Exercise 2.2.26

Solvable for $s=10$ (add the two pairs of equations to get $a+b+c+d$ on the left sides, 12 and $2+s$ on the right sides). So 12 must agree with $2+s$, which makes $s=10$. The four equations for $a,b,c,d$ are singular! Two solutions are $\left[\begin{array}{cc}1\hfill & 3\hfill \\ 1\hfill & 7\hfill \end{array}\right]$ and $\left[\begin{array}{cc}0\hfill & 4\hfill \\ 2\hfill & 6\hfill \end{array}\right]$, $A=\left[\begin{array}{cccc}1\hfill & 1\hfill & 0\hfill & 0\hfill \\ 1\hfill & 0\hfill & 1\hfill & 0\hfill \\ 0\hfill & 0\hfill & 1\hfill & 1\hfill \\ 0\hfill & 1\hfill & 0\hfill & 1\hfill \end{array}\right]$and $U=\left[\begin{array}{cccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill -1\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \end{array}\right]$