(a) Prove that u + v and u - v are orthogonal in Rn if and only...

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(a) Prove that u + v and u - v are orthogonal in Rn if and only if ||u|| = ||v||.
(b) Draw a diagram showing u, v, u + v, and u - v in IR2 and use (a) to deduce a result about parallelograms.

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Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

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Question Posted: Apr 15, 2016 05:53 AM

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(a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal. (b) Draw a diagram showing u, v, u + v, and u - v in IR2 and use (a) to deduce a result about parallelograms.
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(a) Prove that u + v and u - v are orthogonal in Rn if and only...

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a By Exercise 55 u v u v u 2 v 2 Thus u v u v 0 if and only if u 2 ...View the full answer

Linear Algebra A Modern Introduction

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