b) A system of differential equation is given as follows: x₁ = 9x₁ - 4x₂ x₂ = 8x₁ - 3x₂ where x₁ and X2 are functions of . Given that the eigenvalues of A= H and 5 with the corresponding eigenvectors i) Write a matrix P that diagonalizes A. ii) Write a diagonal matrix D such that P¹ AP = D. iii) Hence, find the general solution to the system. and 0 respectively. 8-3 are 1
b) A system of differential equation is given as follows: x₁ = 9x₁ - 4x₂ x₂ = 8x₁ - 3x₂ where x₁ and X2 are functions of . Given that the eigenvalues of A= H and 5 with the corresponding eigenvectors i) Write a matrix P that diagonalizes A. ii) Write a diagonal matrix D such that P¹ AP = D. iii) Hence, find the general solution to the system. and 0 respectively. 8-3 are 1
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Question
![b) A system of differential equation is given as follows:
x₁ = 9x₁ - 4x₂
x₂ = 8x₁ - 3x₂
where x₁ and X2 are functions of . Given that the eigenvalues of A=
and 5 with the corresponding eigenvectors
i) Write a matrix P that diagonalizes A.
ii) Write a diagonal matrix D such that P¹ AP = D.
iii) Hence, find the general solution to the system.
[4=[83] are 1
and
respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F328e8f08-7997-4c38-bd75-b66ace13a203%2Fdb97ac0a-5ab7-4b70-8e7e-6fff61d5c4a0%2Fdhfns7o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b) A system of differential equation is given as follows:
x₁ = 9x₁ - 4x₂
x₂ = 8x₁ - 3x₂
where x₁ and X2 are functions of . Given that the eigenvalues of A=
and 5 with the corresponding eigenvectors
i) Write a matrix P that diagonalizes A.
ii) Write a diagonal matrix D such that P¹ AP = D.
iii) Hence, find the general solution to the system.
[4=[83] are 1
and
respectively.
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