Linear Algebra- Subspaces

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 [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.

sutupidmath

f i suppose is a function right?

Dick

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.

HallsofIvy

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?