Suppose that $B$ is a matrix in reduced row-echelon form that is equivalent to the augmented matrix of a system of equations with $m$ equations in $n$ variables. Let $r$, $D$ and $F$ be as defined in Definition RREF. Prove that $d_k\geq k$ for all $1\leq k\leq r$. Then suppose that $r\geq 2$ and $1\leq k <\ell\leq r$ and determine what can you conclude, in general, about the following entries. \begin{align*} \matrixentry{B}{k,d_k}& & \matrixentry{B}{k,d_\ell}& & \matrixentry{B}{\ell,d_k}& & \matrixentry{B}{d_k,k}& & \matrixentry{B}{d_k,\ell}& & \matrixentry{B}{d_\ell,k}& & \matrixentry{B}{d_k,f_\ell}& & \matrixentry{B}{d_\ell,f_k}& \end{align*} If you cannot conclude anything about an entry, then say so. (See Exercise TSS.M46 and Exercise TSS.M70.)