Find the Jordan Canonical form of the following matrice:

$\displaystyle \begin{bmatrix} 1 && 2 \\ 3 && 2 \end{bmatrix} $

For this one, here is what I have so far:

First, I found the eigenvalues are 1 and 2, and the basis of eigenvectors are $\displaystyle \beta = \{ (- \frac {1}{3} ,1 ) , ( 1 , ( \frac {1}{2} ) \} $

Now, I know I have to find $\displaystyle [T] _{ \beta } $, but I'm bit rusty on this, I can't remember how to do it, any hint, please?

Thanks.