Linear and multilinear algebra; matrix theory Definition

Reduced row echelon form

Definition

Let $F$ be a field and let $A$ be a matrix over $F$ . The matrix $A$ is in reduced row echelon form when these three conditions hold:

$A$ is in row echelon form.
The leading entry of each nonzero row is $1$ .
In each column that has a leading entry, all the other entries are $0$ .

Remarks

The matrix $\begin{pmatrix} 1 & 2 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix}$ is in reduced row echelon form. Each matrix is row equivalent to exactly one matrix in reduced row echelon form. Gauss–Jordan elimination computes this matrix. The number of nonzero rows of the reduced row echelon form of $A$ is the rank of $A$ .

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Matrix definition
Row echelon form definition
Reduced row echelon form definition

Tag	`0NNR68BFRY`
URI	`m2://0NNR68BFRY`
Kind	definition
Writing	W0 stub
MSC	15A06
Defines	Reduced row echelon form
Uses	Row echelon form

Reduced row echelon form

Definition

Remarks

Reading path

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