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Math Help - Subspace

  1. #1
    Junior Member
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    Subspace

    Hi people,

    F_1={ f \in F( \mathbb{R};\mathbb{R})/ f(0)=f(1)}
    F_2={ f \in F( \mathbb{R};\mathbb{R})/ f(2)=0}

    I have to check if F_1 anf F_2 are linear subspaces of F( \mathbb{R};\mathbb{R}) or not????

    Please help???
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  2. #2
    MHF Contributor

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    Quote Originally Posted by bhitroofen01 View Post
    Hi people,

    F_1={ f \in F( \mathbb{R};\mathbb{R})/ f(0)=f(1)}
    F_2={ f \in F( \mathbb{R};\mathbb{R})/ f(2)=0}

    I have to check if F_1 anf F_2 are linear subspaces of F( \mathbb{R};\mathbb{R}) or not????

    Please help???
    A subset of a vector space is a subspace if and only if it is closed under addition and scalar products. In particular, that means that if f and g are in the subset, af+ bg, for any numbers a and b, must also be in the set.

    In the first case, if f and g are in the set they must have the property that f(0)= f(1) and g(0)= g(1). Suppose h(x)= af(x)+ bg(x) for numbers a and b. What are h(0) and h(1). Are they equal?

    In the second case, if f ang g are in the set they must have the property that f(2)= 0 and g(2)= 0. Suppose h(x)= af(x)+ bg(x) for numbers a and b. What is h(2)? Is it equal to 0?
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