Question: Given {v1,..., vn) in a vector space V, define T: Rn V by T(r1,..., rn) = r1v1 + + rnvn. Show

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)}.

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b If T is onto let v be any vector in V Then v Tr 1 r n for some r 1 r n ... View full answer

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