[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]

For Example, verify that the following matrix is the inverse of [math]\mat{I} - \mat{Q}[/math] and hence is the fundamental matrix [math]\mat{N}[/math].

[[math]] \mat{N} = \pmatrix{ 8/3 & 1/6 & 4/3 & 2/3 \cr 4/3 & 4/3 & 8/3 & 4/3 \cr 4/3 & 1/3 & 8/3 & 4/3 \cr 2/3 & 1/6 & 4/3 & 8/3 \cr}\ . [[/math]]

Find [math]\mat{N} \mat{c}[/math] and [math]\mat{N} \mat{R}[/math]. Interpret the results.