$B=\begin{bmatrix}3&-2&1\\\\-2&6&-2\\\\1&-2&3\end{bmatrix}$
so far I have found
$char(f)=\begin{bmatrix}3-x&2&1\\\\-2&6-x&-2\\\\1&-2&3-x\end{bmatrix}$
from this the equation is $-x^3+12x^2-44x+48$ which factorizes to $-(x-6)(x-4)(x-2)$ so $\lambda=2,4,6$
I'm not sure what to do next, do I try and find a basis $E_\lambda$