Let
V be an F-vector space with basis B = (v1, v2, . . . , vn). Let W be any
F-vector space and let w1,w2, . . . ,wn be some elements.
Let
S, T : V → W be two linear transformations. Suppose S(vi) = T(vi) for i =1, 2, . . . , n. Show that S = T.