18. Uniqueness of a Point

Let $v_1,\ldots,v_n$ be vectors in a vector space $V$.

Prove that every vector in $\operatorname{span}\{v_1,\ldots,v_n\}$ has a unique representation as a linear combination of $v_1,\ldots,v_n$ if and only if $v_1,\ldots,v_n$ are linearly independent.