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Are the functions f, 9, and h given below linearly independent? f(x) = e5z - cos(9x), g(x) = e5z + cos(9x), h(x) = cos(9x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (ešz – cos(9a)) + (ebz + cos(9x)) + (cos(9x)) = 0.

Are the functions f, 9, and h given below linearly independent? f(x) = e5z - cos(9x), g(x) = e5z + cos(9x), h(x) = cos(9x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (ešz – cos(9a)) + (ebz + cos(9x)) + (cos(9x)) = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Are the functions f, 9, and h given below linearly independent? f(x) = e5 – cos(9x), g(x) = e®z + cos(9x), h(x) = cos(9x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (ešz – cos(9z)) + (ebz + cos(9z)) + (cos(9x)) = 0.
Transcribed Image Text:Are the functions f, 9, and h given below linearly independent? f(x) = e5 – cos(9x), g(x) = e®z + cos(9x), h(x) = cos(9x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (ešz – cos(9z)) + (ebz + cos(9z)) + (cos(9x)) = 0.
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