Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 4 - Vector Spaces - 4.3 Subspaces - True-False Review - Page 272: g

Answer

False

Work Step by Step

Let $A=(0,1,1)$ be the point in yz-plane and $B=(1,1,0)$ be the point in xy-plane. Then $A+B=(0,1,1)+(1,1,0)=(1,2,1)$ This point $(1,2,1)$ is not belong to $S$. Hence, $S$ is not a subspace of $V$
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