Answer
0
Work Step by Step
For f and g in C[0,1], the inner product is defined as follows
$\langle f,g\rangle=\int_0^1f(t)g(t)dt=\int_0^1(1-3t^2)(t-t^3)dt=\int_0^1(t-4t^3+3t^5)dt=\left[\frac{t^2}{2}-t^4+\frac{t^6}{2}\right]_0^1=0$
Linear Algebra and Its Applications (5th Edition)
by Lay, David C.; Lay, Steven R.; McDonald, Judi J.
Published by
Pearson
ISBN 10:
032198238X
ISBN 13:
978-0-32198-238-4
Chapter 6 - Orthogonality and Least Squares - 6.7 Exercises - Page 385: 21
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