I need to solve this:
Let V be a finite-dimensional vector space. Prove that every affine set that contains the origin of is a subspace of V.
So I think I see why this is true, I'm just having trouble getting started. If the affine set did not contain the origin, then it wouldn't be closed under scalar multiplication. I assume I need to start by considering we have an affine set containing the origin of V - do I just proceed to showing that this satisfies all the properties of a subspace?