Chapter 5.2, Problem 11E

Interpretation Introduction

Interpretation:

To show that matrix of the form $\text{A = }\left[\begin{array}{cc}\text{λ}& \text{b}\\ \text{0}& \text{λ}\end{array}\right]$ with $\text{b}\ne \text{0}$ has only one-dimensional Eigen space corresponding to the Eigen value $\text{λ}$.

Concept Introduction:

In the case of two dimensional differential equation system, where Eigen values are same or degenerate, there are two possibilities. Either eigen values have two eigen vectors associated with it or there is only one eigen vector.