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 sum of all singular values:\n[[15, -17, -12, 21, -19, 18, 14, 19, -5, -7, -9, 7],\n [-4, 1, 14, -17, 25, 16, -4, -17, 24, -26, 2, 19],\n [14, -22, 17, 2, 25, 23, 22, -7, -19, -2, -26, 9],\n [17, -11, -22, 23, 23, 2... | 582 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-16, 1, 15, 25, -16, -21, 13, 3, -13, -14, 8, -21],\n [22, 6, -16, -26, 0, 3, 19, -1, 1, 14, 5, -17],\n [-15, 26, 9, 23, 16, -5, -11, -9, -20, 25, 9, -25],\n [-18, 17, 3, 1, 2, -8, 1, 14, -2, 2, -4, ... | 99 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -8, -14, 18, 18, 7, 20, 6, 20, -11, 16, 3],\n [-24, 0, -7, 5, -6, 19, 26, -22, 22, -25, -5, -20],\n [15, -17, 25, 13, -26, -11, 14, 1, 21, -7, -1, -12],\n [14, 3, -15, -25, -17, 0, -6, -11, 10, 18, -5, 12],\n [14, -5, 22, -1... | 557 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[13, 7, -23, -25, -18, 3, 10, -8, 24, -18, -22, -11],\n [-1, -20, -25, -13, 4, -5, 6, 13, 22, 4, -8, -21],\n [19, 13, 16, 19, -17, 22, -15, -1, -23, 24, 22, -22],\n [3, -3, 19, 12, 8, -22, -22, -19, 8, -26, -25, -20],\n [-12, -13, -14... | 105 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-14, -5, 15, 11, 26, 1, 25, -22, 3, 5, 18, -7],\n [-7, 14, -18, -20, -20, -1, 6, 23, 4, 17, -13, 20],\n [8, 3, 8, -8, -18, -9, -26, -10, -5, -15, -9, -25],\n [-3,... | 96 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[22, 0, -18, -15, 24, 20, -9, 22, -13, -17, -7, -5],\n [7, 21, 11, -22, 3, -26, -1, -20, -20, 18, -22, -7],\n [23, 1, -4, -19, 20, -11, 14, 21, -21, -16, -14, -25],\n [22, -25, -14, -8, 6, 10, -2, 21, 11, 19, 13, -9],\n [2, 10, -16, 1... | 94 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -11, 20, -13, -23, 25, -3, -14, -22, 13, 6, 18],\n [10, -19, 12, -8, -17, 15, 12, -8, 4, -13, -2, -19],\n [-23, 20, -22, 9, 17, -21, 3, 13, 11, 10, 14, -8],\n [15, 16, -9, -6, 10, 16, -10, 4, -6, -16, -11, -18],\n [24, -4, 12, -4,... | 96 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, 19, -21, -26, -16, 16, -10, 12, -18, -11, 26, 0],\n [14, -22, 11, -19, -18, -14, -24, 0, 23, 10, -7, 6],\n [-14, 25, -3, 23, 15, -3, -7, 0, -9, 1, 9, 6],\n [5, -20, -12, -13, 8... | 88 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, 8, 22, -5, 26, -18, -26, -12, 26, 3, -24, -21],\n [4, -22, -23, -2, -16, 16, -13, -2, 22, 25, 0, 2],\n [25, 14, -26, 19, -22, -6, 13, 10, 7, -25, 18, 24],\n [-9, -12, 19, 6, 25, -16, 24, 2, ... | 549 | 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, -1, 2, 20, -21, -8, 23, -2, -17, 9, 21, 24],\n [16, -17, -11, -12, 22, 7, 19, 13, -12, -26, -21, 25],\n [-8, 16, -21, 24, -23, -17, 16, 13, -18, -2... | 97 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-12, -13, -1, -2, -8, -7, 24, -1, 5, -4, -13, -5],\n [3, 1, 11, 13, 3, 24, -24, 8, -23, 12, 7, 18],\n [-16, -14, -25, 9, 26, 3, -11, 5, -12, -4, 20, 8],\n [18, -10, -9, 5, -11, -26, -13, -25, -21,... | 90 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[22, -9, -13, -7, 15, 18, 22, -26, -4, 13, -11, 18],\n [12, -8, -19, -3, 26, 17, -11, -14, 23, 3, -14, -6],\n [-8, 0, 11, 17, 11, 24, -4, -11, 19, -3, 17, 23],\n [... | 80 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -9, 22, 26, 24, -17, -26, 1, 6, 12, -9, 16],\n [18, -18, 1, -4, -1, 22, 16, 6, -7, -11, -8, 5],\n [-16, 19, 17, 13, 20, -1, -26, 11, -15, -18, 23, -19],\n [4, -7, -8, 5, -22, 4, -5, -7, -15, -8, 10, -25],\n [-... | 537 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 12, -15, -10, 14, 15, -25, 12, 23, -21, 24, 4],\n [22, -2, 1, 18, -1, -23, 2, -12, 7, 6, -11, 13],\n [12, -22, 25, 7, -5, 10, -17, 4, -13, 7, 26, -8],\n [10, -6, 10, -3, 5, 3, 10, ... | 511 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, -3, 5, 6, 12, -17, -5, 21, 20, 14, -13, -23],\n [2, -21, 20, 13, 15, 12, 22, -2, 18, -19, -16, -26],\n [-21, 11, 1, 5, -18, 7, 22, -25, -5, 12, -4, 24],\n [25, -24, 16, 18, -11, 14, 3, -8, 17... | 97 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 12, -19, -23, 10, 5, 22, 11, 2, 2, -26, -24],\n [15, 18, -8, -13, 5, -4, 16, -1, -9, 16, -12, -2],\n [9, 16, 11, -5, -9, -15, 0, 21, -7, -11, 23, 19],\n [22, -12, -17, 12, -22,... | 94 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-15, -17, -24, -19, -22, 21, 9, 21, -5, 8, -4, -23],\n [-11, 10, -5, -6, 23, 0, 25, 13, -19, -20, 15, 7],\n [3, 25, -2, 11, -12, 19, 1, 13, -18, -22, 10, 14],\n [-5, 12, 13, -12, 8, 26, 0, -10, -8, -9, -17, -25],... | 553 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[23, 24, -7, 3, 24, 25, -14, -22, 10, -16, 15, -21],\n [11, -2, 18, 11, 12, 13, 15, 16, 2, 10, 13, 6],\n [-20, -9, 17, 24, 13, 8, -17, -4, -13, -8, 24, 3],\n [-18, -22, 12, 18, 23,... | 85 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, 12, 10, -9, -17, -4, -4, 13, 9, 6, 18, 15],\n [-15, -7, 7, -21, -17, -17, -24, 11, 1, -12, 17, -18],\n [-23, 11, 23, 3, 11, 6, -15, 8, -15, 8, 15, 11],\n [26, -10, 6, 7, -8, -7, -1, ... | 90 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, -3, 23, -24, 19, 22, -3, 19, 26, -19, 17],\n [-13, -25, -21, -15, 9, -1, 2, -23, 3, 21, 25, -11],\n [-19, 5, 8, 13, -3, 4, 18, 12, 7, -22, -13, 10],\n [9, -10, -7, -26, -11, 16, -4, -16, 22, -23, 21, 17],\n [-4, 4, 4, -22, 0, 2... | 96 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 19, 6, -5, -21, 11, 19, 21, 11, 25, -16, 19],\n [14, -20, -3, -19, -15, -17, -16, -7, 11, 17, -4, -5],\n [18, -5, 12, 14, -24, 8, -11, -9, -14, -5, -18, -21],\n [20, -18, -9, 25, 18, 6, 11, 24... | 548 | 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, -4, -23, -22, -1, 0, -23, -6, -2, -16, 4],\n [-10, -20, 14, 0, 22, 24, -14, 4, -23, -18, 16, 18],\n [3, -3, 21, 15, -23, -24, 26, 12, 2, -6, ... | 108 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -1, -22, 24, 20, -20, 9, -20, 12, 15, 9, 23],\n [-21, -6, -26, -25, -24, 12, 7, -13, -2, 10, 10, -11],\n [-12, 21, -3, 14, -19, -25, 15, -1, -9, -9, -8, 10],\n [6, 5, -2, 0, -6, -4, -16, -6, 16, 4, 8, 8],\n [... | 517 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -22, -19, 16, -12, 10, -13, 1, -17, -21, 19],\n [-7, -23, 19, -24, 4, 23, -7, 16, -2, -2, -15, 21],\n [-7, 14, 26, 16, 1, 4, -18, -18, 12, -18, 6, 9],\n [1... | 95 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 22, 6, -19, -9, -11, 4, 21, 14, -10, 2, 14],\n [-10, -1, -17, -12, 4, 13, 22, -19, 22, 18, 13, -25],\n [26, -12, -3, 1, -21, 13, -24, -11, -25, -17, -24, -16],\n [20, -2, -25, -18, -8, 22, 3, -26, -4, 13, -26, -1... | 103 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, 4, 4, 14, 13, -9, -5, -10, 18, -4, 11, 1],\n [-20, 7, -25, 17, -25, -5, -26, 7, 10, -16, 0, -13],\n [-19, -10, -14, 13, 20, -20, -12, 14, 19, -12, 16, 9],\n [... | 87 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, 6, -26, -17, -9, -5, 26, 26, 4, -25, -4, -24],\n [19, 17, -3, -2, 14, -14, -17, -21, -22, 23, 12, -11],\n [16, -6, 15, 13, -22, 6, -24, -12, -17, -26, -17, -11],\n [4, 17, 1, 10, 0, -1... | 88 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, -20, -13, 18, -26, 25, 6, 7, -11, 4, -25, -15],\n [-8, -12, -11, -11, 1, -16, -21, 0, -10, 12, -16, -14],\n [21, -14, -19, -2, 14, 10, -13, -6, 16, 17, -7, -7],\n [15, 0, 6, 4, -11, -2... | 88 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[8, 9, 23, -13, -7, 1, -14, 22, 17, -20, -24, -22],\n [26, 25, 6, 19, -18, 26, 0, -12, 7, -9, -23, 7],\n [18, -6, -9, 25, 9, 8, -20, 7, 19, 10, -25, 14],\n [-11, 1, 3, 4, -19, 11, 8, -20, -9, 21, 9, -6],\n [-23, 5, -11, -9, 7, -5,... | 548 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, -19, 15, 9, -16, 19, -11, 15, -12, 13, 20, -8],\n [-19, -10, -9, -25, 10, 21, -3, -10, -12, 24, -3, -4],\n [0, -5, 20, -14, 22, 25, -15, 8, 1, -17, -17, 18],\... | 81 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -15, -11, -26, 24, 3, 9, 15, 15, -3, 12, 11],\n [5, 5, -15, -17, -15, -14, -12, 3, 26, -14, 24, 21],\n [16, -26, -9, 12, -15, 23, 17, -18, 22, -23, 0, 1],\n [-3, -23, 1, 25, -7, 2, 6, 3, -24, -8, -6, 13],\n [-6, ... | 101 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 16, -13, -15, -22, 7, -20, -22, 8, -2, 3, 15],\n [-16, -19, 11, 1, -15, 18, 7, 4, -6, -11, -3, -5],\n [-14, -18, 18, 20, -19, -4, 22, -17, 14, -10, 2, 22],\n [24, 24, -25, -16... | 98 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-17, -11, 2, -12, -5, 16, -21, 24, 20, 0, 2, 18],\n [1, -8, 6, -17, -16, 17, 3, -13, -11, -20, 26, -23],\n [-11, 24, 8, -18, 22, 9, -18, 5, 19, -1, 17... | 91 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[19, -23, 26, -17, -14, -20, 8, -22, -9, -20, 11, -19],\n [12, 25, 26, 16, 15, -1, -21, -9, 11, -17, -18, 13],\n [-15, 2, -6, -6, 0, 15, -15, 2, -1, 23, -1, 24],\n [1, -13, 18, -2,... | 101 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -24, 24, -17, 19, 5, -6, -21, 17, 5, 17, 1],\n [-23, 3, 15, 17, -10, 1, 12, -17, -26, 24, 4, 5],\n [-7, 2, 10, -2, 11, -26, -12, 7, -4, 2, 23, -14],\n [-25, 13, -22, -5, -12, -14, 3, -2, -6, -10, 9, 12],\n [7, 14, 7, 22, 26, 2... | 543 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[25, 26, 15, 3, -3, -25, 7, 15, -6, 7, 5, 3],\n [-13, -8, 3, 14, 0, -11, -2, -2, -3, -24, -3, -16],\n [5, -4, -15, 12, -6, 10, 25, 7, -6, -1, 9, 22],\n [23, 7, -18, -9, 17, 15, 12, 3, -24, 23, -25,... | 85 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, 10, -19, 3, -7, -26, 22, -20, -16, 12, -20, 26],\n [9, -7, 6, 20, 7, -4, -3, -18, -4, 19, 21, -10],\n [12, 7, -21, -24, 26, 11, 11, -19, 13, -18, -12, 3],\n [22, -23, 2, 6, -21, 2, -8, 10, 0, -16, 15, -18],\n [-11, 24, -9, -1... | 550 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -17, -20, -1, 1, -25, 17, -13, -20, -10, -12, -5],\n [5, -1, -4, -1, 23, -3, -5, 0, -6, 10, 16, -19],\n [-13, -25, 25, -20, 0, -19, -23, -17, 19, 20, -17, -11],\n [-24, -4, -25, -26, -16, 21, 17, 10, -7, -6, 3, -2],\n [20, -10, 1... | 94 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, -25, 19, 17, -5, 24, 23, 17, -26, -17, 7, 4],\n [-13, 25, 21, -8, 19, 2, 19, 9, 3, -16, 3, -5],\n [26, -25, 12, -2, 18, -19, 5, 17, -20, -5, 2, -25],\n [11, 16, 22, -12, -7, -1, -16, -4, 14, 22, 25, 15],\n [-23, -23, 21, -26, -4,... | 100 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, -23, -24, 17, 23, 9, 21, -20, -17, 6, -13, -9],\n [6, -1, 12, 23, -10, 16, 1, -25, 13, 10, 5, 0],\n [4, -23, 8, 5, -16, 26, -4, 20, -4, 12, 8, -10],\n [25, 22, -7, 16, 23, 5, 11, ... | 549 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-25, -5, -3, -1, -5, -22, -17, -8, 14, -5, 0, -25],\n [-6, -2, -5, -18, 4, 18, -26, -12, 3, -14, -13, 16],\n [7, -2, 6, 16, -6, 5, -11, -22, 0, -1, -8, -5],\n [-17, 25, -12, 7, 3, 8, -13, -4, 22, -20, 19, -1],\n ... | 548 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, -12, -19, -15, 16, -3, 11, -14, -9, 8, 2, -7],\n [7, -24, 13, 8, 15, 4, -20, -18, 26, 23, 21, -10],\n [25, -20, 24, -22, -3, -12, -25, -12, -6, 10, -13, 24],\n [-25, -2, 0, 25, 26, 24, 11, 26, -8, 15, 21, 3],\n [22, -17, 4, ... | 532 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-23, 14, 10, 15, -15, 25, -22, -2, -2, 6, 25, -12],\n [-7, 12, -15, -13, -5, -3, -15, -7, 21, 1, -16, -5],\n [23, 6, -13, -14, -2, 13, -11, 3, -26, 1,... | 89 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, -22, 11, -21, -1, -8, -12, -18, -14, 8, 20, 7],\n [7, 2, 12, 0, 19, 18, -15, 12, -25, 20, 9, 26],\n [-9, -21, 3, -6, -5, -16, 12, 13, 15, -20, -20, 4],\n [-21, -1, 9, -18, 9, -24, 17, 4, 26, 3, 4, 16],\n [16, 13... | 88 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[25, -15, 17, -15, -1, 15, 13, 1, 17, -2, -6, 21],\n [23, 22, -16, -18, 26, 8, 9, 22, 2, 13, -10, 10],\n [21, 22, -19, 26, 17, 20, -22, -4, -17, 20, 14, 20],\n [-12, -11, 0, 5, 13, 24, 18, 19, 8, ... | 544 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[12, 16, -2, -1, 17, -16, 11, -18, 16, 6, 24, -11],\n [22, -7, -20, 6, -14, 20, 8, -23, 4, 3, -24, 14],\n [0, 5, 20, 11, -21, -19, -3, -12, -2, 0, 17, -14],\n [-7,... | 95 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, -18, 0, -15, 7, -4, 8, 13, -18, 16, -14, 25],\n [23, 19, 16, -25, 20, -25, 2, 18, -5, 16, -6, 20],\n [-21, 20, 1, -11, -26, -4, -19, 25, -19, 15, -26, -16],\n [-19, 20, 24, 4, 19... | 555 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[21, -10, 10, -14, -5, 23, -8, 1, 26, 16, -2, 17],\n [-19, 18, 5, 20, -16, 11, -9, 21, 0, 11, 10, 19],\n [15, 9, 14, 7, -12, -14, 0, -8, 9, -14, -20, 18],\n [-26, 14, -6, -11, 22, 2, -3, -8, 0, 21, 20, -26],\n [0, -13... | 93 | 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, 4, 11, 15, 10, 26, 2, -21, -19, -2, -22, -17],\n [-4, -26, -14, 10, -1, -8, -1, 21, 23, 24, 15, -25],\n [14, -8, -15, 17, 8, 5, 26, -14, 9, -26, 6,... | 93 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 24, 2, -6, 15, -18, 2, -15, -19, -17, 7, 20],\n [-7, -11, 15, 18, -16, 21, -13, 4, 13, 24, 7, -23],\n [23, 21, -20, 15, 11, -26, 23, 19, -3, 15, 1, -3],\n [-14, 11, -17, -1, -25, 6, 1, 0, -21... | 555 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[16, -1, -26, 22, -8, 18, -15, 17, 1, 18, 11, 4],\n [-14, 26, 16, 25, 26, 26, -16, -15, -4, 20, 2, -18],\n [-13, 5, -24, -20, -21, 8, 0, 1, -4, -17, -10, -12],\n [-13, -16, 2, -9, ... | 84 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, 17, -18, -22, -15, 2, -26, 6, -6, -6, 0, -25],\n [-19, -15, -5, 22, -18, 17, 11, 2, -24, -5, -23, 2],\n [14, -14, -3, -25, -24, -12, -3, 23, -1, -19, 13, 26],\n [20, -22, -19, 19, 12, 19, 5, 4, -19, -10, -4, 12],\n [23, -14, 17, ... | 86 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -4, -25, -18, 10, 15, 5, 16, -5, -9, 15, 19],\n [-4, -18, 0, 7, -18, -6, -10, -22, -13, -9, -3, 24],\n [-18, 4, -6, 8, -1, -10, -23, -20, -24, 14, 4, -6],\n [-13, 17, 0, 11, -4, -17, 19, -6, 23, ... | 86 | 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, -3, 9, 0, 25, 16, -17, -14, 25, -5, 18, -21],\n [23, -6, 0, 17, 7, -21, -20, 8, 3, -16, 3, -6],\n [14, 19, -16, -21, -8, 20, -2, 5, 0, 19, -15, -14... | 88 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, -1, -26, -26, 15, -24, 15, -23, -3, -15, -13, 13],\n [-3, 3, 12, 6, 22, -6, -12, 20, 5, 10, 26, 4],\n [-26, 24, 6, 7, 16, 17, -16, 13, 25, 9, 26, 7],\n [-18, 4, 2, -14, -17, -18, 18, -24, 22, -9, 0, 5],\n [-19, -14, -9, -1, -11, ... | 95 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, 15, 23, 8, 1, -7, -5, -26, 15, -19, -19, -7],\n [-10, -12, 16, 21, -5, -11, 6, -3, -7, 3, 6, -2],\n [19, 19, 9, -19, 3, -11, 13, -12, 0, 23, 18, -17],\n [-3, 4, 11, -8, -26, -25, 12, -15, 3, 13, -14, -2],\n [6, -2, -9, -19, 5... | 517 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-11, 26, 4, 4, 8, 10, -13, 20, 12, -2, -26, 2],\n [1, 2, -17, -19, 13, 3, 3, 14, -21, -12, -3, -14],\n [-18, 23, -7, 9, 25, 22, -14, 0, -9, -19, 15, 22],\n [-19, 24, 25, -3, 17, 13, 0, 24, -7, 8, -19, -3],\n [13, -15... | 97 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-14, -9, -22, 4, -10, -12, 7, -5, -22, -11, 6, 14],\n [-23, 6, 1, -16, -22, 15, 14, -20, 24, -3, 17, 23],\n [-23, -15, -23, -2, -24, -10, -1, 23, -18, 19, -14, -22],\n [20, 26, -22, -15, 1, -17, -... | 91 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, -23, 24, -24, -1, 10, 7, 15, -18, 17, -13, 20],\n [6, 21, 11, -22, 24, 20, 1, 6, -10, -6, -20, 13],\n [8, -20, -19, 24, 17, 15, 4, -22, -22, -3, -5, 17],\n [-14, -5, -1, -26, -10, -8, -25, 23, 25, -16, 3, 19... | 535 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 22, -9, 25, -15, -2, 0, 14, 26, -18, 22, -14],\n [22, -5, -25, 12, 21, -12, -4, -14, 18, 20, -7, -14],\n [0, 15, -10, 4, -1, -5, 14, 5, -5, 1, 15, 20],\n [-26, -23, -11, 16, -4, 11, 14, 21, 9, -13, 16, 16],\n [-24... | 88 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-8, -14, 24, 10, 12, 25, -24, -20, 1, -13, 10, 21],\n [25, -5, 4, -26, 20, -15, -3, 3, 19, 21, 0, -11],\n [-6, -23, -25, -6, -20, 10, -20, -25, -15, -26, -24, -26],\n [8, -11, 24, -19, -6, 24, -22, 4, -1, -26, -4, -1... | 87 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -26, -18, -7, 11, -9, 2, 10, 22, -15, 10, 5],\n [-15, 10, 12, -15, 6, 16, 5, 6, -3, 4, 20, 3],\n [-1, -25, 25, -10, -26, 25, 4, 2, -16, 18, -23, 9],\n [-19, 9, 20, -6, -16, -15, -1, 0, 7, -17, -18, 12],\n [-14, -... | 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[[13, 5, 13, -24, -17, 13, 26, 2, 18, -8, -2, -7],\n [20, 11, 19, -17, 24, -16, -13, 24, 4, -22, 16, 1],\n [-8, 6, -25, 2, -9, 19, -17, 11, -12, -5, 0, ... | 89 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, 24, -18, 2, 24, 24, -6, -10, 6, 7, -1, -9],\n [7, 11, -2, 25, 24, 7, 23, 21, 18, -12, -25, -4],\n [18, -21, 12, -8, 7, 10, 19, -4, -12, -25, 11, -2],\n [17, -19, -16, 2, -22, 10, -7, -15, -11... | 84 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 10, -4, 2, -14, 5, 17, -17, 16, 21, -21, -6],\n [8, -24, -6, -7, 23, 16, 7, -24, 18, 18, 13, 10],\n [26, -22, 23, -16, 21, -10, -23, -19, 14, 20, -5, 5],\n [0, -21, 4, -23, 20, 12, 3, 16, 26, ... | 89 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-24, 26, 16, -16, 20, 1, 1, 3, 8, -20, 6, 21],\n [0, 2, 0, 15, 4, 20, -22, 7, 10, -6, -1, 16],\n [-22, 6, 15, -25, -4, 24, 16, 2, -9, 8, -17, 12],\n [6, 5, 15, 10, -4, -26, -10, 19, 9, 0, 21, 12],\n [-26, 11, -13, -2... | 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[[9, -23, 0, -19, -18, -6, 8, 1, 0, -20, 23, 18],\n [7, -13, 2, 19, 2, -6, 22, -25, 24, -17, -3, 0],\n [24, 24, 5, 18, -4, 21, 25, 17, 9, -6, -5, -4],\n... | 91 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 5, 14, 5, -19, -9, -26, -3, 20, -10, -9, -7],\n [-1, 23, 3, 10, 0, 12, -4, -1, -22, -13, 8, 26],\n [5, 18, -23, -5, 22, 6, -14, -19, 11, 19, -18, 17],\n [1, -26, -12, -20, -10, -15, ... | 85 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, -7, -21, -26, -18, 5, 6, -9, 10, -8, 6],\n [-22, -15, -26, -21, -10, -19, -22, 8, 1, -12, 1, -3],\n [-1, -19, 8, -11, -20, -10, 24, 8, 4, -20, 24, -24],\n [-9, 26, 0, -10, 5, -16, -15, 19, 9, -15, -15, -7],\n [... | 90 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[18, 10, -15, 26, 8, 5, -25, 6, -9, 20, -11, -2],\n [-1, -22, -11, 17, -11, -16, -19, -24, 26, -11, -20, 1],\n [-25, 24, 8, 4, -16, 14, -16, -26, 3, 3, 6, -15],\n [-17, 17, 19, 16, -23, 15, 22, 6, ... | 90 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 13, 16, 10, -6, -12, 6, 26, 22, -15, 3, -23],\n [12, -16, 17, 0, 21, -9, -13, -12, 22, 7, -4, 8],\n [-22, -26, -1, -17, -12, 5, 15, -3, 9, 18, -11, -17],\n [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[[14, -6, 26, -24, 5, -21, -20, 24, -12, 7, 19, 19],\n [-15, -9, -2, 11, -25, -6, -4, 6, 0, 16, 2, 20],\n [11, -10, -19, -6, -4, 25, -9, 17, -19, 25, -3... | 84 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -19, -14, 7, 15, -10, 21, 17, 11, -12, 4, 20],\n [21, -24, 18, 23, 8, 9, -22, -1, -1, 25, -3, -21],\n [-20, 25, 1, 18, -13, 12, -6, -16, -15, 23, 23, 7],\n [8, 25, -20, 26, -4, -26, -7, 5, 7, 23, -7, -13],\n ... | 570 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -15, 13, -6, 18, 7, 7, 9, 23, -24, 12, -21],\n [-26, 14, -15, 12, -26, -7, 9, 11, 21, 20, -24, 23],\n [24, 18, -7, 19, 19, -19, -16, 17, -26, 3, 14, 25],\n [-13, -7, 19, 3, 18,... | 87 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-26, -15, -4, -19, 6, -15, -10, 3, 12, 16, -14, -6],\n [-18, 1, -20, -9, 23, 15, 6, 19, -4, 26, -26, 12],\n [-8, -8, -23, -20, 2, 21, 12, -16, 2, -19, 18, -18],\n [-22, 4, -17, 16, -3, -10, 20, -16, 7, -3, -19, 17],\n [12, -3, -2... | 532 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 16, -26, 12, 16, 5, 21, 24, 1, -3, -14, 6],\n [-15, 6, -13, -14, 21, 10, 0, -23, -23, 13, 20, -11],\n [12, 13, -9, -11, 20, 4, -1, -4, 25, 21, 21, -25],\n [11... | 102 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-12, -8, -23, 8, 10, -15, 4, -11, 13, -6, -7, 23],\n [-5, 17, -22, -19, -19, 6, 0, 3, 1, 13, 24, -9],\n [25, -17, 13, -14, 10, 16, 13, 24, -4, -8, -4, 14],\n [-11, -15, 9, -23, -15, 0, -13, -11, ... | 515 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -21, 24, -17, 18, -11, -25, -19, 14, 12, -22, 3],\n [-19, 2, -24, -14, 25, 0, 24, -15, 24, 13, 24, -21],\n [12, 22, -12, 19, 20, -19, 13, 25, -3, 5, 4, 11],\n [-24, 21, 8, -14, 20, 15,... | 94 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, -25, -7, -7, 20, 12, 24, 5, -24, -1, 14, -15],\n [23, -24, 1, -18, -1, -21, -22, -18, 19, 7, 1, -1],\n [8, -26, -23, -14, 13, 26, -6, -9, -7, -23, 5, 0],\n [-2, -20, 18, 3, -4, 2, -6, 6, -9, 0, -... | 85 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, 23, -12, 11, 0, 15, -10, -17, 9, 13, -22, 24],\n [23, 21, 0, 1, -23, -20, -19, -12, 14, 2, 12, -18],\n [-7, -26, -20, 7, 20, -17, 14, 21, -21, -2, -15, 13],\n [14, 12, -13, -16, -15, -8, 15, ... | 571 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[15, 17, -6, -25, -14, 5, -14, 2, -22, -1, 11, 5],\n [21, -9, -10, -7, -12, -12, 20, -23, -18, 17, 19, 6],\n [-17, 20, 16, -26, 13, 26, -18, -5, -1, 8, 6, -17],\n [11, -8, -23, -8, -20, -15, 0, 5, 0, -6, -22, -8],\n [24, 25, 26, -... | 565 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 25, -2, -23, 0, 15, -5, -3, 26, -8, 14],\n [0, -8, 20, 14, -14, 4, -25, 0, -19, -15, 2, 2],\n [-5, 3, -18, -22, 9, -14, 20, -25, 6, -23, -17, 6],\n [-25, -15, -11, 8, -18, -24, 1, 25, -11, 13, -8, -16],\n [11, 19, 4, -26, ... | 517 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, -18, 4, -8, 16, 7, -11, -3, -11, -12, 4, 25],\n [-20, 17, -12, -25, 12, 25, -5, -3, -2, -15, 25, 24],\n [-13, 7, 19, -7, -13, -9, 8, -10, 21, 18, -4, -5],\n [22, 4, 2, -2, 5, 4, -21, 10, -10, 20, 4, -6],\n [-... | 551 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[24, -21, 15, -19, -1, -17, 11, 17, -26, -25, 16, 8],\n [-26, -23, -24, -3, -10, 0, -2, -7, 12, 17, 24, 3],\n [-21, -20, 0, -22, -1, 9, -16, 15, -4, -24, 23, -12],\n [17, 26, -2, -... | 99 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[22, -12, 18, 20, 23, -10, -18, -25, 23, 26, 14, 2],\n [24, 15, 19, 4, 5, -26, 3, 1, -1, -9, -26, 14],\n [25, 21, -8, 8, 6, -19, 25, 22, 0, 10, 15, -19],\n [17, 21, 5, -8, 3, 9, -17, 9, -11, -24, -5, 24],\n [-5, -6, 3, 0, -25, -19... | 546 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[21, -7, 4, 9, -3, -5, -18, 22, -10, 7, 26, -16],\n [-21, 24, 22, -4, 21, 22, 20, 18, 22, 13, -1, -18],\n [-19, 22, 25, 19, -1, 25, -15, 6, 18, -20, -11, -1],\n [-2, 8, 16, 2, 23, 15, ... | 559 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-25, -13, -10, 23, -9, -10, 13, 4, 15, 4, 9, -8],\n [5, -10, -3, 18, 13, -23, -22, 25, 26, 20, 25, 14],\n [-26, -1, 15, -24, -4, -14, -5, 4, -19, 3, 19, -15],\n [-5, 16, -12, 3, -3, 22, -2, 26, -25, -26, -7, 18],\n [17, -1, -19, ... | 590 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 3, -5, 5, -15, 3, -22, -25, -21, 16, 16, 8],\n [-17, -11, 21, -5, 24, -13, 13, -11, 21, 12, -26, -11],\n [-7, 5, -25, -5, -22, -25, 22, 12, 17, 14, 5, -16],\n [-1, 24, 4, -12, -15... | 543 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -26, 18, 22, 15, -9, 22, -4, -11, 20, 15, -2],\n [-22, -16, 16, 19, -21, 20, -13, 17, -1, 0, -13, 16],\n [2, -9, -9, -13, -20, 1, -22, 22, 13, 22, -12, 22],\n [7, -22, 25, -23, -10, -26, -17,... | 574 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[24, 5, 18, 23, 26, -25, 1, -22, -13, 18, -17, 17],\n [5, 11, 20, 1, -26, -24, 12, -2, 3, 9, 11, 3],\n [-12, 4, 16, -2, -4, 19, -1, 23, -5, -11, -10, 0],\n [-10, -10, -7, -25, 9, -4, 1, -1, 16, 23, 18, 24],\n [-15, -10, 14, 1, -16, 11... | 86 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-26, -5, 19, -23, 25, 8, 23, 25, 12, 6, -11, 18],\n [8, -15, 9, 24, 19, -20, -23, -15, -20, 19, -12, -21],\n [-10, -10, 17, -23, -20, 9, -20, 11, 9, 15, 6, -4],\n [1, 1, 6, -5, 12, -5, -2... | 101 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, 8, 19, 0, 11, 8, -20, 11, -7, -4, 23, 2],\n [26, -5, -6, 15, -22, 13, 26, 20, 21, 16, -17, 6],\n [-26, 22, 9, -11, -8, -22, -4, -24, 19, 23, -9, -24],\n [15, 24, -24, -13, -19, 5, 3, -8, -21,... | 552 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[13, 14, -25, 18, -13, 22, 1, -17, 11, 1, -14, 1],\n [18, -10, -22, 20, -22, -8, 7, 14, 16, 12, 4, -2],\n [24, -26, 23, -5, 11, 21, 2, -25, 14, 15, 3, -10],\n [9, ... | 95 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, 12, -23, 10, 22, 16, -23, 23, -4, -18, 13],\n [-3, 2, -20, -9, -25, 1, 16, 14, 2, 18, -10, 4],\n [-10, 4, -4, -17, -21, 11, 20, 0, -16, -7, 19, -22],\n [5, -22, -5, -26, -7, 24, -12, -16, 5, 1, 1, -10],\n [7, -3, -25, 0, -18,... | 93 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, -25, -15, 12, 13, 4, 2, -19, -12, -1, 21, 9],\n [14, -23, 23, 6, -15, 23, 26, -16, 3, 26, 18, -1],\n [23, 3, 9, 6, 18, 4, -25, -12, -25, 26, -15, -9],\n [-19, -24, 8, 6, 4, -23, -4, 10, 18, 18, 8, 13],\n [26,... | 590 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, -23, -2, -24, -17, -22, -15, 7, -15, 26, 11, -12],\n [-6, -23, -16, -17, -20, -18, -9, 20, 0, 16, 1, 5],\n [-17, 7, -22, -7, 3, 6, -8, -25, -9, -13, -22, -9],\n [18, 24, -12, -4, 23, -23, 7, -3, -15, 2, -21, -3],\n [20, -5, -10, ... | 92 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 25, 11, 7, 7, 4, 4, 5, 9, -5, -8, 18],\n [8, 11, 15, -12, 11, -19, 5, 9, 10, 3, 24, 21],\n [-4, 16, -20, -5, 9, 12, 1, -15, -24, 18, 11, 17],\n [9, -6, -5, -4, -20, -20, -6, 17, -13, 15, -20, ... | 525 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, -7, -9, -18, 5, -10, -8, 22, -14, -26, 18, 11],\n [17, 11, 9, -17, 8, -1, 21, 6, 13, -19, -7, -25],\n [12, 13, 1, 2, 26, -2, -1, -19, 3, 25, -26, 1],\n [3, -14, 14, 22, -6, -6, 13, -16, 0, -22, -14, -15],\n ... | 554 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 21, 21, 22, 15, 15, 8, -16, 1, 17, -7, -25],\n [14, 6, 9, -17, 18, -8, -2, 0, 8, -4, 16, 7],\n [-19, -25, -2, -18, -2, 18, 2, -5, -13, 25, 21, 16],\n [21, -16, 23, 24, 24, -14, 6,... | 527 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[21, -7, 0, -25, 25, 2, -21, -7, 10, -8, -16, 21],\n [-9, 12, -5, 24, -13, 15, -21, -6, -19, -9, -5, -21],\n [8, 8, 19, 18, 26, -18, -11, -16, 21, -6, 15, -4],\n [18, -7, -10, 4, 25, -9, 2, 21, 5, -19... | 86 | MATH |
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