Chapter 8.1, Problem 24E

(a)

To determine

The stochastic matrix $2\times 2$ with columns and rows labeled D and R to display the democratic governors and republican governors if $70\%$ of the democratic governors were succeeded by Democrats and $30\%$ by Republicans. Also, $40\%$ of the republican governors were succeeded by Democrats and $60\%$ by Republicans

(b)

To determine

To calculate: The second power and third power of the matrix for the matrix, obtained in part (a)

(c)

To determine

To calculate: The percentage of democrat governors in the three elections if all current governors are democrats. Also, stochastic matrix that displays the transition of successful governors by democrats to republicans denoted by D to R is,

$\begin{array}{l}\begin{array}{cc}D& R\end{array}\\ A=\begin{array}{c}D\\ R\end{array}\left[\begin{array}{cc}.7& .4\\ .3& .6\end{array}\right]\end{array}$