## Elementary Linear Algebra 7th Edition

The set $W$ of all functions such that $f(0)=0$ is a vector subspace of $C(-\infty, \infty)$.
The set $W$ of all functions such that $f(0)=0$ is a vector subspace of $C(-\infty, \infty)$. Let $f,g\in W$, then $f(0)=0, g(0)=0$. Now, $(f+g)(0)=f(0)+g(0)=0+0=0$ also for any $c\in R$ $(cf)(0)=cf(0)=c0=0$.