Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector:À = 2 with eigenvector = [] aand generalized eigenvector i = [_]Write the solution to the linear system' = Ar in the following forms.A. In eigenvalue/eigenvector form:[x] =B1[18-18).+B. In fundamental matrix form:x(1)=[a]C. As two equations: (write "c1" and "c2" for c₁ and c₂)x(t) =y(t) =Note: if you are feeling adventurous you could use other eigenvectors like 47 and other generalized eigenvectors like w - 3 v.Just remember that if you change , you must also change for its fundamental solution!C₁

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Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 2 with eigenvector = and generalized eigenvector = Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x] = ₁ C1 ]+[ ]). 3. In fundamental matrix form: [x]- C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = []

Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 2 with eigenvector = and generalized eigenvector = Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x] = ₁ C1 ]+[ ]). 3. In fundamental matrix form: [x]- C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = []

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 29EQ

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