Does the coordinate vectors(Vi)s spans R^n , if S in a set of a n dimensional vector space

Question

Let $S = \{v_1,v_2,\dots ,v_r\}$ be a nonempty set of vectors in an $n$- dimensional vector space $V$.

Prove that if the vectors in $S$ span $V$, then the coordinate vectors $(v_1)S, (v_2)S,\ldots, (v_r)S$ span $R_n$, and conversely.