Exercise 2.1.31

$M=\left[\begin{array}{ccc}\hfill 8\hfill & \hfill 3\hfill & \hfill 4\hfill \\ \hfill 1\hfill & \hfill 5\hfill & \hfill 9\hfill \\ \hfill 6\hfill & \hfill 7\hfill & \hfill 2\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill 5+u\hfill & \hfill 5-u+v\hfill & \hfill 5-v\hfill \\ \hfill 5-u-v\hfill & \hfill 5\hfill & \hfill 5+u+v\hfill \\ \hfill 5+v\hfill & \hfill 5+u-v\hfill & \hfill 5-u\hfill \end{array}\right];M_3(1,1,1)=(15,15,15)$ $M_4(1,1,1,1)=(34,34,34,34)$ because $1+2+\cdots +16=136$ which is $4(34)$