Answer
$W$ 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 $R^2$.
Elementary Linear Algebra 7th Edition
by Larson, Ron
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
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter 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.
