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: 38


$W$ is not a vector subspace of $R^3$.

Work Step by Step

Let $W=\left\{\left(x_{1}, x_{2}, 4\right) : x_{1} \text { and } x_{2} \text { are real numbers }\right\}$, $u=(1,2,4)\in W$ and $c=2\in R$, then \begin{align*} cu&=2(1,2,4)\\ &=(2,4,8)\not\in W. \end{align*} Hence, $W$ is not a vector subspace of $R^3$.
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