Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (d)/Statement

Suppose now that, as well as the movement between Delta and Surrey, people immigrate from elsewhere (Abbotsford). This changes the dynamical system so that $${\begin{bmatrix}d_{n}\\s_{n}\end{bmatrix}}={\begin{bmatrix}1.1&0.2\\0.1&1\end{bmatrix}}{\begin{bmatrix}d_{n-1}\\s_{n-1}\end{bmatrix}}.$$ Assume that $d_{0}$ and $s_{0}$ are the same as in the previous case. In the long run, what will the ratio $d_{n}/s_{n}$ be?