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.
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.
The only eigen value of $\displaystyle A$ is $\displaystyle \lambda=-1$ (double) and $\displaystyle \dim V_{-1}=2-\mbox{rank}(A+I)=2-1=1\neq \mbox{multiplic.}(-1).$ That is, $\displaystyle A$ is not diagonalizable or equivalently, there is no $\displaystyle P$ invertible such that $\displaystyle P^{-1}AP=D$ (diagonal).