The AddRow(A, i, j, s) command replaces row i of A with row i + s * row j.  This command can also be called as AddRows(A, i, j, s).

The MultiplyRow(A, i, s) command replaces row i of A with s * row i.

The SwapRow(A, i, j) command interchanges rows i and j of A.  This command can also be called as SwapRows(A, i, j).

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{LinearAlgebra}\right)\:$

$A≔⟨⟨1\,3\,7⟩|⟨4\,5\,6⟩⟩$

$A≔\left[\begin{array}{cc}1& 4\\ 3& 5\\ 7& 6\end{array}\right]$

$B≔\mathrm{AddRow}\left(A\,2\,1\,-3\right)$

$B≔\left[\begin{array}{cc}1& 4\\ 0& \mathrm{-7}\\ 7& 6\end{array}\right]$

$\mathrm{SwapRow}\left(B\,1\,3\right)$

$\left[\begin{array}{cc}7& 6\\ 0& \mathrm{-7}\\ 1& 4\end{array}\right]$

$\mathrm{MultiplyRow}\left(A\,2\,x\right)$

$\left[\begin{array}{cc}1& 4\\ 3x& 5x\\ 7& 6\end{array}\right]$