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## Homework Statement

A=[0 -9; 1 -6]

Can this matrix be diagonalized?

## Homework Equations

det(A-[itex]\lambda[/itex]I)=0

## The Attempt at a Solution

det(A-[itex]\lambda[/itex]I)=0 gives the eigenvalues of the matrix and yields two eigenvalues that are equal, [itex]\lambda[/itex]= -3

A matrix with repeating eigenvalues are defective and can therefore NOT be diagonalized.

I would further say that rank(A)=1 and nullity(A)=n-rank(A)=2-1=1... Matlab does not agree with me... what is wrong with my reasoning here?