The eigenvalues of M are: ${\lambda }_1=-1.3747,{\lambda }_2=11.0454,{\lambda }_3=0.3293\text{ (all are simple roots)},$

The general solutions for the eigenvectors are:

$v_1=\left[\begin{array}{c}-1.2012t\\ -0.0738t\\ t\end{array}\right],v_2=\left[\begin{array}{c}0.4498t\\ 0.7593t\\ t\end{array}\right],v_3=\left[\begin{array}{c}0.8514t\\ -1.7855t\\ t\end{array}\right]$

Instances of eigenvectors of M are:

$v_1=\left[\begin{array}{c}-1.2012\\ -0.0738\\ 1.0000\end{array}\right]$$,v_2=\left[\begin{array}{c}0.4498\\ 0.7593\\ 1.0000\end{array}\right]$$,v_3=\left[\begin{array}{c}0.8514\\ -1.7855\\ 1.0000\end{array}\right]$