Question

How to determine whether matrices are in echelon form, reduced echelon form or not in echelon form ?

Answer 1

Identify row echelon and reduced row echelon forms of matrices

Properties of row echelon form:

1. The first non-zero element in each row is called the leading entry which has to be $1$.
2. Each leading entry is one column to the right of the leading entry of the previous row.
3. If there are any rows with all zero elements they are kept below the rows having a non-zero element.

Row echelon matrix $\left[\begin{array}{ccc}1& 1& 2\\ 0& 1& 3\\ 0& 0& 5\end{array}\right]$

Properties of the reduced row-echelon form:

1. Firstly, the matrix must satisfy all the properties of the Echelon form matrix.
2. The leading entry in each row is the only non-zero entry in that column.

Reduced echelon form $\left[\begin{array}{cccc}1& 3& 0& 0\\ 0& 0& 1& 2\\ 0& 0& 0& 0\end{array}\right]$

By these properties, we can identify whether a matrix is in Echelon form, Reduced Echelon form, or not.