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Consider the system of differential equations x₁ = 2x1 + 0x2 y₂ = 4x1 +4x2 " where 1 and 2 are functions of t. Our goal is to find the general solution of this system. a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is A =

Consider the system of differential equations x₁ = 2x1 + 0x2 y₂ = 4x1 +4x2 " where 1 and 2 are functions of t. Our goal is to find the general solution of this system. a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is A =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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We assume that X1 is assoicated to the smallest eigenvalue and X2 to the largest eigenvalue

Give an eigenvector associated to the largest eigenvalue. Answer: ab sin (a) and X₂ = ə sin (a) əx f ə əx c) The general solution of the system of linear differential equations is of the form X = c₁ X₁ + c₂X₂, where c₁ and co are constants, and X1 = 8 f a Ω 8 A₂ α Ω P AL P
Transcribed Image Text:Give an eigenvector associated to the largest eigenvalue. Answer: ab sin (a) and X₂ = ə sin (a) əx f ə əx c) The general solution of the system of linear differential equations is of the form X = c₁ X₁ + c₂X₂, where c₁ and co are constants, and X1 = 8 f a Ω 8 A₂ α Ω P AL P
Consider the system of differential equations ab sin (a) where x1 and Ix2 are functions of t. Our goal is to find the general solution of this system. a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is A əx f ∞ a Ω x₁ = 2x1 + 0x2 y₂ = 4x1 +4x2 " Eigenvalues: Give an eigenvector associated to the smallest eigenvalue. Answer: b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated by semicolons.
Transcribed Image Text:Consider the system of differential equations ab sin (a) where x1 and Ix2 are functions of t. Our goal is to find the general solution of this system. a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is A əx f ∞ a Ω x₁ = 2x1 + 0x2 y₂ = 4x1 +4x2 " Eigenvalues: Give an eigenvector associated to the smallest eigenvalue. Answer: b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated by semicolons.
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