A Country Has Two Main Political Parties $\vec{P}=(f, s, n)$ Gives the Number of People Who Are Members of the s

Short Answer

A country has two main political parties. The vector $\vec{P}=(f, s, n)$ gives the number of people who are members of the first party, the second party, and neither party, respectively. Suppose $\vec{P}_{\text {new }}=\mathbf{T} \vec{P}_{\text {old }}=\left(\begin{array}{lll}0.80 & 0.11 & 0.10 \\ 0.17 & 0.85 & 0.15 \\ 0.03 & 0.04 & 0.75\end{array}\right) \vec{P}_{\text {old }}$ . Let $\vec{P}_{2005}=(25,30,18)$ be the population vector (in tens of thousands) in the year 2005. What is $\vec{P}_{2006}$ ?