(adsbygoogle = window.adsbygoogle || []).push({}); 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[itex]\cap[/itex]B?

(4) Is E[itex]\cup[/itex]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[itex]\cap[/itex]B={(0,0)}

(4) E[itex]\cup[/itex]B={(2a,a),(b,b)|a,b[itex]\in[/itex]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

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# Union and addition of two subspaces a subspace?

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