**Matrix Row Operations**

** **

**a.** Any two rows of the matrix may be interchanged.

**b. **The numbers in any row may be multiplied by any nonzero real

**c. **Any row may be transformed by adding to the numbers of the row the product of a real number and the corresponding numbers of another row.

Examples of these row operations follow.

Row operation 1:

becomes . Interchange row 1 and row 3.

Row operation 2:

. Multiply the number in row 1 by 3.

Row operation 3:

. Multiply the number in row 3 by -2; add then to the corresponding numbers in row 1.

The third row operation corresponds to the way we eliminated a variable from a pair of equations in the previous sections.