Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: λ = -2 with eigenvector v = H and generalized eigenvector w = H Write the solution to the linear system ' = Ar in the following forms. In eigenvalue/eigenvector form: -848-81.0 = e help (matrices) In fundamental matrix form: [x(t)] = [88]) a help (formulas) help (matrices) As two equations: (write "c1" and "c2" for C1 and C2 ) e t x(t) help (formulas) y(t) = = help (formulas) Note: If you are feeling adventurous you could use other eigenvectors like 4 and other generalized eigenvectors like w - 3 v. 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: λ = -2 with eigenvector v = H and generalized eigenvector w = H Write the solution to the linear system ' = Ar in the following forms. In eigenvalue/eigenvector form: -848-81.0 = e help (matrices) In fundamental matrix form: [x(t)] = [88]) a help (formulas) help (matrices) As two equations: (write "c1" and "c2" for C1 and C2 ) e t x(t) help (formulas) y(t) = = help (formulas) Note: If you are feeling adventurous you could use other eigenvectors like 4 and other generalized eigenvectors like w - 3 v. 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

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 43EQ

See similar textbooks