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Determining a subspace?

  1. May 18, 2009 #1
    Hey, this isn't for homework per se, but if anyone could lend me a hand figuring this out I'd appreciate it a lot!

    1. The problem statement, all variables and given/known data

    Determine whether Q is a subspace of R2/R3 in the following cases:

    2. Relevant equations

    Q = [tex]\{\left v = \left( v1, v2, 0 \right) | v1,v2 \in R \right\}[/tex]

    Q = [tex]\{\left v = \left( v1, 0, 0 \right) | v1 \in R \right\}[/tex]

    Q = [tex]\{\left v = \left( v1, v2 \right) \in R2 | v1 = v2 + 1, v1,v2 \in R \right\}[/tex]

    3. The attempt at a solution

    I honestly am not sure where I'm meant to start here. I know there are 3 conditions where a subspace may be valid; when it's equal to zero, If X and Y are in U, then X+Y is also in U
    and If X is in U then aX is in U for every real number a.

    How exactly am I meant to go about applying those rules? If someone could set me off on the right track that'd be awesome.
     
  2. jcsd
  3. May 18, 2009 #2
    [tex]\{\left v = \left( v1, v2, 0 \right) | v1,v2 \in R \right\}[/tex]

    (0,0,0) is clearly in Q

    Let x = (x1,x2,0) and y =(y1,y2,0) be vectors in Q

    then x+y = (x1+y1, x2+y2, 0) is also in Q

    and ax = a(x1,x2, 0) = (ax1, ax2, 0) is in Q
     
  4. May 18, 2009 #3

    Mark44

    Staff: Mentor

    To correct your terminology, there are 3 conditions for verifying that a subset U of a vector space V is a subspace of that vector space. 1) Zero is an element of U. The other two are fine.
    See RandomVariable's reply.
     
  5. May 19, 2009 #4
    Cool, thanks very much guys. Makes sense now!
     
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