Suppose that h: V W is one-to-one so that by Theorem 2.20, for any basis B

Question:

Suppose that h: V → W is one-to-one so that by Theorem 2.20, for any basis B = (1, . . . , n) ⊂ V the image h(B) = h((1), . . . , h(n)) is a basis for W.
(a) Represent the map h with respect to B, h(B).
(b) For a member of the domain, where the representation of has components c1, . . . , cn, represent the image vector h() with respect to the image basis h(B).