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: 16


$W$ is not a vector subspace of $M_{3,1}$.

Work Step by Step

Let $u=\left[\begin{array}{lll}{2} & {0} & {\sqrt{2}}\end{array}\right]^{T}\in W$ and $c=2\in R$. Now, $$cu=2\left[\begin{array}{lll}{2} & {0} & {\sqrt{2}}\end{array}\right]^{T}=\left[\begin{array}{lll}{2} & {0} & {2\sqrt{2}}\end{array}\right]^{T}$$ which is not an element of $W$. Hence, $W$ is not a vector subspace of $M_{3,1}$.
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.