messages listlengths 1 1 | ground_truth stringclasses 140
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-11, -17, -22, 24, -20, -5, -3, 13, 15, -5, 8, 19],\n [25, -24, 20, 15, -20, -8, 15, 19, -19, -4, -7, 6],\n [-21, -12, -22, -13, -18, -1, 5, 4, -21, -26, -8, -12],\n [7, -8, 22, -16, -9, -3, 19, 24, -18, -16, 16, -23... | 86 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[15, -20, -21, 18, -16, -3, 13, -2, 10, -24, -23, -23],\n [14, -26, 3, -12, 18, 4, 10, 23, -22, 16, -6, 8],\n [-23, -20, 2, 9, 8, 5, 15, 25, -16, 23, 6, 26],\n [14... | 101 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[25, 7, 22, -24, -23, -2, -22, -15, 26, -3, -8, 5],\n [-15, 10, 20, 0, -9, -2, 24, -4, -24, -25, -16, 19],\n [26, 10, 3, -14, 13, -21, -15, 12, 16, -19, -18, -23],\n [10, 9, 5, -15... | 82 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, -13, -17, 13, -26, 14, -6, -22, -18, -18, -9, -22],\n [-11, 7, -23, -6, 23, 10, 13, 17, -13, 0, 22, -15],\n [0, 7, -23, 16, 17, 24, -25, 15, 15, 5, -25, -5],\n [-8, -1, -7, 9, -9, 25, 23, -13, -7, 18, -3, 20],\n [20, 4, 25, 9, -1... | 93 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -7, 14, 17, -25, 16, -26, -4, 21, -2, -1, -24],\n [4, 0, -14, 20, 6, -2, -11, 20, 11, -1, 20, 25],\n [-9, -10, 19, -2, -1, -9, 22, -26, 19, -20, 3, 6],\n [-2, -2, 0, 8, 16, -9, 3,... | 531 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, 17, 11, 15, 15, 18, 24, 3, -10, -11, -23, 3],\n [-7, 8, -22, 18, -13, 14, 14, 13, 1, -17, 25, 3],\n [23, 5, -15, 18, -11, -1, 8, 14, -11, -10, 21, -4],\n [15, -5, 23, -6, 7, 19, -22, 11, 25, 4, 6, 20],\n [-24, 26, -8, -9, 1, -12,... | 91 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, -18, 19, 14, 9, 14, 13, 19, -22, 21, 15, 4],\n [8, 14, -24, -8, -8, -26, -5, -8, -1, -12, -8, -2],\n [12, 4, 3, 6, -11, 13, -15, 1, 3, -21, 15, -13],\n [-22, 9, -4, 5, 4, -13, 5, 22, 0, -26, 22, 25],\n [-18, -11, 8, -17, 22, ... | 545 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 9, -25, 8, 9, -19, -18, 1, 13, 17, -17, -22],\n [10, 20, 4, 25, 2, -24, -1, 4, -25, -12, -14, 1],\n [17, -13, -15, -12, -6, 2, 18, 8, 20, -7, -9, 11],\n [-12, -15, 7, -22, -10, -14, -14, 9, -11, 13, -24, 25],\n [... | 104 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-12, 18, 9, 11, 7, 7, 5, 11, -2, -24, 25, 16],\n [20, 2, -6, -18, -6, -6, -20, 20, 5, -5, 15, -16],\n [7, -13, 21, 14, -5, -2, -11, 6, -25, 12, 17, 23],\n [-21, 7, 19, 21, 15, 10, -5, -11, -20, 20, -14, 22],\n [2... | 548 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 19, 18, 4, 25, -23, 14, 19, 2, 22, -26, 5],\n [-26, -23, -7, 13, 10, -13, 25, -13, -25, -6, 2, -15],\n [-9, 11, 14, 5, 14, -5, 9, 15, -15, -6, -19, 1],\n [26, -5, 25, -11, -15, 22, -10... | 96 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-18, 6, 13, 7, -3, 26, 18, 18, 6, 6, 2, 11],\n [21, 22, -14, -9, 8, 20, -25, -2, -21, -2, 26, -7],\n [-13, 23, -23, -19, 7, 1, -25, -10, -23, 21, 7, 0],\n [-8, 1, 11, 7, 5, 14, 4, -21, -21, 1, -1... | 553 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, 12, -1, 3, -5, -16, -5, -3, 2, 24, -17, 7],\n [19, -2, -6, 12, -14, -25, -21, -26, 1, -5, -16, 12],\n [-22, -9, -7, -15, -6, 0, 23, 14, 7, -9, 7, -25],\n [26, -13, 12, -26, 1, 14, 0, 3, -5, -15, -26, 6],\n [14, 21, 22, -26, -22,... | 85 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, 5, -17, -22, -13, 12, 15, 16, -8, -16, 8, 12],\n [19, 11, -5, 25, 18, 19, 3, 25, 3, 20, 23, -16],\n [-5, -17, 16, -8, -12, 8, 8, -26, 20, 18, 20, 26],\n [-9, -1, -9, 14, -9, 16, -9, 5, 11, 0, 22, 2],\n [22, 14, -7, 8, -4, -15... | 520 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-7, 8, -18, 25, 10, -21, -17, 26, -18, 6, -11, 5],\n [11, 21, -7, -7, -24, -13, -6, -19, 25, 19, -3, 20],\n [-6, 15, 5, -10, 13, 24, -23, 15, -4, 9, 25, -5],\n [-2, -23, -17, -3, ... | 93 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-14, 0, 23, -12, -15, -17, 22, 11, 1, 16, 8, 11],\n [-7, -15, -24, -25, 1, -5, 8, 18, 25, -18, -4, -10],\n [-13, 25, 5, 13, 9, 6, -17, -14, 7, -22, -21, 6],\n [-22, -3, 20, -19, -9, -2, -9, 9, -1, -7... | 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[[-9, 13, -4, -24, -16, 0, 10, -15, 6, 1, -21, -21],\n [17, -6, -2, 20, 9, -9, 17, 12, -22, -4, -4, -4],\n [8, 2, -22, -10, 11, 25, -25, -8, 20, -24, 3,... | 94 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -23, -23, 11, 23, -26, 15, -24, 1, 19, -16, 10],\n [-25, -18, -10, 5, 24, 4, -6, -10, 25, 15, -10, 16],\n [0, 1, 12, -26, -11, -24, -12, -23, 9, 3, 2, -4],\n [-22, 20, -16, -8, -1... | 530 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 1, -22, 1, 20, -16, 7, -12, 24, -22, 21, -6],\n [4, 13, -20, 8, -6, 13, -22, -13, 7, -17, -9, -10],\n [11, 22, 5, -10, -5, -2, 24, -11, 3, 7, -22, 17],\n [6, -22, 13, 15, -24, 11, ... | 543 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 3, 7, 18, -10, 24, 8, 9, -21, 18, 2, -4],\n [-13, -18, -12, 11, -2, -7, 16, -5, -20, -9, -10, -13],\n [-1, 13, 5, 2, 13, -20, -18, -15, -24, 5, 6, -12],\n [-18, 22, 17, -10, 1, 18, -14, 20, -6... | 499 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[13, 18, -11, 12, -19, -9, 0, -18, 1, -5, -16, -5],\n [22, -13, -4, -25, -12, 23, -22, 2, 6, 21, 17, 3],\n [19, -10, -26, -13, 20, 17, -10, -18, 8, 4, -15, 18],\n ... | 88 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[26, 6, 18, 11, 25, 2, 17, -17, 5, -2, 1, 2],\n [24, 8, 20, 5, 19, 9, -20, -17, 19, 7, 6, -1],\n [21, 21, -14, 3, 5, 6, -21, 9, -25, -20, 3, 19],\n [-1, -2, 6, 15,... | 101 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, -2, -11, 22, 21, -9, 5, 19, 11, 25, 26, -12],\n [10, 22, 6, -14, -20, -8, -6, 10, -18, -23, 4, -20],\n [-14, 13, 9, -19, -1, 0, 21, -1, 18, 15, -13, -7],\n [15, 18, 1, -19, 25, -... | 577 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, 12, -25, 7, 26, -7, 9, 25, -4, 8, 7, -6],\n [11, 19, -19, 16, 24, 3, 20, -7, 25, -7, -4, -7],\n [19, -4, -23, -17, 13, -22, 5, -9, -2, -10, -22, 8],\n [15, -6, 9, -8, -4, -22, 6,... | 535 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -22, 17, 24, 9, 20, -2, 18, -14, 8, 5, -19],\n [-5, -21, 22, -16, -20, -12, -23, 13, 7, 16, 13, -5],\n [3, -8, 10, 23, 11, 3, 5, -8, 25, -2, 10, 18],\n [-4, -15, -18, 10, -10, 23, 8, 24, 20, 22, 14, 3],\n [-23, 14, -23, -3, -2... | 535 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-18, -4, 13, -21, 23, -8, -7, -9, 0, 6, 2, -18],\n [18, 17, 23, 0, 26, 12, -16, 23, 15, -19, -13, 19],\n [-14, -20, -12, 11, 17, 16, -9, 9, 4, -23, -14, 12],\n [3... | 82 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 20, -19, 14, 6, 26, -15, 21, 12, -15, -15, -16],\n [21, -19, 24, -19, 10, 22, -11, 9, -9, 17, -6, -23],\n [23, -20, 7, 7, 18, 9, 10, 3, -1, -15, -16, 2],\n [-24, -16, -18, -1,... | 85 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, -9, -13, 5, -15, 15, -25, 26, -1, -4, 8, 6],\n [14, -2, -23, -6, 21, -23, 4, 22, -12, -23, -23, 17],\n [-24, 25, -22, -8, 11, 5, -18, -24, 7, -2, 26, -17],\n [5, -22, 2, -20, -12, -25, -17, -16, ... | 92 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-14, -20, 24, -26, 18, 22, 17, 26, -1, 19, -11, -15],\n [-11, 7, 0, 25, -2, -8, -20, -15, 19, -3, 23, 12],\n [-22, -26, -20, 21, -1, -3, 21, -10, -23, -11, 9, -22],\n [-22, 25, 16, 19, -10, 14, -6, 3, 22, 24, 6, 18],\n [-4, 15, 2, 15... | 92 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[11, -20, -9, 24, -8, -10, -13, 14, 21, -17, -2, 14],\n [17, -18, -11, 21, -3, -6, 7, 12, 25, -20, -20, 1],\n [24, 8, -17, 11, 5, 7, -3, 25, 23, 14, 20, 19],\n [14, -25, 15, -23, -26, -5, -16, 21,... | 536 | 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, -12, 6, -12, 5, -5, 23, -21, 3, 14, -10],\n [17, -25, -11, 20, -15, 20, 18, -15, 24, 21, 12, -10],\n [15, 14, -21, 14, -1, -26, -11, 19, 13, 20... | 89 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-16, -24, 3, -9, -10, 24, -18, 3, -11, -19, 14, -1],\n [-22, -22, 19, -3, -13, -22, 9, -2, -10, -21, -20, 19],\n [-12, -21, 5, 15, 13, 0, 13, -22, -11, 25, -16, 12],\n [-2, -25, 1, -20, 11, 24, 23, -26, -9, -15, ... | 535 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-25, -19, -2, -9, 18, -10, 3, -19, 15, 19, 2, 24],\n [-8, 10, -3, -9, -17, -11, 23, 14, 15, 17, -22, -12],\n [-4, 4, 3, -20, -7, 12, -24, -24, 4, -20, -26, 0],\n [23, -26, -21, -7... | 81 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -22, -23, -2, 18, 25, 22, 18, -5, 21, -14, -4],\n [6, -2, -17, -9, 0, 22, -1, 22, 15, 25, -25, -17],\n [-7, 11, -24, -17, 1, -8, -10, 17, 26, 17, -4, 1],\n [0, 5, 11, -15, -7, -21, -24, -24, -4, -18, 6, 9],\n [-1... | 114 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 13, -24, 23, -26, -19, 14, -10, -19, 16, 6, -1],\n [-25, 20, 22, 2, -12, 3, 23, 17, 19, -15, -25, -6],\n [2, 2, -11, 24, 4, 6, -25, 17, -23, 12, 22, -22],\n [-25, 18, -19, 23, 9, -21, ... | 88 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-25, -22, 10, 14, -21, 24, 15, 24, -8, -11, -15, -3],\n [-18, -24, -10, 3, 0, -3, 15, 23, 12, -20, -18, -11],\n [-16, -18, -26, 17, 8, -7, 24, -19, -2... | 89 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[13, 18, 22, -23, 15, -25, 3, 20, -7, 3, -9, 3],\n [19, 8, -26, -24, -4, 18, 13, -5, 22, 21, 21, 17],\n [24, 21, -12, 14, -11, 0, 5, 7, 15, -15, -9, -9],\n [-23, 7, 12, -8, 16, 18, 25, 4, 22, 4, 15... | 94 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[15, 6, -5, -9, 0, -12, -2, -17, -11, -23, 4, 5],\n [-3, -9, 5, 26, 1, -16, -19, -26, -25, -6, 22, 25],\n [-8, 15, 3, 26, 13, -2, 26, -18, 15, 25, 1, 10],\n [5, 14, -16, 23, -6, -3, -26, -11, 25, -3, -17, 5],\n [1... | 545 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-24, -26, 19, 24, -2, -11, 14, -22, 9, -21, -15, 19],\n [-4, 19, 11, -22, -25, -24, 14, -20, -1, -15, 23, 18],\n [-26, -26, 6, 26, 12, 26, -18, -26, -12, -2, 17, 9],\n [-17, 23, 4, 24, -7, -22, 1,... | 93 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-23, -3, 2, -19, 7, 21, -18, -10, -17, -3, 18, -5],\n [-10, 4, 17, -18, -12, 15, 24, 3, -10, -20, 19, 18],\n [-1, 26, -25, 21, 2, 22, -21, 6, 11, -26, -17, 25],\n [4, -3, -19, 1, 1, 21, 1... | 93 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 9, 8, -14, -12, 6, 1, 21, 7, 11, -26, 4],\n [22, -10, -5, 5, 2, -26, 21, 1, 14, -25, -2, -6],\n [10, -1, 13, -26, 5, -18, 19, 22, -22, 13, -10, 26],\n [2, 17, -8, 13, 2, 24, -15, -19, 16, 16, 4, -12],\n [7, -1, 8,... | 90 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, -11, 21, -1, -5, -12, -15, 12, -24, 26, -3, -25],\n [-23, -4, -4, -19, 15, 17, -15, -18, -16, 18, 4, -26],\n [8, 16, -12, -20, 1, 21, -21, -7, -3, 15, 9, 11],\n [-15, -24, 1, -15, -11, 17, -12, 4, 26, -6, -9, 21],\n [-21, -10, -... | 88 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -23, -6, -7, 23, -10, 25, 19, 7, -13, -17, -7],\n [8, -12, 12, 0, -12, -8, -1, -15, -3, 26, 9, 6],\n [-22, -18, 13, -13, 19, 9, -2, -20, 7, 16, -20, 4],\n [25, 5, -6, 22, -12, 3, -23, 7, -18, -... | 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[[8, -11, 9, 3, 10, 5, -12, -6, 13, 2, 3, -2],\n [-7, -17, 4, -26, -17, -9, 22, 9, -14, 5, -5, -21],\n [6, -26, -24, -22, 23, 0, -15, 6, 14, 0, 22, -14]... | 83 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-24, -12, -24, 26, 14, -10, 22, 17, -20, -16, 19, -7],\n [-26, 5, 11, -6, 4, -10, -2, 14, 6, -15, 25, 1],\n [22, -1, 9, -19, 5, 24, 24, -1, -22, 16, 11, -14],\n [-8, -21, 18, -21, -11, 2, -9, 5, 2, 1... | 93 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-9, -16, 16, 16, -17, -17, 9, -18, 15, -14, -4, -26],\n [-11, -8, -15, -22, -22, -20, 17, -13, 6, -21, -9, -21],\n [24, 3, -15, 23, 8, -16, -23, -14, -26, 25, 11, 26],\n [2, -13, -6, 14, 4, 14, -... | 541 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[14, 18, 0, 7, -15, -15, -12, -7, -17, 19, -1, -10],\n [-17, -16, -10, -16, -12, -23, -2, 9, 26, 20, 4, 19],\n [2, 4, -18, 21, -26, -24, -23, -8, 14, -5, 24, -19],\n [-2, -23, 18, ... | 83 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-10, 26, 9, 9, -14, -7, 24, 11, -8, -5, -11, -21],\n [-16, -17, 4, -9, 5, 14, 15, 20, -3, 19, -11, 2],\n [12, -2, 13, -2, 13, 18, -8, -17, -26, 0, -5, 1],\n [21, 8, -24, 11, -1, 1... | 84 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -5, -26, 26, 17, 16, -17, -16, -19, -10, -21, -20],\n [4, 10, -23, -20, -11, -2, 9, 8, -13, 9, 26, -18],\n [-16, -26, -18, -2, 13, -12, -3, -19, 25, 2, -20, 19],\n [-9, -24, 20, -3, -7, 4, -1, 11... | 102 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 21, -14, -1, -19, -1, 22, -13, 14, -21, -11, 8],\n [7, 13, 0, 9, -15, -26, 2, -10, -9, 22, -11, 8],\n [-18, 17, 12, 11, 16, -21, -1, -10, -3, -17, 5, -24],\n [-8, 8, 0, -2, -6, -25, -7, -4, 6, 23... | 93 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-21, -14, -7, -22, 18, 0, 22, 24, -8, -26, -23, -25],\n [17, -1, 6, 17, 18, 11, -20, 2, 25, -22, -18, -14],\n [19, 13, 21, 19, 2, -9, 3, -17, -8, 21, -18, -6],\n [-26, 14, -1, -13, 12, 2, 16, 25, -20, -3, 0, 15],... | 554 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[11, -21, 2, -4, 18, 24, 10, 5, -26, 22, 7, 17],\n [1, 23, -20, 10, 2, -8, 21, 17, -8, 24, -7, 26],\n [-12, -3, 14, 26, -19, 24, -20, -8, 1, -15, -1, 8],\n [-23, 7, -20, 0, -24, 6, -15... | 512 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, 10, -8, -10, -26, 2, 2, -3, -8, 16, -17, 9],\n [-10, -10, 5, -11, 24, 25, 19, -4, -11, 5, -25, 13],\n [-21, -17, 7, 3, 24, 9, -21, 18, 6, -22, 1, -20],\n [19, -8, 16, 23, 23, -1, ... | 521 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 13, 7, 0, -24, 19, 12, -14, 12, -11, -24, -1],\n [-22, -24, 1, 20, 25, 16, 3, -4, -9, -22, -5, 18],\n [-26, 0, -13, 14, -18, -23, 26, -2, 4, 5, -25, 21],\n [10, 25, 23, -25, -13, -12, -2, -17... | 556 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, 13, -10, -4, -17, 6, -19, -22, 7, 24, 0],\n [4, -2, -25, -7, 16, -24, 14, 13, 11, 19, 13, -12],\n [0, -3, 8, -4, -19, -5, -11, -21, 12, 18, 25, 2],\n [-1, -18, -8, -20, 21, -2,... | 511 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-17, 3, -12, 21, 20, -1, 14, 1, 26, -8, -26, 7],\n [11, -3, 14, -3, -9, -26, -17, -23, -13, -6, -1, 11],\n [25, -22, -12, -3, -17, 8, -10, 5, -18, 4, 14, -12],\n [23, -24, 13, 8, 24, -14, -5, 21, -20, -7, 10, -1],\n ... | 98 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[16, -13, 19, 24, -22, 20, -14, -3, -11, 2, -8, -10],\n [4, 21, 2, 5, 19, -10, -20, 11, -22, -3, 6, 21],\n [-4, -13, 7, -23, -26, -25, 2, -18, 1, 6, -4, -7],\n [4, 21, 19, 18, -1, 4, 5... | 526 | 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, -12, 18, -25, 11, -24, -1, 6, 22, -3, 6, 3],\n [16, -23, 16, 18, -5, 22, -7, 2, -6, 18, -10, -25],\n [7, -5, 23, -21, -2, -25, 16, -10, -18, -7, 1... | 83 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 7, -1, 25, -12, -21, -2, -9, -20, -25, 7, -26],\n [19, -25, 15, 9, -23, 1, -4, 12, -7, 10, 17, -15],\n [5, 11, 4, -9, 2, 7, 24, 2, 0, 4, 21, 7],\n [-10, -7, 4,... | 77 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-15, 17, 9, -12, -8, -9, -1, -16, 3, 1, -4, -12],\n [21, -16, 16, -6, 18, 12, 4, -12, -10, -2, -3, 18],\n [9, 6, 17, -23, -26, 11, -16, -6, -2, 23, 1, 23],\n [25, -21, 19, -21, -5, -1... | 525 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[16, 8, -21, -18, 18, 0, -26, 3, -12, 5, -7, -23],\n [7, 21, 11, -7, 20, 24, 1, 12, -2, -16, 23, -19],\n [7, 0, 17, -5, -19, 6, 12, -18, -5, -18, 4, 7],\n [-23, 19, -13, -19, 26, 14, 8, -5, 24, -21, 6, 26],\n [-9, -19, -20, 5, -20... | 501 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 24, -17, 23, 17, -18, -5, -17, -7, -7, 24, 0],\n [26, 11, -17, -8, 14, 3, -11, 13, -15, -22, 16, 24],\n [-24, -3, -1, 4, 20, 25, -24, -26, -16, 18, -22, -20],\n [6, -14, 15, 4, 25, 23, -14, -2... | 571 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[12, -7, 21, -1, 7, 5, 6, 13, -22, -17, 9, 3],\n [-18, 19, 5, -6, 15, 23, -1, -4, -18, -22, -19, 17],\n [25, 24, 19, 16, -16, 9, -9, 4, 14, -19, 9, 24],\n [-8, -5, -25, -16, -24, 6, -17, 26, 18, -2... | 88 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[10, 0, -21, 18, 14, -10, 20, 3, -12, -8, 3, 13],\n [-18, 7, 19, -1, 19, 10, 8, 15, -25, -14, 16, 16],\n [-18, -6, 14, 17, -26, -7, 22, -22, -15, 16, -6, 21],\n [12, -4, -19, -5, -1, -8, -12, 10, 14, ... | 101 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, 11, 17, -15, 4, 17, 10, 11, 20, -20, -20, 8],\n [0, -1, 13, 16, -8, -5, -26, 7, 23, 5, 26, 2],\n [-5, 24, -7, 1, 18, 23, 24, 1, -19, 20, -6, -9],\n [15, -12, -17, 0, -9, -7, 11, 6, 19, 25, 3, -24],\n [-26, -17, 2... | 91 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[14, 23, -21, -7, -23, 13, -8, 16, 13, -17, -22, -25],\n [4, 17, 26, -7, -21, 16, -8, -9, 3, -20, -10, 26],\n [26, -23, -24, -2, 3, 9, -13, 14, -4, 23,... | 87 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, 13, 5, -16, 1, -22, 8, -2, 25, 14, 24],\n [-20, 6, 15, 0, 17, 20, -6, 0, -2, -5, -16, -21],\n [-24, 3, 1, 14, -10, -4, 24, 7, -6, -22, 23, 17],\n [-12, 19, -25, -3, -17, -7, 8, 14, 20, -6, ... | 87 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 1, -4, 12, 3, 9, 11, -13, 4, 19, -15, 20],\n [-16, -23, -2, 16, -2, 17, -7, -19, -3, -9, 11, -18],\n [-3, 22, -22, 21, 18, -14, -6, -18, -25, 26, 21, -26],\n [-19, -3, 7, -17, 18, -26, 8, 14, -1, -23, 4, -22],\n [-4, 7, -12, -24, ... | 98 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[11, 1, -1, -19, -17, -5, 7, 18, 24, -5, -5, -21],\n [4, 9, -16, -9, 7, -24, 22, 14, 24, 23, 11, 9],\n [-10, 3, 3, 24, 26, 16, 23, 4, 5, 21, -8, -18],\n [22, -11, ... | 95 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[24, 1, 3, 14, 23, -4, 6, 25, -13, -13, 23, -14],\n [-23, 23, -8, -3, 9, -21, -15, -18, -14, -3, 19, -12],\n [19, 23, 3, 5, 5, 7, 8, -9, -8, 23, -12, -5],\n [-2, -3, -21, 9, -17, -15, -22, -7, 10, 21, -9, 20],\n [13, 6, 14, -15, 6... | 529 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[17, 18, -1, 17, -22, 6, 22, -22, 1, -6, -19, -25],\n [10, -13, 7, 26, 17, 19, 10, -6, 0, 23, -9, 21],\n [-22, 7, -9, 8, -1, 2, 14, 1, -21, -1, -9, 3],\n [6, 5, 23, -1, -5, 7, 22, -15, -5, -6, -3, -2],\n [-25, -26... | 549 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[8, -10, -4, -1, 19, 21, -20, 14, -20, -12, 3, -7],\n [-24, -5, 21, 23, -20, 4, 22, 23, -24, 16, 19, -10],\n [24, -5, 25, 10, -24, 21, 3, -3, 6, 16, -17, -20],\n [-11, 5, -25, -19, -12, 21, -24, -... | 578 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, 4, 10, 2, 13, -15, 6, 20, 18, -2, 15, -9],\n [3, -9, -20, -12, 3, -22, -22, 6, -21, 21, 13, -23],\n [-14, 24, 15, -1, 22, -7, 5, 5, 23, 10, 17, -26],\n [-2, -2, 26, -26, -24, 12, -6, 16, -2, 25, -6, 20],\n [-... | 516 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[25, 13, 26, 20, -12, -19, 18, 20, -11, 2, 7, 2],\n [8, 21, -17, 25, -26, -22, -24, 12, 23, -13, 19, 0],\n [19, 2, -26, -9, -24, -1, -6, -3, 18, 25, 20... | 84 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-11, -9, -11, -25, -26, -17, -2, -13, -10, -9, -20, -6],\n [2, 0, 22, -23, -15, -5, 13, 7, -1, 1, -8, 4],\n [-13, -4, -10, -4, -10, -19, 11, -17, 3, -20, -25, 20],\n [-5, -22, -24... | 99 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, -16, -12, -13, 18, -10, -6, 1, 16, 11, -5, 7],\n [-26, -4, 5, -23, 14, 16, -21, -11, -17, 8, -3, -17],\n [-15, 6, 0, -2, -17, -2, 5, 15, -1, -23, -18, 0],\n [-18, 17, -1, -16, 26, 11, 5, 3, 12, -18, -16, -4],\n [-... | 92 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -22, 14, 21, -23, 21, -22, -20, -16, 12, -21, 2],\n [24, -10, 1, 11, -8, 22, 17, -15, 18, 11, -8, 6],\n [18, -22, -26, 8, 8, 20, 20, 4, 9, 13, 8, 13],\n [-15, -9, 1, -14, 3, 13, -10, -18, 12, -5, ... | 96 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, 14, -16, -21, 24, 18, -10, -13, 5, -7, 26, -23],\n [12, 20, -5, 2, 15, 10, -14, -12, 8, -2, 24, -24],\n [24, -15, -13, 13, 5, 23, -23, 2, 4, 5, -3, -16],\n [3, 22, -8, 9, -21, -25, 12, -8, 19, 21, 13, -9],\n... | 590 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -6, -15, -14, 23, -14, 25, 0, 1, -9, 10, -11],\n [26, -6, -17, -13, 1, 2, 20, -16, 3, 13, 0, 22],\n [-24, -26, 5, 12, -6, -25, -17, 4, -9, -20, -22, 2],\n [-23, 19, -24, -14, -24, -19, 23, 24, ... | 81 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 3, -22, -5, 8, -22, -15, 8, -6, -1, -26, 22],\n [-17, 11, -3, 25, 4, 18, 20, -4, -6, -25, 26, 4],\n [-25, 3, -2, 22, -8, -26, 10, 1, -7, 21, -22, 3],\n [-4, 15, 0, 26, 15, -26, -1... | 522 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-22, 2, -12, 3, 19, -21, -21, -4, 25, -22, -5, 14],\n [-7, -7, 12, 3, 21, -10, -4, 13, 23, 25, -14, 19],\n [9, 15, -17, 11, 12, 12, -23, -8, 25, 14, 1, 0],\n [-4, -8, -11, 8, -22, -3, -22, 2, -21,... | 96 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, 4, 8, -6, 7, -10, -18, 2, -19, -8, 20, -21],\n [-3, -21, 13, -24, 4, 4, -15, 25, -19, 16, -1, -1],\n [-12, -14, -5, -14, 19, -18, -3, -24, -4, -15, 14, 17],\n [-16, -8, -18, 10, -17, -18, 6, -14, -7, 17, -16... | 496 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-20, 11, -15, -10, -6, 26, -21, 20, 10, -2, -12, -16],\n [-18, -23, -24, -14, 5, -21, -26, 15, -22, -25, -5, 5],\n [24, 21, 14, 23, 22, -20, -6, -10, 26, -7, -26,... | 93 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -12, -18, 2, -25, 3, 19, -23, -8, -7, -22, -18],\n [-7, 25, 22, -11, 22, -7, -7, -1, 12, 6, -15, -6],\n [-4, -7, -4, 22, 20, -21, 18, -15, 8, -19, 0, -11],\n [20, 26, 5, 2, -20, -11, 2... | 92 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[13, -26, -2, 19, -13, -8, -19, 14, -12, 17, -9, -26],\n [20, 6, -26, 26, 7, -23, -10, -25, 12, -17, 15, 18],\n [10, -1, 0, 12, -2, 2, 19, -9, -5, 24, -1, -1],\n [25, -6, -6, 15, -19, 26, -25, 19,... | 548 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -14, -14, -26, 24, 26, 14, 9, 5, -22, 22, -20],\n [23, 18, 5, 1, 6, 19, -13, -14, 2, 23, 13, -26],\n [20, 22, 22, 0, 3, 7, 19, -26, 7, -20, -26, 15],\n [-9, 8, 23, -8, -14, -4... | 84 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, 14, -1, 20, 4, 8, -20, 13, 18, 5, 26, -5],\n [20, -21, -6, 18, 12, 22, 20, 10, 0, -17, -5, 17],\n [24, -9, -23, 18, 8, 11, 11, 9, -23, 18, -17, 5],\n [-17, 16, 18, -17, -16, 23, 12, -1... | 100 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-17, 6, -15, -19, 13, -5, 12, 12, 20, 17, -11, 21],\n [7, 19, -11, -13, -21, 23, -17, -3, 0, 20, 23, -18],\n [21, -11, -25, 4, 20, -8, -16, -5, 2, 4, -19, -17],\n... | 83 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-15, 11, -4, 21, -19, -12, 3, -18, 18, -6, 17, -13],\n [-19, 20, 9, -18, -1, -7, 11, -21, 7, -4, 12, 6],\n [-6, 14, -1, -22, -18, 18, 6, -2, 25, 20, -10, 13],\n [20, -8, -16, -19,... | 89 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 15, -13, -4, -4, -17, 11, 22, -10, 0, -16, -8],\n [18, 17, 17, 0, 9, -11, -4, 6, 25, -5, -13, -14],\n [-5, -20, 11, -26, 24, 6, -5, -4, -12, 17, -12, 4],\n [1, -24, 15, -2, 6, 6, -4, 1, 26, -11, 10, -22],\n [16, ... | 91 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-18, -4, -7, 7, -11, -5, 19, -4, -26, -13, 25, 22],\n [-4, 11, 13, 23, -19, 5, 13, -25, 21, -14, 0, 19],\n [-20, -24, -6, -19, -26, -10, -1, 2, -19, 11, 24, 16],\n [-19, -19, -2, 15, 15, 18, 0, -5, -24, 22, 26, 20],\n [11, 22, -3... | 565 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -15, 1, 4, 3, 12, -11, 3, -23, 6, 6, 1],\n [-6, -12, -1, -13, -12, -25, -11, 10, -16, -16, 6, -25],\n [6, -24, -7, 6, -1, 22, 7, -13, 25, 2, -25, 23],\n [-19, 0, -19, -20, -16, 25, 12, 3, 12, 22, 20, -6],\n [-6, ... | 88 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[14, -21, 9, -13, 14, -3, 6, 24, 15, 23, -8, 2],\n [26, -21, -24, -9, -6, 2, 25, 26, 15, 25, 9, 4],\n [-19, 5, -11, -5, -25, 24, -12, 13, -10, -14, 8, -2],\n [-17, 18, -16, 6, -13, 7, -5, 17, -23, 17, -1, -26],\n [-17, 9, -25, 2, ... | 489 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-13, -3, -3, -9, -2, -2, 14, -2, 1, 3, -2, -3],\n [13, 12, -14, -25, 7, -11, 21, -3, 23, -25, 2, 12],\n [12, -10, -4, -15, -14, -22, -12, 26, -25, -21, 9, -4],\n [-14, -25, -22, 13, -11, 12, 8, 14, 18, 7, -8, 16],\n [-1, 15, 16, -10,... | 83 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-26, 4, -4, 16, 11, 22, -16, 12, 21, -7, 10, -20],\n [8, -25, 6, 13, -3, 12, -17, 19, -18, 16, 6, 24],\n [-6, -13, 23, -4, -15, -5, 1, 0, -17, -9, -3, -24],\n [-23, 3, -6, -5, 1, -18, 17,... | 88 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 21, 8, 25, -21, 8, -1, -12, -22, -1, 6, -2],\n [-10, 25, 17, -7, 15, -25, -19, -8, 2, 21, -8, -18],\n [-19, 22, -12, 7, -23, 0, 11, 20, -14, 5, 8, 25],\n [21, 19, 9, -17, -4, -4, ... | 546 | 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, -2, 19, -16, -15, 18, -19, -17, 8, 11, -6, 24],\n [-9, -9, -1, -7, -2, 4, -9, -11, 26, 18, 16, -9],\n [21, -13, -20, 11, 22, 2, -4, 20, 15, 22, 7,... | 94 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 26, -26, 8, -22, 25, -21, 9, -22, 17, 5, 12],\n [18, 4, 13, 18, 17, 15, -17, 4, -19, 0, 2, -13],\n [-4, -23, 25, 7, 14, 11, 0, -8, 4, -24, 2, -14],\n [0, 16, 5, 19, 22, 23, 10,... | 87 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[21, 8, 20, 6, 17, 15, -4, 0, 11, -19, 25, 11],\n [24, -23, 21, -22, -11, -9, 18, 18, -9, -19, 2, -6],\n [12, 0, 20, -25, -23, 21, -15, -11, -2, -4, -10, 25],\n [15, 20, 24, 19, -26, -6, 9, -25, -4... | 94 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[25, -1, 6, -26, 13, 16, 17, 9, 12, -2, -14, 12],\n [9, -15, -6, -4, -9, -14, -8, 8, 19, 21, 7, 25],\n [-26, 19, -5, 1, -23, 10, -20, -16, -15, 13, 26, 12],\n [8, ... | 104 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 8, 13, 24, -15, 16, -6, -16, -24, -18, 16, -8],\n [15, -4, -11, -23, 5, -26, -23, -1, 0, 13, -11, 3],\n [11, 6, -11, 6, -7, 4, 21, 0, 5, -5, 9, 0],\n [-2, -25, 19, 11, -4, 25, -15, 10, 19, 10, 23, 21],\n [-6, 21, 15, -16, -6, 10, ... | 89 | MATH |
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