[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Modify the program MatrixPowers so that it prints

out the average [math] \mat {A}_n[/math] of the powers [math]\mat {P}^n[/math], for [math]n = 1[/math] to [math]N[/math]. Try your program on the Land of Oz example and compare [math]\mat {A}_n[/math] and [math]\mat {P}^n.[/math]