Question

While using rank method, what are the conditions for echelon form?

Answer 1

A matrix is in echelon form when:
1) Each row containing a non-zero number has the number “1” appearing in the rowʼs first non-zero column. (Such an entry will be referred to as a “leading one”)
2) The column numbers of the columns containing the first non-zero entries in each of the rows strictly increases from the first row to the last row. (Each leading one is to the right of any leading one above it.)
3) Any row which contains all zeros is below the rows which contain a non-zero entry.
For Example,
Echelon Form
$\left[\begin{array}{ccccc}1& 2& 3& 4& 5\\ 0& 1& 7& 3& 8\\ 0& 0& 1& 4& 6\\ 0& 0& 0& 1& 3\\ 0& 0& 0& 0& 1\end{array}\right]$