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Union and addition of two subspaces a subspace?

  1. Dec 14, 2011 #1
    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
     
  2. jcsd
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