Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = -2 with eigenvector v = H and generalized eigenvector w = [] Write the solution to the linear system 7' = Ar in the following forms. In eigenvalue/eigenvector form: [3(6)] = C1 help (matrices) [8] In fundamental matrix form: [3 (4)] = + C2 e 381 a help (formulas) help (matrices) [8] + - [B] As two equations: (write "c1" and "c2" for C1 and C2 ) x(t) y(t) = = help (formulas) help (formulas) e Note: If you are feeling adventurous you could use other eigenvectors like 4 v and other generalized eigenvectors like w - 3v. Just remember that if you change v, you must also change w for its fundamental solution! Book: Section 3.7 of Notes on Diffy Qs

Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = -2 with eigenvector v = H and generalized eigenvector w = [] Write the solution to the linear system 7' = Ar in the following forms. In eigenvalue/eigenvector form: [3(6)] = C1 help (matrices) [8] In fundamental matrix form: [3 (4)] = + C2 e 381 a help (formulas) help (matrices) [8] + - [B] As two equations: (write "c1" and "c2" for C1 and C2 ) x(t) y(t) = = help (formulas) help (formulas) e Note: If you are feeling adventurous you could use other eigenvectors like 4 v and other generalized eigenvectors like w - 3v. Just remember that if you change v, you must also change w for its fundamental solution! Book: Section 3.7 of Notes on Diffy Qs

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 24EQ

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