Row Operations of Matrices

There are three types of elementary matrix row operations, corresponding to the operations that apply to equations to eliminate variable

• Adding a multiple of one row to another row

• Multiplying of a row by a non-zero scalar

• Interchange of two rows

These operations can be done manually, but also by matrices multiplication with a given matrix and some modified identity matrix. See the three examples below.

Adding a multiple of one row to another

• Placing \(k\) in the second column of row 3 of the identity matrix

• then multiplying the matrices.

• This has k-times the values of corresponding elements of row 2 added to those of row 3 of the matrix.

The value of the determinant in the result is identical to the value of the source matrix \(A\)

Multiplying a row by a non-zero scalar:

The value of the determinant in the result is \(k\) times the value of the source matrix \(A\)

Interchanging two rows

The value of the determinant in the result is identical to the value of the source matrix \(A\)