Exercise 4.2.3

$P_1=\frac{1}{3}\left[\begin{array}{ccc}1\hfill & 1\hfill & 1\hfill \\ 1\hfill & 1\hfill & 1\hfill \\ 1\hfill & 1\hfill & 1\hfill \end{array}\right]$and $P_{1}b=\frac{1}{3}\left[\begin{array}{c}5\hfill \\ 5\hfill \\ 5\hfill \end{array}\right].P_2=\frac{1}{11}\left[\begin{array}{ccc}1\hfill & 3\hfill & 1\hfill \\ 3\hfill & 9\hfill & 3\hfill \\ 1\hfill & 3\hfill & 1\hfill \end{array}\right]$and $P_{2}b=\left[\begin{array}{c}1\hfill \\ 3\hfill \\ 1\hfill \end{array}\right]$.