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Math Help - Vector Spaces

  1. #1
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    Vector Spaces

    Let V be a vector space over a field F. W is a subspace of V if W is a subset of V and W is also a vector space over F.
    Prove that if W is a subset of V such that:
    1. for all a and b in W a+b in W and
    2. for all k in F and for all a in W, ka in W.
    Then W is a subspace of V.
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  2. #2
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    Quote Originally Posted by Coda202 View Post
    Let V be a vector space over a field F. W is a subspace of V if W is a subset of V and W is also a vector space over F.
    Prove that if W is a subset of V such that:
    1. for all a and b in W a+b in W and
    2. for all k in F and for all a in W, ka in W.
    Then W is a subspace of V.
    Basically all the other properties for subspace hold already for W since it is a subset of V. For example, + is associate since a+(b+c) = (a+b)+c already holds in V. Just show that all the properties of a vector subspace holds for W by using the fact V is already a vector space.
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