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Math Help - Subspaces

  1. #1
    Super Member Aryth's Avatar
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    Subspaces

    Consider the vector space \mathcal{F} = \lbrace f : \mathbb{R} \to \mathbb{R} \rbrace.

    (a) Let

    \mathcal{U} = \lbrace f : \mathbb{R} \to \mathbb{R} : f(3) = 0 \rbrace

    Prove true or show to be false: \mathcal{U} is a subspace of \mathcal{F}.

    (b) Let

    \mathcal{V} = \lbrace f : \mathbb{R} \to \mathbb{R} : f(3) = 3 \rbrace

    Prove true or show to be false: \mathcal{V} is a subspace of \mathcal{F}.
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  2. #2
    Super Member Aryth's Avatar
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    I don't really know how to begin this problem. If someone could tell me how to start it I'm sure I'd be able to figure it out...
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  3. #3
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    Remember that a vector space must contain the zero vector. In F, the zero vector is f(x)=0. Thus, V can't be a subspace since it doesn't contain the zero vector.
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