Given {v1,..., vn) in a vector space V, define T: Rn → V by T(r1,..., rn) = r1v1 + ∙ ∙ ∙ + rnvn. Show that T is linear, and that:
(a) T is one-to-one if and only if (v1,..., vn] is independent.
(b) T is onto if and only if V = span {T(v1),..., T(vn)}.