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 - Page 236: 81


$u\cdot (cv+dw)=0$.

Work Step by Step

Since $u$ is orthogonal to $v$ and $w$, then we get $$u\cdot v=0, \quad u\cdot w=0.$$ Keeping this in mind, now, \begin{align*} u\cdot (cv+dw)&=c (u\cdot v)+d (u\cdot w)\\ &=0+0\\ &=0. \end{align*} Hence, $u$ is orthogonal to $cv+dw$.
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