Chapter 6.4, Problem 10P

(a) Find constant $4\times 1$ vectors $\text{a}$ and $\text{b}$ such that the solution of the initial value problem

$\text{x}\text{'}=\left(\begin{array}{cccc}-2& -1& 4& 2\\ -19& -6& 6& 16\\ -9& -1& 1& 6\\ -5& -3& 6& 5\end{array}\right)\text{x, }\text{x}\left(0\right)={\text{x}}_0\in S$

is a closed curve lying entirely in $S$, where

$S=\left\{\text{u:u}=a_1\text{a+}{a}_2\text{b,-}\infty \text{<}{a}_1,a_2<\infty \right\}$

(b) Describe the long-time behavior of any solutions for which ${\text{x}}_{\text{0}}\notin S$.