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: 11


$W$ 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 $V$.
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