Echelon Form of Matrix
An m×n matrix A is said to be an echelon matrix or in echelon form if it has the following structure:
(i) The first element (if any) in each row is a non-zero element.
(ii) Below this non-zero element all other elements in that column are zero.
For example,
are echelon matrices, whereas the matrices,
are not echelon matrices.
The method of transforming a given matrix into a row equivalent echelon matrix by elementary row operations is also referred to as reduction into echelon form.
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