Given $\displaystyle \{v_1, ... ,v_n\}$ in a vector space $\displaystyle V$, define $\displaystyle T: \mathbb{R}^n \rightarrow V$ by $\displaystyle T(r_1, ..., r_n) = r_1v_1+...+r_nv_n$

Show that T is one-to-one if and only if $\displaystyle \{v_1,...,v_n\}$ is independent.