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: 18


$W$ is not a subspace of $R^2$.

Work Step by Step

Let $W$ be a subset of $V$ such that $W=\{(x, y) : x-y=1\}, \quad V=R^{2}.$ It is easy to see that $(0,0)\not\in W$ since $0-0=0\neq1$. Hence, $W$ is not a subspace of $R^2$.
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