messages listlengths 1 1 | ground_truth stringclasses 140 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[12, 25, 2, -12, 16, -19, -6, 12, -8, -4, -16, -16],\n [-3, 26, 9, 13, -3, -24, -5, 26, -25, -3, 17, 3],\n [11, -25, -6, 6, -15, -5, 17, -2, 22, 0, 15,... | 98 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[10, 20, -13, -24, -26, -22, -1, -13, 12, 0, -18, -12],\n [-12, -1, 15, -14, 24, 5, 12, 22, 25, 5, -23, 3],\n [10, -4, 12, 18, -12, 16, 2, 9, -14, 5, -20, 24],\n [-5, 1, -25, 15, 18, 26, -21, 1, 1, 17, 17, -7],\n [3, ... | 88 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[23, -4, 4, 3, 15, 8, -20, -11, -1, 21, 25, 22],\n [-25, -26, 21, -15, -22, 10, 5, -18, 14, 8, -8, 21],\n [-11, -24, -7, -3, 6, -3, 25, -16, 22, -19, 9, 11],\n [13, -7, 8, 21, -2, 8, -2, 2, -9, 19, -9, -25],\n [8, -11, 14, 9, 6, -23, ... | 92 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[8, 23, -2, -3, -14, -20, 9, 18, -7, -26, -19, 19],\n [-11, -13, -15, 24, -4, -12, 1, 7, -25, 5, -4, -5],\n [24, -2, -5, -5, 22, 25, 15, -21, -12, 16, 10, 6],\n [-19, 26, 17, 17, -22, 12, ... | 87 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, -15, -24, -26, 6, 13, -17, 16, 17, 2, -14, -15],\n [4, 19, -25, 24, 23, 8, -4, -10, -1, -19, 2, -1],\n [-17, -1, 7, 24, 14, -20, -23, 26, 23, 18, ... | 88 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-23, 9, -21, 4, -8, 17, 12, 0, -17, -1, -8, 12],\n [-24, 18, -14, 23, 1, -7, 1, -19, 14, 12, -26, -24],\n [-14, 1, 22, -2, 6, 11, 26, -21, 17, 18, 5, 18],\n [20, ... | 80 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-13, -18, 19, -26, 24, 18, -14, -23, -26, 22, 13, 5],\n [7, 1, 4, -19, 12, -1, 7, -24, 23, -15, -26, 17],\n [-22, 3, 3, -10, 21, 20, -4, -12, 10, -6, -13, -25],\n [-16, 24, 12, 11, 7, 11,... | 96 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-25, 18, -1, -13, 24, -20, -24, 20, -4, 19, 16, 20],\n [18, -9, 11, 8, 24, -12, -2, 10, 1, -17, 12, -10],\n [12, -5, -1, 17, -2, -10, -14, -7, -2, -23, -17, -24],\n [14, 18, -9, 20, 9, 20, -5, 7, 20, -19, 13, 22],\n [17, -8, 15, 14, ... | 106 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[11, 8, 3, 4, 22, -22, 17, 23, -13, 26, -16, -18],\n [7, -15, 8, 8, -26, 13, -5, 2, -19, -16, 14, 10],\n [-13, 3, 8, -6, 10, -22, -8, -13, -1, -23, -2, 18],\n [15, -2, -9, 13, -19, 12, 13,... | 91 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[17, 9, 21, -23, -22, 10, -19, 15, 22, 1, 4, -18],\n [24, 2, -13, 13, 14, -5, -16, -4, -26, 19, 10, -6],\n [-1, 19, 9, -4, -26, 24, 13, -12, -6, 20, -18, 26],\n [-18, -17, 25, 26, -1, 14, 8, 25, -2... | 91 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[24, 6, 1, 20, -19, 7, 8, 5, -3, -13, 5, 19],\n [16, -11, -23, 25, 10, -6, -13, 4, 21, -9, -20, -17],\n [-20, 6, -4, -6, -8, 21, -8, 9, 2, -9, -25, -26],\n [20, -2... | 94 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -22, 6, 9, 20, -7, -8, 8, 25, 16, -10, 18],\n [16, 7, -18, -1, -25, 26, -18, -18, 13, -10, -26, -2],\n [16, 13, 15, -2, 12, 8, -24, 23, 10, 17, 17, 24],\n [3, 11, 7, -15, -8, 10, 17, 22, -10, -17... | 86 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 22, 2, 26, 17, -11, 17, 20, -17, 3, -2, 12],\n [-7, -22, -26, 3, 22, -24, 18, -13, 3, 23, -23, -9],\n [10, -2, 21, -26, 26, 19, -12, -18, -12, 22, -3, -23],\n [-15, 10, 10, 16,... | 105 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, 13, 1, 6, 21, 14, -14, 16, 18, -2, 26, 15],\n [9, 0, 11, -20, -22, 16, 18, 24, 4, -4, 15, -17],\n [5, 16, 26, 3, 12, 4, -9, 9, -25, -13, -14, 2],\n [-15, 12, -25, 5, -14, 19, 0, 22, 14, -10, 13, 4],\n [7, -3, 18, 8, 21, -21, -8,... | 90 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[7, 8, 22, -2, -3, -15, -9, -12, 17, -11, 0, -19],\n [19, -2, -10, 2, 26, -19, -12, 0, 19, 23, 25, -20],\n [-24, 2, 17, 26, -3, -24, -7, 19, -12, -2, 3, -13],\n [-... | 83 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-16, -9, -15, -4, -15, -14, -2, 18, 24, -8, 19, 9],\n [18, -19, 2, 26, 5, 24, 17, -9, -21, -9, -8, -5],\n [10, 5, 14, -24, 1, -17, 24, 8, 2, -12, 6, -20],\n [-15, 22, 3, -6, 4, -3, -7, 10, -23, 1, 17, -7],\n [-3,... | 529 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 20, -12, -21, 17, -7, 23, -13, -25, -18, 10, -7],\n [-1, 2, -26, 8, -21, 10, 26, -22, 6, 22, 24, -13],\n [-15, 15, -7, 26, 23, -3, 16, 7, -2, 23, 2, 12],\n [4, 20, 16, 23, -4, 17, 11, -7, -4, 18, 25, -11],\n [23, 15, -19, 23, -6, ... | 91 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 11, -1, -16, 8, -19, 19, -13, -17, -25, 19, -18],\n [-24, -6, -1, -19, 21, -25, -21, 1, 26, 2, -1, -2],\n [-15, -22, 7, 21, 10, -12, 17, 9, -12, 16, 21, -4],\n [-21, 19, 23, 17, 1... | 536 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, -10, -5, 21, 10, -12, 8, 1, -20, 5, -16],\n [-17, -18, -13, -14, -2, -25, 8, -20, -6, -9, -24, 15],\n [12, 14, 22, -16, 12, -3, 19, -8, -23, -1, 11, 15],\n [5, 12, 18, 19, 9, 13, 10, 6, 9, -24... | 91 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[25, -4, -1, -23, -9, -21, 8, -5, 16, -12, -5, 10],\n [25, 15, -15, 20, 22, 15, 11, -9, 18, 8, 3, -3],\n [15, 3, -13, -21, -24, -11, -20, 25, -13, -18, -12, -6],\n [8, -25, 0, -25, 8, -9, -13, -7, -9, -17, -2, -25],\n... | 93 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, 11, -12, -6, -17, -4, 12, -22, -26, -14, -6],\n [-1, 23, 18, -6, 26, -9, 10, 18, 5, 9, -10, 8],\n [22, -16, -6, 25, 26, -1, -23, 7, 25, 21, -9, 13],\n [8, 14, 2, 25, 2, 11, 15, -6, 15, -14, 22, 14],\n [-10... | 554 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[26, 5, 4, -11, 5, 5, 7, -16, -17, -12, -10, 13],\n [-9, -18, -2, 13, -13, -2, 23, -5, 25, 3, -7, -6],\n [17, 5, 24, 19, 22, -6, 8, 5, 3, 12, 22, -15],\n [14, 20, -9, -6, -14, -6, -19, 19, 13, 19, -20... | 83 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, 11, -6, 13, 12, -6, -17, 11, 19, -23, 18, -7],\n [-10, -20, -23, 2, -13, -24, -3, 10, -11, 25, -23, -3],\n [7, 3, -9, -8, 4, -8, 22, 19, -8, -5, -... | 88 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, 9, 16, -7, -9, 16, -6, -23, 23, 6, 0, -20],\n [-21, -12, -9, 5, -16, -7, -3, -12, 21, -20, -6, 15],\n [-1, 17, -13, 10, -6, -9, -22, -24, -4, -1, 10, -3],\n [22, -8, 24, -2, -6, -... | 538 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[20, -12, 21, 19, 13, -9, 15, -7, -21, -15, -25, -20],\n [-11, -24, 18, -24, 0, 23, 16, 13, 11, 6, 1, -26],\n [-19, 10, 5, 21, 16, 10, -23, 3, -21, 19, -8, 5],\n [-18, -15, -16, 19... | 88 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-10, 12, -18, 8, -14, -12, -9, 24, 6, -21, 0, -4],\n [0, 7, 19, 11, -13, 9, 26, -19, 8, -8, 3, -13],\n [-7, 22, -2, 13, -3, -13, -1, 11, -4, -5, 21, -8],\n [19, 24, -24, 15, -8, -... | 94 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[7, 0, 14, -26, -19, -4, 11, -21, -5, -2, -9, -10],\n [-15, -21, -1, 0, -19, -8, 15, -26, 2, 18, 22, 8],\n [13, -13, 8, 21, 18, -7, 22, -14, 11, 22, 19, 22],\n [-19, 16, -7, 6, -1, 12, -6, 26, 22, ... | 102 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[13, -25, -10, 14, -15, 8, 16, -26, 18, -12, -1, 10],\n [-6, 22, 4, -2, -4, -3, 11, 1, -6, 16, -9, 9],\n [8, 18, -18, 26, 11, 3, 17, 7, 5, -24, -24, 1]... | 90 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 19, 17, -6, 17, -16, 12, -23, 24, -26, 1, -3],\n [8, -14, 20, 7, -16, 9, 24, -10, 8, -9, 13, -5],\n [-3, -8, 10, 12, -6, -19, 1, -22, -10, 10, 9, -8],\n [0, 26, 7, -16, 18, 20, -15, -6, -16, 12, 1, -22],\n [-10, -7, 14, 19, -15, ... | 98 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-12, 10, -14, 13, -19, -22, -18, -26, 9, 8, -25, 13],\n [-4, -18, 7, 19, -13, -23, 3, 4, 11, -16, 8, -19],\n [-24, -13, -14, 18, 5, 7, 18, -8, 11, -11, -25, 13],\n [-10, 7, 15, -11, 1... | 522 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, -15, 24, 10, -10, -4, -1, 2, 6, 0, -2, -17],\n [20, -4, -6, -6, 16, -14, 10, 6, -3, 17, -16, -10],\n [-23, 20, -2, 3, -18, -6, -7, -8, -8, -15, 10, 15],\n [-10, 10, 21, 12, 1, 14, 8, ... | 84 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 5, 26, -2, 6, -20, 25, -15, -11, -11, 16, 26],\n [9, -14, -20, 9, 20, 24, -18, 5, -16, -19, 6, -4],\n [-2, -19, 18, -5, -23, 13, -24, 2, 14, 2, 7, 7],\n [1, -14, -12, -4, 17, -1, -23, -1, 13, -18, -22, 5],\n [... | 541 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -2, -9, -8, -4, 11, -9, -1, -21, -23, 17, 24],\n [2, 7, -10, 16, 16, 26, -11, -25, 7, -19, -14, 15],\n [-19, 3, 5, 9, 20, 3, -26, 16, 12, -10, -7, -3],\n [23, -5, 2, -5, 17, -18, 10, -17, 9, 10, 1, 1],\n [15,... | 530 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[23, 25, 18, 2, -19, 14, 21, -8, 21, 12, 19, 1],\n [19, 0, -23, -12, 8, 10, -26, -24, 20, -3, 0, 13],\n [9, 7, 2, -3, -3, 15, -23, -24, 7, 22, -4, 26],\n [25, -4, 18, -22, 4, 26, 14, -21, 10, -17, 13, -20],\n [12, 11,... | 93 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-24, -1, -12, 9, 5, 5, -23, -9, 22, -8, 16, 25],\n [8, 13, -13, 6, -13, 7, -23, -3, 2, -8, -21, 6],\n [22, 13, -8, 26, -26, -22, 0, -11, -21, 13, -14, 21],\n [8, -8, -15, -11, 16, -17, -2, -7, 4, -23, 17, -4],\n [-25, -5, 24, 10,... | 540 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[11, -7, 0, 14, -7, 17, -8, -7, 8, 20, -25, 3],\n [26, 7, -5, -24, -21, -12, 0, -17, -18, 6, 5, 21],\n [-21, 14, 9, -25, 2, -23, -26, -8, -1, -2, -17, 26],\n [-12, -5, 24, 21, -6, ... | 89 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, 10, -18, -9, -6, -25, 16, 11, 13, 9, 23],\n [16, 10, -12, 1, -9, 7, -5, -16, -14, -23, -5, -20],\n [16, -3, -23, 1, -12, -26, -24, -13, 11, 23, ... | 85 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -19, 16, -18, 20, 6, 6, -8, -24, -17, 13],\n [20, 15, -26, 2, 23, 7, 24, -14, -26, 7, 2, 21],\n [20, -14, 21, 22, 26, 2, 12, -3, -1, -10, -20, -14],\n [-22, -1, 22, -24, -20, 22, 12, 26, -2... | 94 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -8, 17, 2, -20, 1, -18, 1, -21, 2, -10, -11],\n [-4, 4, -24, -6, -1, 9, 15, 10, 26, -5, 15, -15],\n [15, -14, -16, -11, -19, 13, 13, 18, -25, 3, 3, -15],\n [-17, 17, -16, -12, -11, -10, -1, -2... | 91 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -13, -3, 23, 22, 5, 9, 5, -12, 16, 8, -24],\n [-11, -22, -6, -17, -8, -2, -23, 2, -8, 16, -25, -17],\n [16, -2, -7, 21, -8, -4, -3, -16, 19, 7, 1, -22],\n [-22, 24, -6, -15, 23, -23, 22, 15, -7, 1... | 90 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 26, 3, 19, -7, 12, 26, -15, 22, -10, 15, 3],\n [2, -8, 19, -16, 7, 23, -20, 17, 7, -7, 23, 11],\n [-3, -17, 5, 25, -12, 10, -7, -24, 10, 13, -19, 13],\n [17, -4, 13, -16, 19, -19, 2, 3, -17, 12, 1, 22],\n [9, ... | 477 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 11, 11, 1, 26, 3, -24, 1, -24, 18, 7, -11],\n [-5, 5, 11, -19, -19, -21, -13, 5, 8, -17, -24, -15],\n [22, 4, 2, -22, 25, -2, 14, 4, -6, -7, 12, -5],\n [-23, -14, 18, 15, 23, 22, -7, 25, -14, -... | 85 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[10, 18, 24, -19, 14, 22, 8, 24, -16, -3, 22, -6],\n [24, -25, 13, -8, 12, 1, -10, -21, -8, 11, 1, -25],\n [11, 10, 24, 25, -23, -5, -1, 22, 16, 9, -14, 25],\n [5, -10, 14, 9, 19, ... | 90 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[13, -4, -24, 13, 23, -17, -2, 25, 22, -19, -16, -22],\n [18, 26, 10, 18, 11, 2, -22, -18, 21, -25, -26, 13],\n [24, 3, -16, 1, 17, -15, 12, -1, -14, -19, 1, 3],\n [-18, 12, 4, -6, 20, 7, 4, 25, -2, -15, -26, -5],\n [13, 10, 20, -26, ... | 88 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -11, 1, -11, -23, 18, -1, 1, 5, 18, -25, 4],\n [-24, -19, -3, -12, 16, 4, -18, 12, 18, -25, -19, -20],\n [17, 24, 12, 15, -11, 8, 3, -17, 11, -9, 23, -22],\n [26, 2, 12, 7, 16, 18, -4, -22, 3, -21, 19, 17],\n [-2... | 95 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 8, 26, -1, -11, -21, 17, 16, 20, 20, 21, 15],\n [-15, -14, -23, 12, -25, -1, 0, 0, -12, -19, -20, 20],\n [19, 13, -15, -14, 16, -10, -10, 9, -6, -19, -22, -1],\n [-11, 9, 1, 2, 20, -15, 10, 3, -4, -11, -13, -... | 526 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, 19, 12, 26, 4, 16, -3, -26, -16, -6, -23, -20],\n [-1, 20, 23, -15, 4, -10, 6, -16, 1, 5, -26, 20],\n [1, 26, 15, -20, -25, 15, -3, -23, 17, -8, -1, -16],\n [13, 23, 16, -16, 18, -24, -15, -24, 15, 0, 22, -25],\n [22, -11, -25, ... | 103 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 13, 24, -13, 12, 4, -13, -21, -15, -11, -10, 18],\n [-4, -13, -20, 19, 5, -12, 17, -10, 14, 20, 17, 7],\n [-22, 18, 0, 25, -4, 13, -13, -12, 16, 6, 26, 4],\n [8, -10, 1, -8, 1... | 82 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[15, 0, -16, 11, 7, 16, -8, -21, 19, 25, 11, 22],\n [15, 1, -26, 8, 13, -19, 25, 20, -20, -16, 12, -23],\n [-2, -15, -1, 11, 19, -15, 16, 24, 26, 10, 19, 26],\n [-3, -11, -14, -2, 25, -23, -16, 5, 22,... | 90 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, 12, 14, -23, 3, 3, -5, -16, -25, 17, -15, 3],\n [9, -9, -1, 26, -20, -26, -1, -4, -1, 18, -21, -21],\n [17, -19, -3, -5, -8, 10, -9, 4, 10, 3, 15, 6],\n [-17, 10, -15, 3, 0, 12, -18, -6, -15,... | 553 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[7, 14, -5, -3, 22, 10, 17, -26, -17, 16, -11, 19],\n [-19, 22, -2, 23, -15, -2, -10, -1, 19, 21, -13, 14],\n [9, -4, 16, -21, 20, -22, 16, -2, -9, -14, 16, -13],\n [1, -9, 1, 24, 0, 5, 20, -18, 13, 5, -7, 1],\n [6, -... | 99 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[16, -9, -4, -12, 6, -6, 12, -4, 0, 18, 17, -9],\n [-3, 24, 20, 13, 24, 15, -20, 23, 21, -7, 0, -21],\n [0, -18, 26, 18, 4, -6, -1, 13, 21, 18, -14, 22],\n [-4, -7, 10, 26, 1, -10, 1, 14, -25, -2, 23, 14],\n [-21, -16, 11, -21, 18, -1... | 91 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[14, -19, -24, 21, 19, -18, 3, 26, -16, 8, 10, 15],\n [-14, 9, -14, -15, 10, -17, -18, 25, -20, -25, -4, 12],\n [13, 12, -6, -4, 2, -13, -1, 24, -22, 4, -2, 4],\n [23, -7, 17, -10,... | 89 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-20, 17, -4, 14, -16, 15, 26, 6, 23, 9, 10, 14],\n [-10, 8, 21, -22, 21, 5, -24, 25, 20, 8, 25, -13],\n [21, 4, 4, -10, -3, 25, -4, -9, 23, -13, 23, -12],\n [-12,... | 83 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[7, -4, 23, 15, -3, 22, -14, -9, -14, 22, 10, 16],\n [12, 15, -10, -12, -9, -4, 24, 3, 7, -23, -24, -20],\n [-9, 15, -20, 13, -21, -5, -26, -23, 19, 22, 25, 23],\n... | 91 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[26, -21, -8, -9, -21, 18, 6, -4, -4, -1, -14, -20],\n [-12, 17, 0, -1, 6, -12, 9, 18, 0, -22, -25, 6],\n [-11, -4, 11, -11, -13, 2, -1, 8, -12, -24, -4, 2],\n [7, 6, 14, 14, -4, -20, -24, 5, 4, -9, 16, -20],\n [14, -26, -13, 25, ... | 503 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[20, 16, 17, -18, -14, -12, 0, -12, 1, 10, -8, -1],\n [25, -1, -2, -1, -1, 19, 1, 22, -9, 5, 26, -24],\n [-25, 6, 15, -8, -10, 17, 6, -15, 22, -24, 16, 22],\n [-1, 8, -19, 25, 9, 26, -20, 19, 19, 9, -... | 93 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, -20, -22, -16, -12, -24, -22, -4, 26, 10, -18, -12],\n [-24, 2, -21, -10, -1, -6, -19, -6, -16, 11, -19, 15],\n [-3, 8, -13, -13, -17, -15, 11, 17, 19, 7, 14, -17],\n [-10, -10, -24, ... | 91 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -6, -25, -9, 20, 6, 10, 7, -7, 8, 24, 23],\n [-9, 19, -3, -19, 3, 17, 26, -17, -4, 25, 22, -16],\n [-25, -1, 9, 6, 20, -14, 13, -2, -23, 15, -8, -9],\n [10, 3, -8, -4, -11, -26, -15, -3, 7, 26, -19, -9],\n [21, -22, -1, 3, -14, -8... | 85 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-22, 7, 19, 7, -14, 12, 15, 18, 21, -13, -16, 15],\n [11, -23, 26, 6, -20, 14, -19, 10, 24, -17, 16, -12],\n [11, -12, -22, 2, -8, 24, -17, -15, -23, 4, -9, -11],\n [13, 9, -2, -4, -15, 7, 9, 10, ... | 92 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-8, 3, 18, -9, -13, 9, 9, -7, 25, -8, 18, 17],\n [-20, 17, 26, -23, 7, -25, -22, -17, 5, 15, 14, -14],\n [12, -22, -17, -17, 11, 0, 24, -6, -19, -26, 1, 22],\n [1... | 83 | 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, -15, -23, -3, 2, -18, -23, 24, -3, -13, -22, -9],\n [15, -8, -15, -9, -10, 3, -3, -16, 8, -4, -10, -26],\n [-12, 5, -18, -12, 1, -3, 8, -5, 0, -8, ... | 83 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 21, -10, -20, -14, -25, -23, -17, 12, -3, -10, 25],\n [-21, -8, -22, 5, -17, -18, 0, -14, -8, -6, -3, 11],\n [-23, -3, 8, -24, -23, 10, 13, 21, 8, 4, 17, -2],\n [13, -14, -23, 19, -13, -14, 0,... | 546 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-17, -12, 15, 21, 17, -9, -4, 6, -11, 11, 8, 7],\n [1, -25, 3, -14, 14, -11, -22, 1, 26, 12, 18, -7],\n [-3, 0, 3, 18, 0, -1, -20, 15, 20, 26, 11, -22],\n [-4, 1,... | 93 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -19, 24, -6, -7, -19, 19, 4, 23, 2, 21, -18],\n [-12, 3, -1, -17, 2, -11, 9, -7, 18, 10, -5, -20],\n [-4, 14, 13, 2, -11, 11, 1, 21, 11, 4, -13, 26],\n [6, -18, 0, -3, -14, -1... | 95 | 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, 22, -1, 6, 10, 21, -12, -25, 14, -20, 5, -23],\n [-7, 23, 26, 9, 5, 1, -14, -26, 8, 21, 3, 9],\n [-2, -11, -8, -26, -22, 24, -5, -3, 16, 18, 25, ... | 89 | 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, 1, 25, 10, -19, 17, 7, 17, -22, -22, 4, 18],\n [-18, 15, 5, 6, -24, 3, 23, -15, 2, -24, -1, 3],\n [-18, -1, -25, -24, 19, -23, -2, 24, -14, 12, 17,... | 84 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 6, 16, -9, 23, 26, 3, -1, -11, -14, 12, 6],\n [-1, 21, -26, 22, 11, -25, 22, -21, 19, 23, 11, 15],\n [-3, -9, 0, 14, -19, 1, -17, -10, 2, -21, -13, -5],\n [-21, -1, 12, -15, 8... | 96 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[17, 9, 1, 18, -10, 13, 25, -24, -15, 12, -15, -25],\n [19, -5, -4, 3, -22, -18, -6, -16, -22, 8, 0, 22],\n [-25, -3, 4, 6, 12, 3, 19, 10, 24, 1, 4, -16],\n [-4, -25, 13, 14, 0, 8,... | 94 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -10, -4, 16, -10, -13, 2, -7, 3, -8, 26, 12],\n [-14, -9, -4, 19, 6, 12, 13, -9, -18, 6, 5, -10],\n [-8, 0, -21, 8, 10, 7, -7, -2, -23, -17, -17, -3],\n [-6, -16, 0, -11, -1, 3, 22, -11, -20, -11, 8, -11],\n [13,... | 79 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-12, 25, -23, -5, 23, 11, -4, -1, 24, -16, 1, -25],\n [-19, 2, -16, 10, -9, 23, -13, -17, 8, -18, 8, -16],\n [17, -15, -24, 26, 12, -13, 1, -16, 12, -2, -6, -17],\n [16, -12, -8, 21, -5, -6, 25, 17, 5, 23, -4, -14],\n [-22, -23, ... | 528 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -19, 12, 20, -1, 10, 7, -20, 13, 1, 12, 12],\n [1, -13, 26, 23, 11, -23, 15, -9, 17, 21, -2, -20],\n [11, 1, -22, -24, 17, 4, 20, 15, -7, -8, 21, -16],\n [13, -24, -4, -20, -4, -20... | 559 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[16, 8, 22, 19, 11, -19, 10, 0, 1, 13, 7, 5],\n [-12, 17, -10, 6, 20, 19, 25, -11, 2, -18, 6, 22],\n [2, -14, -6, -6, -22, -17, -21, 24, -14, -26, -7, 20],\n [19, -19, -17, -18, 22... | 83 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -19, -10, 25, 0, 6, 19, -10, 15, -15, 21, 19],\n [0, 21, -19, -4, 15, 22, 2, 23, -7, -11, -10, -11],\n [-8, -19, 11, 11, 26, 2, 14, 9, -1, 4, 17, -15],\n [-10, -12, -18, 12, 15, 21, -15, 5, -2... | 77 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-11, -19, 21, -9, 25, 21, 16, 12, 22, 22, -15, 18],\n [-17, -20, 19, -26, 22, 9, -6, 10, 25, -3, -2, -20],\n [15, -10, 2, 3, -20, 6, -20, -3, -16, -18... | 90 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[10, -2, -1, 12, -7, 6, -13, 9, -10, -6, 19, -11],\n [19, -11, -7, 2, 1, -19, -3, -24, -2, -8, 6, -25],\n [-12, -5, -17, -9, -5, 19, 22, 0, -14, 6, -22, -1],\n [-14, 0, -13, -3, -2... | 97 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[16, -1, -20, 11, 3, 15, -22, -16, -26, 7, -26, -8],\n [-25, -6, -7, -4, -6, -3, -23, -15, -5, -7, -9, -26],\n [3, 6, -3, -13, 9, -22, -16, -3, 4, -14, -11, -3],\n [-14, -3, -1, -25, -11, 11, 19, -... | 85 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 8, 12, -17, -26, 15, -6, -18, 20, -12, 8, -22],\n [14, -5, 14, -4, -20, -4, 17, -2, 0, 14, -21, 7],\n [-18, 22, 6, 24, -21, 10, 4, 7, 14, 2, -13, 9],\n [9, 26, -12, -19, -1, 9, 21, -6, 1, -23, -11, -5],\n [-15, -1... | 86 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, -15, -26, 26, -19, 21, 23, -14, -12, 26, 17, -19],\n [-17, 19, -22, 23, -8, 20, 11, -16, 26, 16, -7, -7],\n [-6, -9, 23, -17, 7, -1, 3, -18, 19, 24, 4, 15],\n [-23, -21, -13, -23, -1... | 98 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -16, -7, 8, 26, 20, 19, -16, 25, -19, -23, 0],\n [17, 13, 11, 20, 3, 17, 21, 21, 0, -6, 25, -7],\n [-23, -16, -14, -18, -23, -15, -18, -14, 21, -1, 11, 15],\n [-14, 12, 1, -8, ... | 89 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -16, 22, -22, -20, -8, 2, -12, 8, 20, 10],\n [-15, 3, -7, 10, -24, -18, 14, 12, -1, -25, -4, -4],\n [-6, -11, -18, -14, 1, 0, 24, 25, -10, 11, 9, -26],\n [-9, 24, -18, -14, 13, ... | 533 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, -3, -16, -5, -12, -17, 14, 0, -18, 25, 1, -26],\n [-10, 4, 17, -17, 10, 2, -9, 20, 11, 12, 22, -21],\n [13, -15, 26, -13, 17, -17, -7, -12, 4, -20, 14, -17],\n [-17, 21, 12, 1, 3, 10, -24, 23, 16, -12, -6, 25],\n... | 94 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -1, 18, 1, 19, -9, 17, 9, 15, 2, -10, -23],\n [17, 18, 2, -23, -17, -2, 4, -24, 20, -25, -2, 22],\n [-21, -1, -19, 8, 0, -2, -9, -26, 21, 12, -24, -23],\n [14, 10, 24, -12, -19, 11, 23, -8, 20, -1, 12, -17],\n [11, -13, 22, 1... | 534 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, -26, -21, -14, -5, 4, -5, 10, 20, 0, 23, 25],\n [-13, 20, -22, 9, 5, 7, -20, 15, 21, -17, 23, -10],\n [3, -6, -14, -26, -26, 20, 6, 11, -2, -1, -14, 1],\n [6, 10, 14, 3, 22, 21, -19, 22, 20, -26, -15, -22],\n [-3, -21, -2, -26, ... | 94 | 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, 10, 19, 22, 8, -23, -11, -11, -6, -1, 9, -8],\n [-10, 18, -1, -5, 1, -26, 17, 9, 16, 10, -25, -10],\n [13, 11, -6, -18, -14, -16, -11, -11, -25, 15... | 95 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[9, 2, -1, -23, 22, -13, 23, 0, 6, -5, 21, -24],\n [-4, -6, 14, -4, -23, -6, 10, 16, 4, -6, -1, 14],\n [8, 11, -3, -16, 14, 2, 20, -24, -26, 25, -8, 19],\n [22, -5, -13, 22, -13, 17, -11, 6, -14, 11, ... | 89 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[7, 6, 23, -3, -18, -14, -25, -20, 21, -6, -8, -2],\n [20, -5, -16, 6, 5, -6, 12, -7, -19, 15, 10, -18],\n [-2, -2, 6, -25, -8, 19, -7, 15, 14, 15, 2, -21],\n [-10, -2, 11, -23, 3, -7, -24, -4, 24, -9, -1, 9],\n [-19, -10, 4, 10, 18, ... | 88 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, 25, 2, -11, -15, -10, 10, 0, -2, -14, -19, -22],\n [-15, 14, -24, 8, 6, -5, 23, 17, -18, 14, -9, 23],\n [2, 12, 0, 9, 18, -10, 7, 19, -24, -22, -13, -24],\n [-4, 12, 3, 23, 18, -4, 0, -17, -2, -... | 88 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-11, 9, 6, -7, -14, 6, -22, 10, -13, 0, -4, -13],\n [13, -23, 12, 25, -8, 20, -23, 3, -8, 4, 4, -18],\n [26, -14, -13, 19, -17, 21, 4, 10, -4, 0, -21, -1],\n [-25, 18, -14, 24, 23, -8, -26, 13, 5,... | 92 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 13, -20, 19, -4, -8, 19, -5, -14, -6, -26, -8],\n [6, -23, 15, -24, 0, 25, 14, 8, 1, -21, -21, 17],\n [-4, 6, -11, -3, -22, 14, 15, -14, 20, -15, -22, 10],\n [4, 1, 1, 3, -9, 17, 0, 8, -1, 12... | 547 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, 19, 2, 23, 21, 25, -5, -23, 25, -21, 11, -1],\n [-16, -1, -10, -3, 1, 8, 4, -14, 8, -11, -12, 16],\n [-9, 20, 10, 21, 21, 22, 14, 0, 8, 25, 18, 8],\n [1, 12, 11, -18, -15, -12, -6, 25, 8, 15, 6, 24],\n [-8, -4, -14, 17, -26, 24,... | 97 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-20, 3, 16, -20, 9, 2, -3, 25, 12, -23, 2, 17],\n [-22, 2, 3, 2, -1, -8, -1, 10, 0, 3, 24, 26],\n [3, -24, 16, -20, 22, -18, 26, 14, 15, -14, -12, -22],\n [2, 8, 0, 0, -19, 5, -7,... | 101 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[20, 4, 8, -26, -19, -15, -8, -2, 5, -15, -14, 1],\n [-26, 24, -21, -19, -23, -22, -2, -5, 1, 12, -4, -23],\n [25, -23, 20, -6, 10, 14, -25, -20, 22, -11, -10, -7],\n [-4, 7, -16, 7, 6, -1, -25, -4, 14, -5, 7, -12... | 555 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 0, -17, -11, 15, 15, 24, -17, -21, 22, -22, -21],\n [20, -2, 24, 23, -23, 13, 21, 5, 24, 25, 8, -17],\n [7, 9, -21, 16, 19, -11, 26, -8, 7, -2, 4, 22],\n [14, -10, 20, 3, 12, 4, -8, 8, 2, -26... | 522 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-22, -23, -5, -9, 8, -10, 23, 23, -3, -25, -14, -12],\n [-22, -24, 10, 10, 10, -24, 8, 25, -4, 1, 3, -9],\n [25, 9, 6, -1, 21, 13, -10, 13, -20, -19, 26, 4],\n [-15, 21, 4, 17, -8, -17, 12, -15, -7, 10, 21, 14],\n [-20, 25, -13, -16,... | 94 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, 13, 12, 20, -21, -22, -13, 26, 18, 15, 23, -23],\n [-19, -3, -16, -10, 23, -6, -1, 16, 21, 17, 18, 0],\n [-11, -1, 26, 6, 4, 21, 20, -21, 17, -19, -20, 7],\n [17, 26, -13, -11, 16, 25,... | 97 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, -23, 24, 17, 20, 8, -4, 0, -1, 25, -19, 16],\n [-11, 14, -24, 5, -22, -7, -13, 5, -1, 20, -21, 9],\n [13, 24, -22, -14, 5, -11, -26, -14, -16, 26, -19, -2],\n [13, 5, -3, 1, -13,... | 533 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-20, -26, 14, -24, 17, 24, -12, 4, -11, -17, 2, -21],\n [2, -10, 26, -5, -3, -10, -6, 24, 23, -16, -20, 15],\n [12, -22, 17, 21, -6, -9, 8, -7, -12, -22, -14, 24],\n [-15, -6, 10, -21, -20, -1, 15... | 89 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-9, -8, -24, -18, 9, 4, 22, -10, -4, 7, 14, 14],\n [-22, -12, 20, -24, -8, 1, -24, 11, -23, -3, 4, 18],\n [18, -16, 10, -26, -18, -10, -26, -24, 20, -1, 26, 4],\n [-1, -4, 3, -17, -19, 17, -2, -5,... | 93 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -4, -9, 19, -8, 1, -1, -17, 20, -23, -25, -24],\n [-20, -11, 4, -17, -8, 1, -10, 1, -8, 10, -4, -7],\n [-14, -14, 16, -16, 21, -12, -10, 23, 1, -8, -23, -5],\n [-5, 10, 12, 7, 6, 17, ... | 93 | MATH |
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