[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]

Consider the Markov chain with transition matrix

[[math]] \mat {P} = \pmatrix{ 1/2 & 1/2 \cr 1/4 & 3/4}\ . [[/math]]

Find the fundamental matrix [math]\mat{Z}[/math] for this chain. Compute the mean first passage matrix using [math]\mat{Z}[/math].