Chapter 6.2, Problem 8P

Determine whether

${\text{x}}_1\left(t\right)=e^{-t}\left(\begin{array}{c}1\\ 0\\ -1\end{array}\right)$,      ${\text{x}}_2\left(t\right)=e^{-t}\left(\begin{array}{c}1\\ -6\\ 1\end{array}\right)$, ${\text{x}}_3\left(t\right)=e^{2t}\left(\begin{array}{c}0\\ 16\\ -6\end{array}\right)$

form a fundamental set of solutions for $\text{x}\text{'}=\left(\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right)\text{x}$.