See here. If you scroll down to the end, the wiki article has a proof.
Hi,
I was given this problem in my diff equation class and I have no idea how to go about proving it. Thanks a lot for your help:
Let A=A(t) be an n x n matrix continuous on (a,b) and let c be in (a,b) and let W(t) be the Wronskian of a set of n solutions of the equation x=Ax.
Show that for any a < t < b,