# Algebra: Vector Spaces

Let V be the vector space of all functions f: R->R. Determine whether the following subsets of V form subspaces.

a) U = {f belongs to V | f(0) = 0}

b) W = {f belongs to V | f(x) = k1 + k2 sinx for some k1,k2 are reals}.

https://brainmass.com/math/vector-calculus/subset-vector-space-subspace-398502

#### Solution Preview

a) U is a subspace of V iff for any f1,f2 in U => f1+f2 is in U and k f1 is in U, where k is a scalar.

If f1 is in U, then f1(0)=0

If f2is in U, then ...

#### Solution Summary

The solution verifies if a subset of a vector space is a subspace.

$2.19