Elementary Transformation

Any one of the following operations on a matrix is called an elementary transformation.

Interchange of any two rows (or columns), denoted by $R_{i} \leftrightarrow R_{j}$ ; or $C_{i} \leftrightarrow C_{j}$ ;
Multiplication of the elements of any row (or column) by any non-zero number $k$ and denoted by $R_{i} \to k R_{i}$ ; or $C_{i} \to k C_{i}$ ;
Addition of a constant multiple of the elements of any row to the corresponding element of any other row, denoted by $R_{i} \to R_{i} + k R_{j}$ ; or $C_{i} \to C_{i} + k C_{j}$ ;

🪴 TJ's Notes 1.0