Overview

# echelon form

#### More Like This

Show all results sharing this subject:

• Mathematics

GO

Show Summary Details

## Quick Reference

Suppose that a row of a matrix is called zero if all its entries are zero. Then a matrix is in echelon form if (i) all the zero rows come below the non-zero rows, and (ii) the first non-zero entry in each non-zero row is 1 and occurs in a column to the right of the leading 1 in the row above. For example, these two matrices are in echelon form:Any matrix can be transformed to a matrix in echelon form using elementary row operations, by a method known as Gaussian elimination. The solutions of a set of linear equations may be investigated by transforming the augmented matrix to echelon form. Further elementary row operations may be used to transform a matrix to reduced echelon form. A set of linear equations is said to be in echelon form if its augmented matrix is.

Subjects: Mathematics.

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.