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Consider the system (image 1), where a ∈ R−{0}. a)Determine all values of the real constant b such that the system matrix, where f(t) = g(t) = 0, has complex eigenvalues. b) Solve the system where b=−2, f(t)=g(t)=0 and verify that the fundamental matrix has the form ( image 2) c)Suppose b=−2,f(t)=sec(at) and g(t)=0. Determine a particular solution for the system.

Consider the system (image 1), where a ∈ R−{0}. a)Determine all values of the real constant b such that the system matrix, where f(t) = g(t) = 0, has complex eigenvalues. b) Solve the system where b=−2, f(t)=g(t)=0 and verify that the fundamental matrix has the form ( image 2) c)Suppose b=−2,f(t)=sec(at) and g(t)=0. Determine a particular solution for the system.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the system (image 1), where a ∈ R−{0}.

a)Determine all values of the real constant b such that the system matrix, where f(t) = g(t) = 0, has complex eigenvalues.

b) Solve the system where b=−2, f(t)=g(t)=0 and verify that the fundamental matrix has the form ( image 2)

c)Suppose b=−2,f(t)=sec(at) and g(t)=0. Determine a particular solution for the system. 

 

´a11 sin(at) + b11 cos(at) a12 sin(at) + b12 cos(at) (t) = *) = (a21 sin(at) + b21 cos(at) a22 sin(at) + b22 cos(at) )
Transcribed Image Text:´a11 sin(at) + b11 cos(at) a12 sin(at) + b12 cos(at) (t) = *) = (a21 sin(at) + b21 cos(at) a22 sin(at) + b22 cos(at) )
/ 교(t) = -az(t) + ay(t) + f(t) ly (t) = abx(t) + ay(t) + g(t)
Transcribed Image Text:/ 교(t) = -az(t) + ay(t) + f(t) ly (t) = abx(t) + ay(t) + g(t)
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