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Homework Help: Determine whether the following subsets are subspaces

  1. Aug 10, 2009 #1
    1. The problem statement, all variables and given/known data

    H = {(x,y,z) [tex]\in[/tex] R^3 | x + y^2 + z = 0} [tex]\subseteq[/tex] R^3

    T = {A [tex]\in[/tex] M2,2 | AT = A} [tex]\subseteq[/tex] M2,2

    3. The attempt at a solution

    Our lecturer wasn't quite clear about how to go about this.

    He talked out closed under addition and multiplication but thats about it.

    Help would be greatly appreciated
  2. jcsd
  3. Aug 10, 2009 #2


    Staff: Mentor

    This is pretty basic stuff in linear algebra, so I'm surprised that your lecturer wasn't sure how to do this. What he said, though, is pretty much what you need to do.

    For your first problem, here's what you need to do:
    1. Show that the zero vector is in H.
    2. Show that if h1 and h2 are any two vectors in set H, then h1 + h2 is also in H. (Closure under vector addition)
    3. Show that if h1 is a vector in H and c is any real number, then c*h1 is in H. (Closure under scalar multiplication) Note that the first step can be accomplished by using c = 0.

    For your second problem use matrices instead of vectors, but the steps are essentially the same.
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