You want to approximate a matrix A by keeping only the largest singular value and corresponding vectors using MATLAB. Which code snippet correctly performs this low-rank approximation?

hard📝 Application Q15 of 15

MATLAB - Linear Algebra

You want to approximate a matrix A by keeping only the largest singular value and corresponding vectors using MATLAB. Which code snippet correctly performs this low-rank approximation?

A[U, S, V] = svd(A);<br>A_approx = U(:,1) * S(1,1) * V(:,1)';

B[U, S, V] = svd(A);<br>A_approx = U(:,1) * V(:,1)';

C[U, S, V] = svd(A);<br>A_approx = S(1,1) * V(:,1)';

D[U, S, V] = svd(A);<br>A_approx = U(:,1) * S(:,1) * V(:,1)';

Step-by-Step Solution

Solution:

Step 1: Understand low-rank approximation using svd
Keeping only the largest singular value means using the first column of U, the first singular value, and the first column of V.
Step 2: Construct the approximation
The approximation is A_approx = U(:,1) * S(1,1) * V(:,1)', multiplying the first singular value and vectors.
Final Answer:
[U, S, V] = svd(A); A_approx = U(:,1) * S(1,1) * V(:,1)'; -> Option A
Quick Check:
Low-rank approx = U(:,1)*S(1,1)*V(:,1)' [OK]

Quick Trick: Multiply first U column, singular value, and V column for approximation [OK]

Common Mistakes:

Omitting singular value in multiplication
Using entire S matrix instead of first singular value
Incorrect matrix dimensions in multiplication

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More MATLAB Quizzes

You want to approximate a matrix A by keeping only the largest singular value and corresponding vectors using MATLAB. Which code snippet correctly performs this low-rank approximation?

Step 1: Understand low-rank approximation using svd

Step 2: Construct the approximation

Final Answer:

Quick Check:

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