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 - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 14


$W$ is not a vector subspace of $R^3$.

Work Step by Step

Let $u=(3,4,5),v=(6,8,10)\in W$. Now, $$u+v=(3,4,5)+(6,8,10)=(9,12,15)$$ which is not an element of $W$, in other words, $W$ is not closed under addition. Hence, $W$ is not a vector subspace of $R^3$.
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