Row Operation

A row operation is a procedure that can be performed on the rows of a matrix. There are three basic row operations.

• Switching rows
• Multiplying a row by a nonzero constant
• Adding rows

When a matrix represents a system of equations, row operations can be used to solve the system by the Elimination Method. The following examples show the results of the operations.

Switching Rows

The rows of a matrix can be switched to obtain a new matrix. [ ccc 2 & -1 & 3 4 & 6 & -2 3 & 5 & 2 ] [and thirdrows]Switch first [ ccc 3 & 5 & 2 4 & 6 & -2 2 & -1 & 3 ]

Multiplying a Row by a Constant

Multiplying a row by a nonzero constant means multiplying every element in the row by the same nonzero number. [ ccc 2 & 3 4 & -2 3 & 2 ] [ second rowby -2]Multiply the & [ ccc 2 & 3 -2( 4) & -2( -2) 3 & 2 ] [2em] = &[ ccc 2 & 3 -8 & 4 3 & 2 ]

Adding Rows

One row can be added to another row by adding corresponding elements. [ ccc 2 & 1 3 & 5 ] [ rowto thefirst row]Add the second & [ ccc 2 + 3 & 1 + 5 3 & 5 ] [2em] = & [ ccc 5 & 6 3 & 5 ]