Consider Archetype J, and specifically the row-reduced version of the augmented matrix of the system of equations, denoted as $B$ here, and the values of $r$, $D$ and $F$ immediately following. Determine the values of the entries \begin{align*} \matrixentry{B}{1,d_1}& & \matrixentry{B}{3,d_3}& & \matrixentry{B}{1,d_3}& & \matrixentry{B}{3,d_1}& & \matrixentry{B}{d_1,1}& & \matrixentry{B}{d_3,3}& & \matrixentry{B}{d_1,3}& & \matrixentry{B}{d_3,1}& & \matrixentry{B}{1,f_1}& & \matrixentry{B}{3,f_1}& \end{align*} (See Exercise TSS.M70 for a generalization.)