1. Consider the matrix: 3 × 3: [1 2 3] A = 334 [5 6 7 Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A₁. 2. Use the svd() function in MATLAB to compute A₂, the rank-2 approximation of A. Clearly state what A₂ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A₁ or A₂? Explain.

1. Consider the matrix: 3 × 3: [1 2 3] A = 334 [5 6 7 Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A₁. 2. Use the svd() function in MATLAB to compute A₂, the rank-2 approximation of A. Clearly state what A₂ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A₁ or A₂? Explain.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I need help with question 2. Here's the code used for question 1.

%Define matrix A

A = [1, 2, 3; 3, 3, 4; 5, 6, 7];

%Compute SVD of A

[U, S, V] = svd(A);

%Rank-1 approx

A1 = U(:,1) * S(1,1) * V(:,1)';

RMSE = sqrt(mean((A(:) - A1(:)).^2));

%Display A1 rounded to 4 decimal places

disp(round(A1, 4));

%Display RMSE

disp(RMSE);

1. Consider the matrix: 3 × 3:
[1 2 3]
A = 334
[5 6 7
Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A₁.
2. Use the svd() function in MATLAB to compute A₂, the rank-2 approximation of A. Clearly state what A₂ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A₁ or A₂? Explain.

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