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