So I have the Eigenspace of:
$ \begin{align*} -5x -y + 3z &= 0 \\ -18x -3y + 9z &= 0 \\ -16x -3y + 9z &= 0 \end{align*} $ I get the solution $y = 3z$, and hence the vector for a basis $(0,3,1)$ but I know I need a second vector to complete the basis. And the only other solution I can find is $x = 0$ and I don't think that's very useful? The only thing I can think of is if we use the fact that you can't find the other vector for the basis, it means it's not diagonalisable.