What are Elementary Row Operations

• Since a row of our augmented matrix is equivalent to an equation.
• We can use similar techniques as we used in elimination method.

Row Swap

Interchange two rows:

$$R_1\leftrightarrow R_2$$

• It doesn’t really matter which equation is on top or bottom.

Row Scale

$$R_2:2R_2$$

• We do this is elimination all the time to get terms to cancel out.

Row Addition

$$R_3:R_3+2R_1$$

• Adding a scalar multiple of one row to another.

Example:

• Two systems are equivalent if they have the same solutions.
• Since our original system has the same solutions as our modified system, we can say that row operations do not change the matrix, the two matrices are equivalent.