# Union and addition of two subspaces a subspace?

1. Dec 14, 2011

### csc2iffy

1. The problem statement, all variables and given/known data
This problem is broken into 5 parts:
(1) Let E={(2a,a)|a∈ℝ}. Is E a subspace of R2?
(2) Let B={(b,b)|b∈ℝ}. Is B a subspace of R2?
(3) What is E$\cap$B?
(4) Is E$\cup$B a subspace of R2?
(5) What is E+B

2. Relevant equations
E={(2a,a)|a∈ℝ}
B={(b,b)|b∈ℝ}

3. The attempt at a solution
(1) Yes, closed under addition and scalar mult.
(2) Yes, closed under addition and scalar mult.
(3) E$\cap$B={(0,0)}
(4) E$\cup$B={(2a,a),(b,b)|a,b$\in$ℝ}
I don't know how to show if tis is a subspace of R2 or if that is the correct union
(5) i also do not know how to add them