Union of two vector spaces Can someone tell me how to union two vector spaces, it might be simple question but I forgot how to do that.
Lets say I was given two vector spaces $W$ and $U$:
$$W =  \operatorname{span}\{ (1,2), (1,1) \}$$
$$U = \operatorname{span}\{ (3,4), (2,2) \}$$
What is $W \cup U$?

If these are both subspaces of $\mathbb{R}^2$, then in fact $U = W = \mathbb{R}^2$, so $W \cup U = \mathbb{R}^2$.
