I'm trying to find a matrix $P$ such that $J=P^{-1}AP$, where $J$ is the Jordan Form of the matrix: $A=\begin{pmatrix} -1&2&2\\ -3&4&3\\ 1&-1&0 \end{pmatrix} $
The characteristic polynomial is: $p(\lambda)=(\lambda-1)^3$, and a eigenvector for $A-I$ is $\begin{pmatrix} 0 \\ 1 \\-1 \end{pmatrix}$. Now, how can I find other $2$ vectors?
Thanks for your help.