Chapter 9.4, Problem 28E

Let $\text{X}\left(t\right)$ be a fundamental matrix for the system $x^{\prime }=Ax$. Show that $x\left(t\right)=X\left(t\right)X^{-1}\left(t_0\right)x_0$ is the solution to the initial value problem $x^{\prime }=Ax,x\left(t_0\right)=x_0$.