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Show that e, = [1 2 3] is an eigenvector of the matrix A and find its corresponding eigenvalue. Find the other two eigenvalues and their corresponding eigenvectors. Write down in spectral form the general solution of the system of differential equations 2dx=7x-y-z = 4x - y 2=-3x+3y +z Hence show that if x = 2, y = 4 and z = 6 when t=0 then the solution is x = 2e', y = 4e', z = 6e¹ 712 I T + NIW MIN -12

Show that e, = [1 2 3] is an eigenvector of the matrix A and find its corresponding eigenvalue. Find the other two eigenvalues and their corresponding eigenvectors. Write down in spectral form the general solution of the system of differential equations 2dx=7x-y-z = 4x - y 2=-3x+3y +z Hence show that if x = 2, y = 4 and z = 6 when t=0 then the solution is x = 2e', y = 4e', z = 6e¹ 712 I T + NIW MIN -12

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 18EQ
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Show that e, = [1 2 3] is an eigenvector of the matrix A= and find its corresponding eigenvalue. Find the other two eigenvalues and their corresponding eigenvectors. Write down in spectral form the general solution of the system of differential equations 2dx = 7x-y-z dt dy = 4x - y dr 2 = −3x + 3y +z dt Hence show that if x = 2, y = 4 and z = 6 when t = =0 then the solution is x = 2e', y = 4e', z = 6e¹ || MIN NIW Ï
Transcribed Image Text:Show that e, = [1 2 3] is an eigenvector of the matrix A= and find its corresponding eigenvalue. Find the other two eigenvalues and their corresponding eigenvectors. Write down in spectral form the general solution of the system of differential equations 2dx = 7x-y-z dt dy = 4x - y dr 2 = −3x + 3y +z dt Hence show that if x = 2, y = 4 and z = 6 when t = =0 then the solution is x = 2e', y = 4e', z = 6e¹ || MIN NIW Ï
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