Matlab

# How to Convert a Matrix into Reduced Row Echelon Form in MATLAB?

MATLAB, or Matrix Laboratory, is a programming language and environment designed specifically for technical computing that allows users to perform a wide variety of tasks, including matrix operations, data visualization, and simulation.

One of the most important matrix operations that MATLAB can perform is the reduced row echelon form of a matrix. The row reduced of a matrix is a special form of the matrix that can be used for a variety of purposes, such as determining the rank of the matrix and solving a system of linear equations.

This blog is going to address the query of how to convert a matrix into a reduced row echelon form in MATLAB.

## What is a Matrix Reduced Row Echelon Form?

Before defining the reduced row echelon form of a matrix, we should know about the echelon form of a matrix.

If A is a matrix, it is in the echelon form if it satisfies the given conditions:

• All zero rows of matrix A must be at the bottom.
• The nonzero row of matrix A must have its first nonzero element on the right of the element present in the row above it.

Let’s define the reduced echelon form of the matrix:

A matrix A is called in the reduced echelon form if it satisfies the given conditions:

• A must be in echelon form.
• In each nonzero row of A, the first nonzero element (called the leading one) must be 1.
• Each column of A containing a leading one must have zero entries except for that leading one.

## How to Convert a Matrix into Reduced Row Echelon Form in MATLAB?

We can easily perform the reduced row echelon operation on a matrix in MATLAB using the rref() built-in function. This function accepts a matrix as an argument and returns its reduced row echelon form.

## Syntax

The rref() function’s syntax is given below:

B = rref(A)

Here,

The function B = rref(A) yields to calculate the reduced row echelon form of the given symbolic matrix A using the Gauss-Jordan method.

## Examples

To understand how to convert a matrix in the reduced row echelon form, consider some examples.

### Example 1: How to Convert a Real Matrix into Reduced Row Echelon Form?

This example converts a real-valued matrix A into a reduced row echelon form using the rref() function in MATLAB.

A = magic(7);

B = rref(A)

### Example 2: How to Convert a Complex Matrix into Reduced Row Echelon Form?

In this example, we convert a complex matrix A into a reduced row echelon form using the rref() function in MATLAB.

A = [1 -7i 9 5-7i; -i 0 1 3+i; 0 17 9-2i 11; 0 0 0 i];

B = rref(A)

## Conclusion

MATLAB is a beneficial high-performance programming tool that has a huge library of built-in functions to perform complicated matrix operations. One such operation is converting a matrix into reduced row echelon form. The rref() function in MATLAB can be used to easily perform the reduced row echelon operation on a matrix. This guide has covered the basics of performing this operation, so you can now use the rref() function on any matrix to quickly convert it into its row-reduced echelon form.