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Math Help - subspaces

  1. #1
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    subspaces

    determine whether w={f:f(x)greater than or equal to 0} is a subspace of C, the set is continuous functions on the real numbers
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  2. #2
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    If f is in w, think about the function -f.
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  3. #3
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    In other words,is w closed under scalar multiplication ?
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  4. #4
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    Quote Originally Posted by Raoh View Post
    In other words,is w closed under scalar multiplication ?

    No, it isn't. Look at DrSteve's post. For example choose f(x)=1 for all x\in \mathbb{R} then, f\in W however [(-1)f](x)=(-1)f(x)=(-1)\cdot 1=-1 . That is, (-1)f\not\in W .


    Fernando Revilla
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  5. #5
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    Quote Originally Posted by FernandoRevilla View Post
    No, it isn't. Look at DrSteve's post. For example choose f(x)=1 for all x\in \mathbb{R} then, f\in W however [(-1)f](x)=(-1)f(x)=(-1)\cdot 1=-1 . That is, (-1)f\not\in W .


    Fernando Revilla
    Just my hunch, but I think Raoh understands the problem, and is trying to get the OP'er to ask the question in post #3. Could be off on that, though.
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  6. #6
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    My question was meant to help the OP'er.
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  7. #7
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Raoh View Post
    My question was meant to help the OP'er.

    Sorry, by error I thought your post was from the original poster.


    Fernando Revilla
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    Wow - it's not too hard to get thanked around here - very polite group!
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