Suppose that the three numbers r1, r2, and r3 are dis- tinct. Show that the three functions exp(r1x), exp(r2x), and exp(r3x) are linearly independent by showing that their Wronskian W = exp[(r1 +r2 +r3)x] · r1 r2 r3 is nonzero for all x.
Suppose that the three numbers r1, r2, and r3 are dis- tinct. Show that the three functions exp(r1x), exp(r2x), and exp(r3x) are linearly independent by showing that their Wronskian W = exp[(r1 +r2 +r3)x] · r1 r2 r3 is nonzero for all x.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![Suppose that the three numbers r1, r2, and r3 are dis-
tinct. Show that the three functions exp(r1x), exp(r2x),
and exp(r3x) are linearly independent by showing that
their Wronskian
W = exp[(r1 +r2 +r3)x] · r1
r2
r3
is nonzero for all x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdea150f5-a6f4-4bae-affd-2af73f9c8aa9%2F69c08292-93ec-47af-a4a3-797fdba05dd5%2Fvwv3r7m.png&w=3840&q=75)
Transcribed Image Text:Suppose that the three numbers r1, r2, and r3 are dis-
tinct. Show that the three functions exp(r1x), exp(r2x),
and exp(r3x) are linearly independent by showing that
their Wronskian
W = exp[(r1 +r2 +r3)x] · r1
r2
r3
is nonzero for all x.
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