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Homework Statement
1. Let X be a set and F a Field, and consider the vector space F(X; F) of functions from X to F. For
a subset Y\subseteq X, show that the set U = {f \in F(X; F) : f |Y = 0 } is a subspace of F(X; F). NB: the
expression \f |Y = 0" means that f(y) = 0 whenever y \in Y .
Homework Equations
The Attempt at a Solution
is this similar to proving a subspace for f(x) =0 for real numbers of x ?
zero vector
for all y in Y 0(y)=0
addition f(y)+g(y) =(f+g)(y)
let g also be in U, and c in Field
multiplication (cf)(y) = c(f(y)) = c(g(y)) + (cg)(y)
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