Suppose that V and W are vector subspaces of Rn. If I define:
V + W = {v+w: v belonging to V, w belonging to W}
How can I prove that V+W is also a vector subspace of Rn and ALSO how could verify that (for example)
<(1,0,1), (-1,0,1)> + <(3,2,1)> = R3