The inn er produ ct of two functions f and g on [a,b] is given by (f, 9) = | 5 (#) g (x) dr. Two distinct functions f and g are said to be ort hogonal if (f,g) = 0. Show that the foll owing set of functions is orthogonal on [–n, 7] . {sin x, sin 2x, sin 3x,...cos x, cos 2x, cos 3x, ...}

The inn er produ ct of two functions f and g on [a,b] is given by (f, 9) = | 5 (#) g (x) dr. Two distinct functions f and g are said to be ort hogonal if (f,g) = 0. Show that the foll owing set of functions is orthogonal on [–n, 7] . {sin x, sin 2x, sin 3x,...cos x, cos 2x, cos 3x, ...}

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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Question

The inn er produ ct of two functions f and g on [a,b] is given by
(f, g) = |
f (x) g (x) dx.
Two distinct functions f and g are said to be ort hogonal if (f, g) = 0. Show that the following
set of functions is orthogonal on [–7, "] .
%3D
{sin x, sin 2x, sin 3x, ...cos x, cos 2x, cos 3x,...}

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