M y question is relating to the matrix as A. I have started off this problem by finding the eigenvalues, which turns out to be 3 ( I should note that it has an algebraic multiplicty of 3)
From there I have found the corresponding Eigenspace which is $E_3=span(-1,1,1)$
I am little confused as to what to do from here.
The Jordan form can be deduced from the information you already have, namely that the eigenspace is 1-dimensional and all of the eigenvalues are 3. The Jordan matrix is, \begin{pmatrix} 3 & 1 & 0\\ 0 & 3 & 1\\ 0 & 0 & 3 \end{pmatrix} where the eigenvalues are on the diagonal, and the size of the Jordan block is 3 by 3, due to the dimension of the eigenspace.