Math Help - linear systems

1. linear systems

G(t) is nxn matrix dependent on t. show solutions of x' = G(t)x form an n-dim subspace of the space of functions C^1(R^+,R^n) .

Not sure how to do this.

2. Ofcourse, $G$ has to be continuous, or else $x$ might not be $C^1$.

Consider the n (unique) solutions to the n problems $\{x_i'=Gx_i, \ x(0)=e_i\}_{1\leq i\leq n}$, where $\{e_i\}$ are the standard basis vectors.