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Math Help - vector space t/f question

  1. #1
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    vector space t/f question

    T/F prove...

    a)The intersection of any two subsets of V is a subspace of V
    b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.

    can sum1 provide a proof for these?
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  2. #2
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    Quote Originally Posted by ruprotein View Post
    T/F prove...

    a)The intersection of any two subsets of V is a subspace of V
    The intersection of two subspaces is again a subspace, correct.
    b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.

    can sum1 provide a proof for these?
    Not true, consider a vector space with dimension 1, then any subspace must have dimension 1 also, because it cannot be larger and it cannot be less because it is 1.
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  3. #3
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    Quote Originally Posted by ruprotein View Post
    a)The intersection of any two subsets of V is a subspace of V.
    Did you mean subspaces but wrote subsets.
    It is false if it is subsets.
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  4. #4
    Super Member Rebesques's Avatar
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    b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.
    True! If V is not {0}, then take W={0}.
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