[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]

In Example, let [math]a = 0[/math] and [math]b = 1/2[/math]. Find [math] \mat {P},~ \mat {P}^2,[/math] and [math] \mat {P}^3.[/math] What would [math] \mat {P}^n[/math] be? What happens to [math] \mat {P}^n[/math] as [math]n[/math] tends to infinity? Interpret this result.