Are the functions f, g, and h given below linearly independent? f(x) = e2" + cos(7x), g(x) = e2" cos(7æ), h(x) = cos(7x). 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. (e2z + cos(7x)) + (e2 – cos(72)) + (cos(7x)) = 0. help (numbers)
Are the functions f, g, and h given below linearly independent? f(x) = e2" + cos(7x), g(x) = e2" cos(7æ), h(x) = cos(7x). 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. (e2z + cos(7x)) + (e2 – cos(72)) + (cos(7x)) = 0. help (numbers)
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, g, and h given below linearly independent?
f(x) = e2" + cos(7x), g(æ)= e2 – cos(7x), h(x) = cos(7x).
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.
(e2z + cos(7x)) +
(e2z – cos(7x)) +
(cos(7x)) = 0. help (numbers)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1cd4af0-0e80-4ce1-845f-b842d7827495%2Ffc4aa787-b99c-48fc-9e19-6041c94a67ed%2Fdja5an_processed.png&w=3840&q=75)
Transcribed Image Text:Are the functions f, g, and h given below linearly independent?
f(x) = e2" + cos(7x), g(æ)= e2 – cos(7x), h(x) = cos(7x).
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.
(e2z + cos(7x)) +
(e2z – cos(7x)) +
(cos(7x)) = 0. help (numbers)
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