LAB $9-$ Diagonalization

Problem $1$: Find the eigenvalues and eigenvectors by hand of the following system:

$\left[\begin{array}{cc}-3& 8\\ 4& 1\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$

Problem $2$: Normalize the Eigenvectors by hand

Problem $3$: Verify that the Eigenvectors are correct. Use MATLAB to calculate the inverse of

Matrix X$.$

$D=x^{-1}Ax$