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Consider the linear dynamical system $\dot x(t) = \left[ \begin{array}{cc} 1.1 & 0.1\\ -1 & 0.2 \end{array} \right] x(t).$

This system is autonomous.

This system is time-invariant.

Whenever $x_1(t)$ and $x_2(t)$ are positive, $x_1(t)$ is increasing.