Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 27

Answer

The set $W$ of all functions such that $f(0)=0$ is a vector subspace of $C(-\infty, \infty)$.

Work Step by Step

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 $c\in R$ $(cf)(0)=cf(0)=c0=0$.
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