(b) Find an operator A that annihlates the following functions. i. In(x) ii. to , α ε R iii. sin(3 In(x))

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Just B and C, please!

(a) Let D = , and an, an-1,..., a1, ao E R. Is anx" D" + an-1x"-1Dn-1+ ... + a1xD+ ao
a linear operator? Prove or provide a counterexample.
dx
(b) Find an operator A that annihlates the following functions.
i. In(x)
ji. ta , α R
iii. sin(3 In(x))
(c) Solve the following using the annihlator method.
i. y" +3y' + 2y = 5 In(x)
ii. x'y" + 7xy' + 10y = 4x? cos(3lIn(x)) + x-3
Transcribed Image Text:(a) Let D = , and an, an-1,..., a1, ao E R. Is anx" D" + an-1x"-1Dn-1+ ... + a1xD+ ao a linear operator? Prove or provide a counterexample. dx (b) Find an operator A that annihlates the following functions. i. In(x) ji. ta , α R iii. sin(3 In(x)) (c) Solve the following using the annihlator method. i. y" +3y' + 2y = 5 In(x) ii. x'y" + 7xy' + 10y = 4x? cos(3lIn(x)) + x-3
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