Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 4 - Vector Spaces - 4.2 Exercises - Page 208: 8

Answer

W is not a vector space.

Work Step by Step

$W\subset \mathbb{R}^{3}$. In order to be a subspace of $\mathbb{R}^{3}$ (definition, p.195) , W must, (a) contain zero, (b) be closed over addition (c) be closed over multiplication by scalars. Checking, (a) fails, because $5(0)-1\neq 0+2(0),$ $\left[\begin{array}{l} 0\\ 0\\ 0 \end{array}\right]\not\in W$ so, W is not a subspace of $\mathbb{R}^{3}$, W is not a vector space.
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.