Exercise 1.3.13

Question

Let $S$ be a nonempty set and $F$ a field. Prove that for any $s_{0} \in S$, $\left\{f \in \mathcal{F}(S, F): f\left(s_{0}\right)=0\right\}$, is a subspace of $\mathcal{F}(S, F)$.

Jephian C.-H. Lin · Accepted Answer

\begin{proof}
It's closed under addition since $(f+g)(s_0)=0+0=0$. It's closed under scalar multiplication since $cf(s_0)=c 0=0$. And zero function is in the set.
\end{proof}

Exercise 1.3.13

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Exercise 1.3.13

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