Chapter 7.8, Problem 3E

Solve $x^{\prime }=Ax$, $x\left(0\right)=x_0$ by transforming $A$ to Hessenberg form, where

$x_0=\left[\begin{array}{c}-1\\ -1\\ 1\end{array}\right]$, and

a) $A=\left[\begin{array}{ccc}8& -6& 21\\ 1& -1& 3\\ -3& 2& -8\end{array}\right]$,

b) $A=\left[\begin{array}{ccc}2& 1& -1\\ -3& -1& 1\\ 9& 3& -4\end{array}\right]$,

c) $A=\left[\begin{array}{ccc}1& 1& -1\\ -3& -2& 1\\ 9& 3& -5\end{array}\right]$.