Originally Posted by

**Halcyon** I'm struggling with where to begin. This is a practice question for my undergraduate Linear Algebra course.

Let f: V -> W be a linear transformation, and let Y be a subspace of W.

a) Prove that X = {v (is an element of) V: f(v) (is an element of) Y} is a subspace of V.

I intuitively feel that this is true - elements of V are being mapped to W, and X contains the elements of V that map to the subspace of Y within W, which suggests that X is within V. However, I have no idea of where to begin with a formal proof.