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Intersection of Subspaces

  1. Nov 5, 2008 #1
    Let H and K be subspaces of a vector space V. Prove that the intersection K and H is a subspace of V.

    Intuitively I can see that this is true... Both H and K must be closed under vector addition and scalar multiplication so there intersection must also be closed under both those.

    How do i prove this mathematically. And is what I've even said correct?

    Thanks :-D
  2. jcsd
  3. Nov 5, 2008 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Try some specific examples to get some empirical validation of your conjecture, or to look for a counterexample.

    (Gives you time to do this)

    Assuming it checks out, we can answer your question by trying to prove it mathematically!

    Definitions are almost always a very good place to start. And since you're learning linear algebra, it's probably a good idea to try and translate the problem into algebraic statements.
  4. Nov 5, 2008 #3
    I really have no idea where to begin... how would I write something like that in an algebraic form?
  5. Nov 6, 2008 #4


    Staff: Mentor

    If K was a subset of a vector space V, how would you go about showing that K was a subspace of V? I know that's not the question you're working on, but maybe it will get you thinking in the right way.
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