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 - Review Exercises - Page 284: 25


(a) $\langle u, v\rangle =-2$ (b) $d(u,v)=\sqrt{\frac{99}{4}}$.

Work Step by Step

$u=(2,-\frac{1}{2},1), \quad v=(\frac{3}{2},2,-1)$, $\langle u, v \rangle =u_1v_1+2u_2v_2+3u_3v_3 $. (a) $\langle u, v\rangle =u_1v_1+2u_2v_2+3u_3v_3=3-2-3=-2$ (b) $d(u,v)=\| u-v \|=\| (\frac{1}{2},-\frac{5}{2},2) \|=\sqrt{\frac{1}{4}+\frac{25\times 2}{4}+4\times 3}=\sqrt{\frac{99}{4}}$.
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