Proving Subspaces in Linear Algebra

[iwonde]

Homework Statement

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.

Homework Equations

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]

Homework Statement

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.

Homework Equations

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?

 

[Dick]

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.

 

[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?