Linear and multilinear algebra; matrix theory Proposition

Augmentation principle for reduced row echelon form

Builds on Reduced row echelon form Augmented matrix

Statement

Let $A$ be a matrix. Say that a matrix $B$ is an augmentation of $A$ when $B$ is formed from $A$ by adjoining further columns to the right of $A$ , so that the first columns of $B$ are the columns of $A$ .

If $B$ is an augmentation of $A$ , then the reduced row echelon form of $B$ is an augmentation of the reduced row echelon form of $A$ .

In other words, the leftmost columns of the reduced row echelon form of $B$ make up the reduced row echelon form of $A$ .

Remarks

This is why one may row reduce an augmented matrix and read the reduced form of the coefficient matrix from its left part. Row operations act on each column separately, so the added columns do not change the operations chosen for the first columns.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Augmented matrix concept
Reduced row echelon form concept
Augmentation principle for reduced row echelon form statement

Tag	`BE3NZP35HY`
URI	`m2://BE3NZP35HY`
Kind	statement, proposition
Writing	W0 stub
MSC	15A06
Status	This copy of the site has no build data. Run `m2 status BE3NZP35HY`.
About	Reduced row echelon form
Uses	Reduced row echelon form, Augmented matrix
Changed	4 November 2026

Augmentation principle for reduced row echelon form

Statement

Remarks

Reading path

Further reading

What this page needs for W1

What links here