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: 6

Answer

$a.) \ \vert \vert u \vert \vert = \dfrac{\sqrt{5}}{2}$ $b.) \ \vert \vert v \vert \vert = \dfrac{\sqrt{17}}{2}$ $c.) \ \vert\vert u+v\vert\vert =3$

Work Step by Step

Given $u =(1,\frac{1}{2})$ and $v = (2,-\frac{1}{2})$ $a.) \ \vert \vert u \vert \vert = \sqrt{(1)^2+(\frac{1}{2})^2} = \sqrt{1+\frac{1}{4}} = \sqrt{\frac{5}{4}} = \dfrac{\sqrt{5}}{2}$ $b.) \ \vert \vert v \vert \vert = \sqrt{(2)^2+(-\frac{1}{2})^2} = \sqrt{4+\frac{1}{4}} = \sqrt{\frac{17}{4}} = \dfrac{\sqrt{17}}{2}$ $c.) \ \vert\vert u+v\vert\vert = \sqrt{(1+2)^2+(\frac{1}{2}-\frac{1}{2})^2} = \sqrt{(3)^2+(0)^2}=\sqrt{9+0}=\sqrt{9}=3$
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