Exercise 2.1.30

$u_7$ and $v_7$ have components adding to 1 ; they are close to $s=(.6,.4)$. $\left[\begin{array}{cc}.8\hfill & .3\hfill \\ .2\hfill & .7\hfill \end{array}\right]\left[\begin{array}{c}.6\hfill \\ .4\hfill \end{array}\right]=$ $\left[\begin{array}{c}.6\hfill \\ .4\hfill \end{array}\right]=$steady state $s$. No change when multiplied by $\left[\begin{array}{cc}.8\hfill & .3\hfill \\ .2\hfill & .7\hfill \end{array}\right]$.