Answer
$W$ is not a vector subspace of $R^2$.
Work Step by Step
Let $u=(2,4), v=(3,9)\in W$. Now,
$$u+v=(2,4)+(3,9)=(5,13).$$
Since $13\neq 5^2$, then $u+v$ is not an element of $W$. Hence, $W$ is not a vector 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 - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 20
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