I want to make sure I am setting up the following problem correctly...

Problem

A medical researcher is studying the spread of a virus in a population of 1000 mice. During any week there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. One hundred mice are currently infected with the virus.

The matrix I have is:

$\displaystyle \left(\begin{array}{cc}0.20&0.10\\0.80&0.90\end{ar ray}\right) $

and then for the initial numbers matrix:

$\displaystyle X = \left(\begin{array}{c}100\\900\end{array}\right)$