Let T: V W be a linear transformation. (a) If U is a subspace of V,

Question:

Let T: V → W be a linear transformation.
(a) If U is a subspace of V, show that T(U) = (T(u) | u in U} is a subspace of W (called the image of U under T).
(b) If P is a subspace of W, show that {v in V| T(v) in P) is a subspace of V (called the preimage of P under T).