$\left[\begin{array}{ccc}-2& 1& 0\\ 0& -2& 1\\ 0& 0& -2\end{array}\right]$

and

$|x(t)|=({x}_{1}^{2}(t)+{x}_{2}^{2}(t)+{x}_{3}^{2}(t){)}^{1/2}$

Then any solution of the first order system of the ordinary differential equation

$\{\begin{array}{r}{x}^{\prime}(t)=Ax(t)\\ x(0)={x}_{0}\end{array}\phantom{\rule{thickmathspace}{0ex}}\phantom{\rule{thickmathspace}{0ex}}$

satisfies

1. $\underset{t\to \mathrm{\infty}|x(t)|=0}{lim}$

2. $\underset{t\to \mathrm{\infty}|x(t)|=\mathrm{\infty}}{lim}$

3. $\underset{t\to \mathrm{\infty}|x(t)|=2}{lim}$

4. $\underset{t\to \mathrm{\infty}|x(t)|=12}{lim}$