Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 0-32198-238-X
ISBN 13: 978-0-32198-238-4

Chapter 4 - Vector Spaces - 4.1 Exercises - Page 198: 3

Answer

Sample answer: $\mathrm{u}=\left[\begin{array}{l} 1\\ 0 \end{array}\right]$, $c=2$

Work Step by Step

Sample answer: $\mathrm{u}=\left[\begin{array}{l} 1\\ 0 \end{array}\right]\in H$, because $1^{2}+0^{2} \leq 1.$ If c=2, $c\mathrm{u}=\left[\begin{array}{l} 2\\ 0 \end{array}\right]\not\in H$, because $2^{2}+0 > 1$ Another answer: $u=\left[\begin{array}{l} 1\\ 0 \end{array}\right]\in H, v=\left[\begin{array}{l} 0\\ 1 \end{array}\right]\in H ,$ $u+v=\left[\begin{array}{l} 1\\ 1 \end{array}\right]\not\in H$
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