1. ## Eigenvalues/Eigenvectors

How do you find the characteristic polynomial, eigenvalues, and eigenvectors of the following matrix?

$\begin{pmatrix}2&-2&3\\0&3&-2\\0&-1&2\end{pmatrix}$

2. Originally Posted by logitech
How do you find the characteristic polynomial, eigenvalues, and eigenvectors of the following matrix?

$\begin{pmatrix}2&-2&3\\0&3&-2\\0&-1&2\end{pmatrix}$
In the usual way (you will find many solved problems like this one by searching the MHF forums or doing a Google search).

Start by calculating $\det \begin{pmatrix}2 - \lambda & -2 & 3 \\ 0 & 3 - \lambda &-2\\0 & -1 & 2 - \lambda\end{pmatrix}$ (I suggest expanding down the first column).

Then solve $\det \begin{pmatrix}2 - \lambda & -2 & 3 \\ 0 & 3 - \lambda &-2\\0 & -1 & 2 - \lambda\end{pmatrix} = 0$ etc.

Please post what you've done and exactly where you get stuck.