Answer
$W$ is not a vector subspace of $V$.
Work Step by Step
Let $f(x)=x^2\in W$ and $c=-3\in R$. Now, $$c[f(x)]=-3x^2$$
which means that $W$ is not closed under scalar multiplication. Hence, $W$ is not vector subspace of $V$.
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: 11
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