Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 5 - Inner Product Spaces - 5.1 Definition of an Inner Product Space - True-False Review - Page 350: b

Answer

False

Work Step by Step

Given any $u, v \in V$ and $k \in R$, we have that \begin{align} \langle k \ u,k\ v\rangle&=k\langle \ u,k\ v\rangle\\ &=k \overline{\langle k \ v,u\rangle}\\ &=k \overline{k}\ \overline{\langle \ v,u\rangle}\\ &=k \overline{k}\ \langle \ u,v\rangle\\ & =|k|^{2}\langle \ u,v\rangle\\ \end{align} So, the statement is false
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