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Math Help - Condition for a set V to be a subset of a set X

  1. #1
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    Condition for a set V to be a subset of a set X

    Prove that a necessary condtion for V to be a subspace of a k-vector space X is that:

    ax + by is an element of V

    for a,b elements of k and x,y elements of V.

    Im not sure what im being asked to prove here. I know that the condition is one of the axioms needed for a set to be a vector space. Basically im looking for help on what the question is asking.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by leftfootwonder7 View Post
    Prove that a necessary condtion for V to be a subspace of a k-vector space X is that:

    ax + by is an element of V

    for a,b elements of k and x,y elements of V.

    Im not sure what im being asked to prove here. I know that the condition is one of the axioms needed for a set to be a vector space. Basically im looking for help on what the question is asking.
    remember, we say P is a necessary condition for Q if Q => P. So that is what you need to show.

    if V is a subspace of X, then the aforementioned condition holds.
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