The maximum value of a such that the matrix below has three linearly independent real eigen vectors is
$\begin{pmatrix} -3& 0 &-2 \\ 1& -1 & 0\\ 0& a & 2 \end{pmatrix}$
(a) $\frac{2}{3\sqrt{3}}$
(b) $\frac{1}{3\sqrt{3}}$
(c) $\frac{1+2\sqrt{3}}{3\sqrt{3}}$
(d)$\frac{1+\sqrt{3}}{3\sqrt{3}}$