Let $\vec{P}=(o, r)$ Be the Population Vector of a City Giving $o$

Short Answer

Let $\vec{P}=(o, r)$ be the population vector of a city giving $o$ , the number of people who own their home and $r$ , the number of people who rent. Suppose that each year, 3\% of the people who own their home move to a rental and $15 \%$ of the people who rent purchase a home and become owners. Let $\mathbf{A}=\left(\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right)$ be such that $\vec{P}_{\text {new }}=\mathbf{A} \vec{P}_{\text {old }}$ . What is $a_{11}$ ?