Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 5 - Inner Product Spaces - 5.2 Inner Product Spaces - 5.2 Exercises - Page 247: 85


(a) False. (b) False.

Work Step by Step

(a) False. One can define infinitely many inner products in $R^n$, for example $$\langle u,v\rangle =t u\cdot v, \quad u,v \in R^n, \quad t\in R.$$ (b) False. The condition $$\langle u,u\rangle=0 \Longleftrightarrow u=0$$ shows that the only vector which has zero norm is the zero vector.
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