Are the functions f, g, and h given below linearly independent? f(x) = e", g(x) = xe h(x) = x²e3". 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. (e3z) + (xe**) + (x2e3) = 0. help (numbers)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
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Are the functions f, g, and h given below linearly independent?
f(x) = e", g(x) = xe*",
h(x) = x²e3".
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.
(e3) +
(xešr) +
(z?e3z) = 0. help (numbers)
Transcribed Image Text:Are the functions f, g, and h given below linearly independent? f(x) = e", g(x) = xe*", h(x) = x²e3". 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. (e3) + (xešr) + (z?e3z) = 0. help (numbers)
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