[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 the Land of Oz example (Example), change the transition matrix by making R an absorbing state. This gives

[[math]] \mat{P} = \bordermatrix{ & \mbox{R} & \mbox{N} & \mbox{S} \cr \mbox{R} & 1 & 0 & 0 \cr \mbox{N} & 1/2 & 0 & 1/2 \cr \mbox{S} & 1/4 & 1/4 & 1/2}\ . [[/math]]

Find the fundamental matrix [math]\mat{N}[/math], and also [math]\mat{Nc}[/math] and [math]\mat{NR}[/math]. Interpret the results.