Knowing how to find Reduced Row Echelon Form (RREF) of a matrix is of great help in solving systems of linear equations. For this reason, we put at your hands this RREF calculator with steps, which allows you to quickly and easily reduce a matrix to row echelon form.
To use this calculator you must follow these simple steps:
Below you will find a summary of the most important theoretical concepts related to how to do reduced row echelon form.
Table of Contents
The Reduced Row Echelon Form of a matrix A is another matrix H that satisfies the following properties:
Here is an example of the reduced row echelon form of a matrix:
Every matrix has a single row-reduced echelon form, regardless of how you perform operations on the rows.
The importance of matrices in reduced row echelon form comes from the following theorem:
Each matrix can be transformed into reduced row echelon form by a sequence of elementary row operations.
Reduced Row Echelon Form is useful because it provides a standard form for writing matrices and systems of linear equations that makes it easy to solve them. For example, if a matrix is in Reduced Row Echelon Form, you can easily find the solutions to the corresponding system of linear equations by reading the values of the variables from the matrix.
To carry out this process, it is necessary to carry out a succession of elementary row transformations, which are:
Here are some examples that will help you better understand what was explained above. These examples have been created using the RREF Calculator with steps.