  If a matrix $A$ has rank $r$, then its row echelon form (from elimination)
contains the identity matrix in its first $r$ independent columns. How do we
\emph{interpret the matrix} $F$ that appears in the remaining columns of that
echelon form\,? $F$ multiplies those first $r$ independent columns of $A$ to
give its $n-r$ dependent columns. Then $F$ reveals bases for the row space and
the nullspace of the original matrix $A$. And $F$ is the key to the column-row
factorization $\boldsymbol{A}=\boldsymbol{CR}$.
