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Math Help - vector subspaces

  1. #1
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    vector subspaces

    I have a vector space A, with B and C are the two subspaces of A.

    I need to disprove that dim(B+C)=dim(B)+dim(C)

    I know the correct formula should be dim(B+C)=dim(B)+dim(C) - dim(B intersect C)

    need to find a counterexample, but am struggling.
    Last edited by cassius2020; October 17th 2012 at 06:04 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: vector subspaces

    Quote Originally Posted by cassius2020 View Post
    I have a vector space A, with B and C are the two subspaces of A. I need to disprove that dim(B+C)=dim(B)+dim(C)
    Choose, for example, A=B=C=\mathbb{R}^2.
    Last edited by FernandoRevilla; October 17th 2012 at 07:02 AM.
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