 17, 4, 16, -5],\n [22, 9, 22, 18, 1, -1, -... | 86 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, -5, 16, 0, -14, -20, 12, 1, -17, -4],\n [-9, -20, -17, -6, 13, -1, -19, -13, 9, 20],\n [-19, -10, -4, 20, 15, 3, 7, 20, 8, 15],\n [-11, -4, 0, 18, -13, -8, -6, -10, 1, -7],\n [16, 15, 7, 22, 21, -8, -19, 21, -13, 17],\n [9, -2, 6... | 75 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, -7, -19, 7, 15, -3, 18, -11, 5],\n [21, -22, -14, 19, 10, -22, 19, -14, -1, -14],\n [-18, -21, -9, -11, 6, -7, -14, 9, 1, -3],\n [-3, 19, 20, -18, -3, -7, -4, -11, -6, 11],\n [4, 18, 3, 11, -2, 19, 18, -20... | 340 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, 11, -4, -7, -17, 18, -8, -14, 6],\n [19, -21, 10, 15, 0, -10, -3, -16, -6, -2],\n [5, 7, 0, -2, -22, -6, 9, 1, -16, 12],\n [13, -9, -11, 16, 0, -9, 2, -1, 22, 14],\n [6, -15, -12, 7, -1, -8, -2, 2, -10, -16],\n [-5, -11, 3, -18... | 61 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[18, 0, 12, -7, 19, -15, -7, -17, 13, 8],\n [5, 12, -6, 7, -14, 0, 22, -22, -11, -6],\n [10, -1, -13, 3, -9, 2, -12, -4, 20, 5],\n [4, -12, -1, 2, 7, -4, 16, -16, -17, -14],\n [-5, 8, -17, -1, -14... | 325 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, -20, -1, 15, -2, 12, 21, 20, 4, -17],\n [-12, -6, 13, 8, 20, -10, 6, 15, -3, 15],\n [12, 16, -22, 21, -10, 4, -20, -3, 5, -17],\n [-14, 22, 10, -19, -10, 15, -22, 2, -22, 9],\n [19, -4, -6, 16, 18, -11, -3, -... | 376 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, -14, -18, 17, 7, 0, 10, -2, -10, 19],\n [18, 18, -11, -1, -19, -14, 8, -21, 13, -12],\n [6, 13, 11, -14, -11, -2, -18, -16, 21, 14],\n [-20, -8, -4, -20, -3, -8, 15, -12, -9, -19... | 373 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-19, 7, 12, 4, 4, 21, 20, -18, 17, -12],\n [20, 12, -12, 15, 15, -18, 14, 14, 3, 10],\n [10, 0, -16, 9, -14, -7, -14, 21, 20, 5],\n [0, -11, 19, -14, 22, -11, -14, -4, 13, 10],\n [-10, -21, 17, 21, 2... | 66 | MATH |
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