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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[itex]\subseteq[/itex] X, show that the set U = {f [itex]\in[/itex] 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 [itex]\in[/itex] 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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