The maximum value of "a" such that the matrix $\begin{pmatrix}

-3&0&-2 \\

1&-1&0 \\

0&a&-2

\end{pmatrix}$ has three linearly independent real eigenvectors is

- $\frac{2}{3\sqrt{3}}$
- $\frac{1}{3\sqrt{3}}$
- $\frac{1+2\sqrt{3}}{3\sqrt{3}}$
- $\frac{1+\sqrt{3}}{3\sqrt{3}}$