Elementary Row Operations

Elementary row operations are used in Matrix Row Reduction to manipulate the rows of a matrix. There are three types of elementary row operations:

1. Row Switching (Swap): Interchanging two rows of a matrix. For example, swapping row 1 and row 2. Written as $R_1\leftrightarrow R_2$
2. Row Multiplication: Multiplying all elements of a row by a non-zero scalar. For example, multiplying row 3 by 2. Written as $k{R}_1\to R_1$
3. Row Addition: Adding a multiple of one row to another row. For example, adding 3 times row 1 to row 2. Written as $R_2+k{R}_1\to R_2$

Matrices obtained from these row operations are called row equivalent.