Chapter 9.10, Problem 1TFR

For Questions (a)-(e), decide if the given statement is true or false, and give a brief justification for your answer. If true you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

The Jacobian matrix for a linear system of the form (9.10.1) is

$J(x,y)=\left[\begin{array}{l}\frac{\partial F}{\partial x}\frac{\partial F}{\partial y}\\ \frac{\partial G}{\partial x}\frac{\partial G}{\partial y}\end{array}\right]$

$\frac{dx}{dt}=F\left(x,y\right),\frac{dy}{dt}=G\left(x,y\right),\left(\mathrm{9.10.1}\right)$