Chapter 6.2, Problem 9P

Determine whether

${\text{x}}_1\left(t\right)=e^{-t}\left(\begin{array}{c}1\\ 0\\ -1\end{array}\right)$,      ${\text{x}}_2\left(t\right)=e^{-t}\left(\begin{array}{c}1\\ -4\\ 1\end{array}\right)$, ${\text{x}}_3\left(t\right)=e^{8t}\left(\begin{array}{c}2\\ 1\\ 2\end{array}\right)$

form a fundamental set of solutions for $\text{x}\text{'}=\left(\begin{array}{ccc}3& 2& 4\\ 2& 0& 2\\ 4& 2& 3\end{array}\right)\text{x}$.