## Linear Algebra- Subspaces

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 $$\in$$ S, {f $$\in$$
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.

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 Quote by iwonde 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 $$\in$$ S, {f $$\in$$ 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.
f i suppose is a function right?

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 Quote by sutupidmath f i suppose is a function right?
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.

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