Question

prove that if the vectors v1,...vn span the vector space V, and T: V into W is an onto linear function. then the vecters T(v1),...,T(vn) span the vecter space W.

Answer 1

i know by theorem, if T is onto then the vectors T(v1),...,T(vn) are Linearly independent. But I first need to prove that v1,...,vn is a basis of V in order to apply this theorem. I already know by assumption that v1,..,vn spans V, so I just need to prove that v1,..., vn is Linearly Independent in V... and that is were I am stumbling.