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: 20


$W$ 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 $R^2$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.