# Thread: invertible and diagonalized matrix

1. ## invertible and diagonalized matrix

Given the matrix A=[29,18][-50,-31] explain why there is no invertible matix P that diagonalizes A.

So I've solved for the eigenvalue and found that it is x2=[-3/5][1] and the A^-1 is [1/29,0][5/3,29/30]. Thank you in advance for your help.

2. ## Re: invertible and diagonalized matrix

Originally Posted by nivek0078
Given the matrix A=[29,18][-50,-31] explain why there is no invertible matix P that diagonalizes A.
The only eigen value of $A$ is $\lambda=-1$ (double) and $\dim V_{-1}=2-\mbox{rank}(A+I)=2-1=1\neq \mbox{multiplic.}(-1).$ That is, $A$ is not diagonalizable or equivalently, there is no $P$ invertible such that $P^{-1}AP=D$ (diagonal).

3. ## Re: invertible and diagonalized matrix

Thank you for explaining that. It makes sense using the rank to solve it.