Elementary Row Operation/Examples/Arbitrary Operation on Identity 1

Example of Elementary Row Operation

The matrix:

$\mathbf A = \begin {pmatrix} 1 & 0 \\ 1 & 1 \end {pmatrix}$

can be obtained from the identity matrix $\mathbf I_2$ by the elementary row operation $e$ defined as:

$e := r_2 \to r_1 + r_2$

Then multiplying the matrix:

$\mathbf X = \begin {pmatrix} a & b \\ c & d \end {pmatrix}$

on the left by $\mathbf A$ we get:

$\begin {pmatrix} a & b \\ a + c & b + d \end {pmatrix}$

which can be obtained by applying that same elementary row operation $e$ on $\mathbf X$.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): elementary matrix