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: 5

Answer

$a.) \ \vert \vert u \vert \vert = \dfrac{\sqrt{17}}{4}$ $b.) \ \vert \vert v \vert \vert = \dfrac{5\sqrt{41}}{8}$ $c.) \ \vert\vert u+v\vert\vert = \dfrac{\sqrt{577}}{8}$

Work Step by Step

Given $u =(-1,\frac{1}{4})$ and $v = (4,-\frac{1}{8})$ $a.) \ \vert \vert u \vert \vert = \sqrt{(-1)^2+(\frac{1}{4})^2} = \sqrt{1+\frac{1}{16}} = \sqrt{\frac{17}{16}} = \dfrac{\sqrt{17}}{4}$ $b.) \ \vert \vert v \vert \vert = \sqrt{(4)^2+(-\frac{1}{8})^2} = \sqrt{16+\frac{1}{64}} = \sqrt{\frac{1025}{64}} = \dfrac{5\sqrt{41}}{8}$ $c.) \ \vert\vert u+v\vert\vert = \sqrt{(-1+4)^2+(\frac{1}{4}-\frac{1}{8})^2} = \sqrt{(3)^2+(\frac{1}{8})^2}=\sqrt{9+\frac{1}{64}}=\sqrt{\frac{577}{64}}=\dfrac{\sqrt{577}}{8}$
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