Are the functions f, g, and h given below linearly independent? f(x) = et – cos(5æ), g(x) = e* + cos(5æ), h(x) = cos(5x). they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial olution to the equation below. Be sure you can justify your answer. (edz – cos(5x)) + (eta + cos(5x)) + COS - cos(5x)) = 0. help (numbers)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Are the functions †, g, and h given below linearly independent?
g(x) = e
4x
f(x) = e4
cos(5x),
+ cos(5x),
h(x)
= cos(5x).
-
they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial
olution to the equation below. Be sure you can justify your answer.
(et – cos(5æ)) +
(et + cos(5x)) +
-
cos(5x))
= 0. help (numbers)
Transcribed Image Text:Are the functions †, g, and h given below linearly independent? g(x) = e 4x f(x) = e4 cos(5x), + cos(5x), h(x) = cos(5x). - they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial olution to the equation below. Be sure you can justify your answer. (et – cos(5æ)) + (et + cos(5x)) + - cos(5x)) = 0. help (numbers)
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