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Linear Algebra- Subspaces

  1. Oct 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Let S be a nonempty set and F a field. Prove that for any s_0 [tex]\in[/tex] S, {f [tex]\in [/tex]
    K(S,F): f(s_0) = 0}, is a subspace of K(S,F).

    K here is supposed to be a scripted F.

    2. Relevant equations



    3. The attempt at a solution
    I don't know how to approach this problem. I know the three requirements that must be satisfied for a subset of a vector space to be defined as a subspace.
     
  2. jcsd
  3. Oct 3, 2008 #2
    f i suppose is a function right?
     
  4. Oct 3, 2008 #3

    Dick

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    Good guess. iwond, can you define your terms? 'Scripted F' doesn't necessarily mean much to people that don't have the same text as you.
     
  5. Oct 5, 2008 #4

    HallsofIvy

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    I'm going to assume that K is the set of all functions, f, such that f(s0)= 0 for a fixed point s0.

    Iwonde, you say, " I know the three requirements that must be satisfied for a subset of a vector space to be defined as a subspace." Okay, what are those requirements? Are they satisified by this set?
     
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