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 - 5.1 Length and Dot Product in Rn - 5.1 Exercises: 7

Answer

$a.) \ \vert \vert u \vert \vert = \sqrt{6}$ $b.) \ \vert \vert v \vert \vert = 2\sqrt{2}$ $c.) \ \vert\vert u+v\vert\vert = 3\sqrt{2} $

Work Step by Step

Given $u = (1,2,1)$ and $v = (0,2,-2)$ $a.) \ \vert \vert u \vert \vert = \sqrt{(1)^2+(2)^2+(1)^2} = \sqrt{1+4+1} = \sqrt{6}$ $b.) \ \vert \vert v \vert \vert = \sqrt{(0)^2+(2)^2+(-2)^2} = \sqrt{0+4+4} = \sqrt{8} = 2\sqrt{2}$ $c.) \ \vert\vert u+v\vert\vert = \sqrt{(1+0)^2+(2+2)^2+(1-2)^2} = \sqrt{(1)^2+(4)^2+(-1)^2} = \sqrt{1+16+1} = \sqrt{18} = 3\sqrt{2} $
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