For the system of differential equations, 6 - 5 18 16 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = = U1 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue X₂. Enter the eigenvectors as a matrix with an appropriate size. U2 = y' = y(t) d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. = C1 + c₂

For the system of differential equations, 6 - 5 18 16 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = = U1 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue X₂. Enter the eigenvectors as a matrix with an appropriate size. U2 = y' = y(t) d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. = C1 + c₂

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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