Chapter 9.6, Problem 12P

(a)

To determine

To show: That if $a_{11}+a_{22}>0$ and $a_{11}{a}_{22}-a_{12}{a}_{21}>0$, then the critical point $\left(0,0\right)$ of linear system is unstable by using the given data.

(b)

To determine

A positive definite function $V$ such that $\dot{V}\left(x,y\right)=x^2+y^2$ by using the given data.