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Consider the system of linear differential equations We want to determine the stability of the origin. a) This system can be written in the form X' = AX, where X(t) = A = sin (a) ə Əx ∞ (t) = 4 x₁ (t)-1/2 #₂ (t) h, (t)=0a1(t)+2 (t) a Ω and b) Find the eigenvalues of A. List them between square brackets and separated by commas if there are more than Eigenvalues:

Consider the system of linear differential equations We want to determine the stability of the origin. a) This system can be written in the form X' = AX, where X(t) = A = sin (a) ə Əx ∞ (t) = 4 x₁ (t)-1/2 #₂ (t) h, (t)=0a1(t)+2 (t) a Ω and b) Find the eigenvalues of A. List them between square brackets and separated by commas if there are more than Eigenvalues:

Linear Algebra: A Modern Introduction
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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Consider the system of linear differential equations We want to determine the stability of the origin. a) This system can be written in the form X' = = AX, where X(t) A = sin (a) ə Əx f ∞ 8 x₁ (t) = 4 x₁ (t) — 1/2 x₂ (t) x2 (t) = 0 x₁ (t) + 2 x₂ (t) a - (x₁ (t) x₂ (t) and A₂ P b) Find the eigenvalues of A. List them between square brackets and separated by commas if there are more than one. Eigenvalues:
Transcribed Image Text:Consider the system of linear differential equations We want to determine the stability of the origin. a) This system can be written in the form X' = = AX, where X(t) A = sin (a) ə Əx f ∞ 8 x₁ (t) = 4 x₁ (t) — 1/2 x₂ (t) x2 (t) = 0 x₁ (t) + 2 x₂ (t) a - (x₁ (t) x₂ (t) and A₂ P b) Find the eigenvalues of A. List them between square brackets and separated by commas if there are more than one. Eigenvalues:
Consider the system of linear differential equations We want to determine the stability of the origin. a) This system can be written in the form X' = AX, where X(t) = A = ab sin (a) ə əx f 8 ₁ (t) = 2 x₁ (t) + 4x2 (t) (t)=0 x1 (t)-3x2 (t) a Ω b) Find the eigenvalues of A. List them separated by semicolons. Eigenvalues: - (216) and
Transcribed Image Text:Consider the system of linear differential equations We want to determine the stability of the origin. a) This system can be written in the form X' = AX, where X(t) = A = ab sin (a) ə əx f 8 ₁ (t) = 2 x₁ (t) + 4x2 (t) (t)=0 x1 (t)-3x2 (t) a Ω b) Find the eigenvalues of A. List them separated by semicolons. Eigenvalues: - (216) and
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