Echelon Form Of Matrix

Echelon Form of Matrix:

An m \times \!\, n matrix A is said to be in reduced row echelon form if it satiesfy the following properties:

1. All zero rows, if there are any appear at the bottom of the matrix.

2. The first entry from the left of a non-zero row is 1. This entry is called a leading one of its row.

3. For each non zero row, the leading one appear to the right and below any leading one in precedding rows.

4. If a column contain a leading one then all other entry in that column are zero.

A matrix is reduced row echelon from appears as a staircase pattern of leading 1s descedending from the upper left corner of the matrix. An m \times \!\,n matrix satiesfies all above the properties.


Example-1: The following are matrices in reduced row echelon form:


Example-2: Let


Interchange row 1 and row 3;


Multiplying the 3rd of A by 1/3 we get;