[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]

Find the fixed probability vector [math]\mat{w}[/math] for each of the following regular matrices.

• [math]\mat {P} = \pmatrix{ .75 & .25 \cr .5 & .5}[/math]. \smallskip
• [math]\mat {P} = \pmatrix{ .9 & .1 \cr .1 & .9}[/math]. \smallskip
• [math]\mat {P} = \pmatrix{ 3/4 & 1/4 & 0 \cr 0 & 2/3 & 1/3 \cr 1/4 & 1/4 & 1/2}[/math]. \smallskip