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 $W \cup U$?

Well, a union of two sets A and B is all the elements that belong to either A or B
In your case W∪U = span{(1,2),(1,1), (3,4),(2,2)} =span{(1,1), (3,4)}. Because some vectors are linear dependent. (note: thats as I rememver it. I will double check it in a while).
Edit
The above answer is wrong. The sum of subspaces is found there. The correct thing is the definition of the union. Another useful fact is that union may or may not be the vector space itself. In this case vectors virtually define the same Linear spaces and W∪U = W∪W = W = $ R^2 $
