Linear algebra-subspace proof?

Question

Prove that the intersection of two subspaces of a real vector space is a real vector space.

Answer 1

Let x and y be vectors in the intersection of two subspaces of a vector space over a field K. Denote these subspaces by V and W. Then for any elements a, b in K, a*x+b*y is an element of both V and W. Hence it is an element of the intersection.