Let

Vbe an F-vector space with basisB= (v1, v2, . . . , vn). LetWbe any

F-vector space and letw1,w2, . . . ,wnbe some elements.

Let

S, T:V → Wbe two linear transformations. SupposeS(vi) =T(vi) fori=1,2, . . . , n. Show thatS=T.