Problem:

Determine elementary matrices that reduce the given matrix to row-echelon form.

$\displaystyle $\left[\begin{array}{ccc}

5 & 8 & 2\\

1 & 3 & -1\end{array}\right]$$

Question:

Given that elementary matrices are obtained by performing ERO's on the identity matrix, what identity matrix is going to be used in this situation? The identity matrix is nxn, but this given matrix is mxn.