RedCrab Math Tutorial

# Row Operations of Matrices

There are three types of elementary matrix row operations, corresponding to the operations that apply to equations to eliminate variables:
• 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.