[Solved] You want to verify if matrix A is diagonalizable using MATLAB. Which approach is correct? — Ans: Check if rank(V) equals size of A after [V,D] = eig(A); | MATLAB

MATLAB - Linear Algebra

You want to verify if matrix A is diagonalizable using MATLAB. Which approach is correct?

ACheck if <code>V*D*inv(V)</code> equals <code>A</code>

BCheck if <code>det(A)</code> is zero

CCheck if <code>rank(V)</code> equals size of A after <code>[V,D] = eig(A);</code>

DCheck if <code>D</code> is a zero matrix

Step-by-Step Solution

Solution:

Step 1: Understand diagonalizability condition
A matrix is diagonalizable if it has enough linearly independent eigenvectors to form a basis.
Step 2: Use rank of eigenvector matrix V
If rank(V) equals the size of A, eigenvectors are linearly independent, so A is diagonalizable.
Step 3: Evaluate other options
Check if det(A) is zero checks determinant, unrelated to diagonalizability.
Check if D is a zero matrix checks if D is zero, which is not correct.
Check if V*D*inv(V) equals A checks reconstruction but does not confirm diagonalizability directly.
Final Answer:
Check if rank(V) equals size of A -> Option C
Quick Check:
Full rank V means diagonalizable [OK]

Quick Trick: Full rank eigenvector matrix means diagonalizable [OK]

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