21-06-2024 07:22

Status :

Tags : linear algebra Matrix

Row echelon form

Echelon form of a matrix

A matrix A is said to be in echelon form if the following hold: i. Every row of a matrix A which has all its entries zero occurs below every row which has a non-zero entry. ii. The number of zeros preceding the first non-zero element in a row is less than the number of such zeros in the succeeding rows. Example A = $\left[\begin{array}{ccc}1& 2& 0\\ 0& 3& 4\\ 0& 0& 5\\ 0& 0& 0\end{array}\right]$

Note:

• A given matrix A is in echelon form if one or more elements in each of the first r rows are non-zero, and these first r rows form an upper triangular matrix. The elements in the remaining rows are zero.
• To reduce the matrix to echelon form, only row transformations are to be applied.

References