Find the Jordan basis of the following matrix: $$\begin{pmatrix} 1& 1& -2& 3& -1\\ 0 & 0 &-1 &2 &0\\ 2& 2& -6& 10& -2\\ 1& 1& -3& 5& -1\\ 0& 0& 0& 0 &0\end{pmatrix}$$
The only eigenvalue of this matrix is zero, so the rank is equal to 1 . So how could I get the Jordan basis, if I am not able to get it classicaly from the chaining of the eigenvectors (Jordan's chain)?