Let V and W be vector spaces with VC Vand WW subspaces. Suppose that T: VW is a linear transformation. Prove the following: 1. T(V') = {T(v') : v′ € V'} CW is a subspace of W 2.T (W'){v' :T(v¹) ¤W′} ¢V is a subspace of V And now we consider the relationship between 7(V^'), 7^¯'(W), ker(7), and Image(T). 1. For what subspace W'W does T`¯¯' (W') = ker(7)3) 2. For what subspace V' V does 7(V) = Image (T)

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