Chapter 2, Problem 6P

To determine

The reason for calculating ${[A]}^{50}*[B]$ gives the column matrix for the population distribution after $50$ years if $A=\left[\begin{array}{ccc}0& 0& 0.33\\ 0.18& 0& 0\\ 0& 0.71& 0.94\end{array}\right]$ and population for consecutive year is calculated as $A\cdot X_0=X_1$, $A\cdot X_1=X_2$, $A\cdot X_2=X_3\dots$