Elementary Row Operation/Examples/Operations on Arbitrary Matrix

Examples of Elementary Row Operations
Let $\mathbf A$ be the matrix:
 * $\mathbf A = \begin {pmatrix} 1 & 2 & 3 & 4 \\ 2 & -1 & 1 & 0 \\ -2 & 3 & 1 & 1 \end {pmatrix}$