Answer
See answer below
Work Step by Step
We see that: $f_3(x)-f_2(x)=\cos^2x-\sin^2x=\cos 2x=f_1(x)$ for all $x \in (-\infty,+\infty)$
Hence the set $\{f_1,f_2,f_3\}$ is linearly dependent in $C^{\infty }(-\infty, + \infty)$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 4 - Vector Spaces - 4.5 Linear Dependence and Linear Independence - Problems - Page 297: 24
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