I want to write $A$ as a product of $4$ matrices $B$,$C$,$D$, and $E$ such that $B$,$C$, and $D$ are elementary matrices and $E$ is row-echelon form.
$$A = \begin{bmatrix}0&1&7&8\\1&3&3&8\\-2&5&1&8\end{bmatrix}$$
Thanks
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