Explanation Procedure used: 1. Calculate the wronskian as, W ( s ) = | y 1 ( t ) y 2 ( t ) y 3 ( t ) y 1 ′ ( t ) y 2 ′ ( t ) y 3 ′ ( t ) y 1 ′ ′ ( t ) y 2 ′ ′ ( t ) y 3 ′ ′ ( t ) | 2. If the wronskian is zero, then the function is linearly dependent. 3. If the wronskian is not zero, then the function is linearly independent. Calculation: Consider the function. S = { e t , e − 2 t , e − t } Here, y 1 = e t , y 2 = e − 2 t , and y 3 = e − t The wronskian is, W ( s ) = | e t e − 2 t e − t d d t ( e t ) d d t ( e − 2 t ) d d t ( e − t ) </

5th Edition

ISBN: 9780128149485

Author: Abell, Martha L. L.

Publisher: Elsevier Science

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Chapter 4, Problem 6RE

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Whether the function S={et, e−2t, e−t} is linearly independent or linearly dependent.

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Chapter 4, Problem 5RE

Chapter 4, Problem 7RE

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Introductory Differential Equations

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Whether the function S = { e t , e − 2 t , e − t } is linearly independent or linearly dependent.

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Whether the function S={et, e−2t, e−t} is linearly independent or linearly dependent.

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Chapter 4 Solutions