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 - 5.2 Inner Product Spaces - 5.2 Exercises - Page 246: 68


see the proof below.

Work Step by Step

Let $f(x)= 1, g(x)=\cos 2nx) $, $C[0,\pi]$ \begin{aligned}\langle f,g\rangle &=\int_{0}^{\pi} \cos 2nx d x\\ &=\left[\frac{1}{2n} \cos 2nx\right]_{0}^{\pi} \\ &=0 \end{aligned}. then $f$ and $g$ are orthogonal in the inner product space $C[0,\pi]$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.