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 - Review Exercises - Page 221: 23


$W$ 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 $-2f(x)=-2(x-1)=-2x+2\not \in W$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.