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Math Help - Determine whether W is a subspace of the vector space?

  1. #1
    Jav
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    Question Determine whether W is a subspace of the vector space?

    W={(x,y): y=ax, a is an integer}, V=R^(2)

    It is not a subspace of V, but I can't find an example, where this is not valid.

    Please, help. Thank you.
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  2. #2
    Lord of certain Rings
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    Re: Determine whether W is a subspace of the vector space?

    Quote Originally Posted by Jav View Post
    W={(x,y): y=ax, a is an integer}, V=R^(2)

    It is not a subspace of V, but I can't find an example, where this is not valid.

    Please, help. Thank you.
    (1,2) \in W, (1,3)\in W. But does \frac12(1,2)+\frac12(1,3)?
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  3. #3
    Jav
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    Re: Determine whether W is a subspace of the vector space?

    Thank you very much for your prompt response.

    I forgot that cu + cv has to be in W as well.

    Thank you again.
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