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  1. Find a similarity transformation which diagonalizes the matrix $$ A=\begin{bmatrix}-2 & 2 &-3 \\ 2 &1& -6\\ - 1 &-2 & 0\end{bmatrix}. $$
  2. 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

Silvia Ghinassi
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    To type matrices and other mathematics on this site, I recommend visiting this page for a primer on how to use $\LaTeX$ and Mathjax here. – JMoravitz Oct 06 '15 at 03:35
  • You're half way there. The following link will help guide you. http://www.sosmath.com/matrix/diagonal/diagonal.html – John Douma Nov 21 '15 at 23:13
  • The problem you're experiencing is based on the fact that your eigenvectors are not linearly independent: indeed 2v1+v2=v3. Also, they all belong to the eigenspace for $\lambda=-3$, you still haven't found an eigenvector for $\lambda=5$. – Karl Kroningfeld Nov 21 '15 at 23:23

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