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 - 5.3 Orthonormal Bases: Gram-Schmidt Process - 5.3 Exercises - Page 257: 49

Answer

see the details below.

Work Step by Step

We have $$\langle x, x\rangle=\int_{-1}^1 x^2 d x=\left[ \frac{ 1}{3 } x^3\right]_{-1}^1=\frac{ 1}{3 }+\frac{ 1}{3 } =\frac{ 2}{3 }.$$
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