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: 19


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

Work Step by Step

Let $u=(2,8), v=(3,27)\in W$. Now, $$u+v=(2,8)+(3,27)=(5,35).$$ Since $35\neq 5^3$, then $u+v$ is not an element of $W$. Hence, $W$ is not a vector subspace of $R^2$.
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