You have a matrix A = [4 1 0; 1 4 1; 0 1 4];. How can you find the eigenvector corresponding to the largest eigenvalue using MATLAB?

hard📝 Application Q15 of 15

MATLAB - Linear Algebra

You have a matrix A = [4 1 0; 1 4 1; 0 1 4];. How can you find the eigenvector corresponding to the largest eigenvalue using MATLAB?

AlargestVec = eig(A);

B[V,D] = eig(A); [~, idx] = max(diag(D)); largestVec = V(:, idx);

C[V,D] = eig(A); largestVec = D(:,1);

D[V,D] = eig(A); largestVec = max(V);

Step-by-Step Solution

Solution:

Step 1: Compute eigenvalues and eigenvectors
Use [V,D] = eig(A); to get eigenvectors V and eigenvalues in diagonal matrix D.
Step 2: Find index of largest eigenvalue
Extract eigenvalues with diag(D), then find index of max eigenvalue with [~, idx] = max(diag(D));.
Step 3: Select eigenvector corresponding to largest eigenvalue
Use index to get eigenvector: largestVec = V(:, idx);.
Final Answer:
[V,D] = eig(A); [~, idx] = max(diag(D)); largestVec = V(:, idx); -> Option B
Quick Check:
Index max eigenvalue, select eigenvector column [OK]

Quick Trick: Use max(diag(D)) to find largest eigenvalue index [OK]

Common Mistakes:

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