Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identically. f(x) = 37, g(x) = 2sin 2x, h(x) = 4cos 2x Enter the non-trivial linear combination. (8)(37) + O (2 sin ?x) + (O (4 cos 2x) = 0 2

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identically.
f(x) = 37, g(x)= 2sin 2x, h(x) = 4cos 2x
Enter the non-trivial linear combination.
(8)(37) + (O (2 sin?x) + (D (4 cos 2x) = 0
2
Transcribed Image Text:Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identically. f(x) = 37, g(x)= 2sin 2x, h(x) = 4cos 2x Enter the non-trivial linear combination. (8)(37) + (O (2 sin?x) + (D (4 cos 2x) = 0 2
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