7. Consider the following system:dxpx + qyсх + dy(a) Explain why if the eigenvalues are distinct real numbers, the general form of the solution canbe written aswhere o1 and 02 are the eigenvectors associated with 1 and A2.(b) Explain why if the eigenvalues are complex numbers of the form a+bi then the general solutionis of the formx(t)()eaty%3Dwhere v is a vector containing arbitrary constants c1 and c2 and other terms involving sin(t)and cos(t).(c) Complete the following table by reflecting on and organizing what you've figured out about thephase portrait for systems of linear differential equations based on knowing just the eigenvalues.EigenvaluesTypical phase portrait Basic format of the general solutiontwo distinct positivereal numbersone positive and onenegative real numbertwo distinct negativereal numbersa complex conjugate pairwith negative real parta complex conjugate pairwith positive real parta complex conjugate pairwith no real partIl||

(a). To show that if the eigen values are distinct real numbers, then the general form of the…

7. Consider the following system: px + qy cx + dy (a) Explain why if the eigenvalues are distinct real numbers, the general form of the solution be written as where o1 and 02 are the eigenvectors associated with d1 and A2. (b) Explain why if the eigenvalues are complex numbers of the form a+bi then the general solut is of the form = eat where v is a vector containing arbitrary constants c1 and c2 and other terms involving si 的

7. Consider the following system: px + qy cx + dy (a) Explain why if the eigenvalues are distinct real numbers, the general form of the solution be written as where o1 and 02 are the eigenvectors associated with d1 and A2. (b) Explain why if the eigenvalues are complex numbers of the form a+bi then the general solut is of the form = eat where v is a vector containing arbitrary constants c1 and c2 and other terms involving si 的

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 35EQ

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