# Stability of trivial solution for DE system with non-constant coefficient matrix

Given the arbitrary linear system of DE's $$x'=A(t)x,$$ with the condition that the spectral bound of $A(t)$ is uniformly bounded by a negative constant, is the trivial solution always stable? All the $(2\times 2)$ matrices I've tried which satisfy the above property yield stable trivial solutions, which seems to suggest this might be the case in general. I can't think of a simple counterexample, so I'm asking if one exists. If there isn't what would be some steps toward proving the statement?

This is indeed homework.

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