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
1. $\dfrac{2}{3\sqrt{3}} \\$
2. $\dfrac{1}{3\sqrt{3}} \\$
3. $\dfrac{1+2\sqrt{3}}{3\sqrt{3}} \\$
4. $\dfrac{1+\sqrt{3}}{3\sqrt{3}}$