## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 4 - Vector Spaces - Review Exercises - Page 221: 23

#### Answer

$W$ is not a subspace of $V=C[-1,1]$.

#### Work Step by Step

Let $W$ be a subset of $V$ such that $$W=\{f : f(0)=-1\}, \quad V=C[-1,1].$$ $W$ is not a subspace of $V=C[-1,1]$ since it is not closed under scalar multiplication. For example, $f(x)=x-1\in W$ and $-2f(x)=-2(x-1)=-2x+2\not \in W$.

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