- Find a similarity transformation which diagonalizes the matrix $$ A=\begin{bmatrix}-2 & 2 &-3 \\ 2 &1& -6\\ - 1 &-2 & 0\end{bmatrix}. $$
- Diagonalize the matrix $$ A=\begin{bmatrix}10 & -2 &-5 \\ -2 &2 & 3\\ -5 &3 & 5\end{bmatrix} $$ by orthogonal transformation.
For Question 2, I found the eigenvalues($-3$ and $5$) and eigenvectors $(-2,1,0),(3,0,1),(-1,2,1)$ but at point $D=P^{-1}AP$ the $P$ comes out as a singular matrix and I got stucked. How to solve now?
For question 4, please explain how to diagonalize by orthogonal