Chapter 5.2, Problem 7E

Interpretation Introduction

Interpretation:

Find the characteristic polynomial for the system of linear equations $\dot{\text{x}}\text{ = 5x + 2y}$ and $\dot{\text{y}}\text{ = -17x - 5y}$ using $\dot{\text{x}}\text{ = Ax}$ equation. Also, determine the eigenvalues and the eigenvectors of the matrix A.

To find the general solution for the given system of linear equations.

Classify the fixed points at the origin.

Concept Introduction:

For two dimensional linear system, equations are $\dot{\text{x}}\text{ = ax + by}$, $\dot{\text{y}}\text{ = cx + dy}$

Above linear system expressed in the form $\dot{\text{x}}\text{ = Ax}$

The standard characteristics polynomials is,

${\text{λ}}^{\text{2}}\text{- τλ + Δ = 0}$, where $\text{τ}$ is the trace of the matrix A, $\text{λ}$ is the corresponding eigenvalue, and $\text{Δ}$ is the determinant of matrix A.