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Linear Algebra- Subspaces

  • Thread starter iwonde
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  • #1
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Homework Statement


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.

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.
 

Answers and Replies

  • #2
1,631
4

Homework Statement


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.

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?
 
  • #3
Dick
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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.
 
  • #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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