# Matrix A

Column
Row

## Introduction to the Row Echelon form Calculator with Steps

REEF reduced row echelon form calculator is an online tool that can easily calculate the reduced row echelon form of a matrix of order up to 4. It uses row operations to form a reduced echelon form, giving an identity matrix. The matrix row echelon calculator helps to solve systems of linear equations.

In matrix algebra, the row reduced echelon form is important to solve systems of linear equations. Because it tells whether the system is solvable or not. So most of the time, you use this method, but in the manual calculation, if you make a minor mistake, it leads to the wrong solution. We introduce a rref matrix calculator that can solve the given system accurately and let you know clearly about how to do reduced row echelon form.

## How to use a RREF Calculator?

The row echelon form of a matrix is a method to solve a system of linear equations. It is done by making all entries of the matrix zeros using row operations. There are two rules for making a reduced echelon form by using the rref echelon form calculator.

1. The first leading element of the matrix and other diagonal entries should be 1.
2. All other entries of the matrix other than diagonal should be zero.

Example:

Consider a matrix of 3-by-3 order given by:

$$A \;=\; \begin{bmatrix} 1 & 3 & 1 \\ 3 & 4 & 0 \\ 4 & 5 & 2 \\ \end{bmatrix}$$

Now, we will reduce the given matrix into row reduced echelon form with this calculator.

Swap row 1 with row 3 then subtract:

$$\frac{3}{4} \;×\; (row \;1)$$

from row 2.

$$=\; \begin{bmatrix} 4 & 5 & 2 \\ 3 & 4 & 0 \\ 2 & 3 & 1 \\ \end{bmatrix} \;=\; \begin{bmatrix} 4 & 5 & 2 \\ 0 & \frac{1}{4} & - \frac{3}{2} \\ 2 & 3 & 1 \\ \end{bmatrix}$$

Now subtract:

$$\frac{1}{2} \;×\; (row \;1)$$

from row 3.

$$=\; \begin{bmatrix} 4 & 5 & 2 \\ 0 & \frac{1}{4} & - \frac{3}{2} \\ 0 & \frac{1}{2} & 0 \\ \end{bmatrix}$$

Swap row 2 with row 3 and subtract:

$$\frac{1}{2} \;×\; (row \;2)$$

from row 3:

$$=\; \begin{bmatrix} 4 & 5 & 2 \\ 0 & \frac{1}{2} & 0 \\ 0 & \frac{1}{4} & - \frac{3}{2} \\ \end{bmatrix} \;=\; \begin{bmatrix} 4 & 5 & 2 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & - \frac{3}{2} \\ \end{bmatrix}$$

Multiply row 3 by

$$- \frac{3}{2}$$

And subtract 2×(row 3) from row 1:

$$=\; \begin{bmatrix} 4 & 5 & 2 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \;=\; \begin{bmatrix} 4 & 5 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}$$

Multiply row 2 by 2 and subtract 5×(row 2) from row 1:

$$=\; \begin{bmatrix} 4 & 5 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \;=\; \begin{bmatrix} 4 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}$$

Divide row 1 by 4:

$$=\; \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}$$

This is the required reduced echelon form of the matrix A. The rref matrix calculator uses this method to solve the given matrix.

## Why use the REEF Reduced Row Echelon Form Calculator?

The echelon form and the reduced echelon form are the basic concepts for solving systems of equations in the form of matrices. The reason is that these methods help us to determine the solution faster than the other methods. The rref echelon form calculator uses row operations to make a reduced echelon form.

As you have seen by the above example, the reduced echelon form method is easy but lengthy. A minor mistake can lead to the wrong solution. So, it would be best to use this row reduced echelon form calculator because it is reliable to find reduced row echelon form.

## How to Transform a Matrix to Reduced Row Echelon Form?

The rref calculator is easy to use, so you can solve any problem by following the given steps:

1. Enter the number of rows and columns of the matrix in the respective boxes.
2. Now give the values of all matrix entries.
3. Click on the calculate button.

You will get the results within a few seconds of clicking the calculate button.

## Benefits of using Reduced Row Echelon Form RREF Calculator

The rref echelon form calculator has many beneficial uses for students and mathematicians. Some of these benefits are:

1. The REEF reduced row echelon form calculator can save you time from manual calculations.
2. The matrix row echelon calculator gives a step-by-step solution to make the solution understandable for you.
3. RREF calculator with steps is a free tool; you don’t need to pay any fee.
4. You can practice with different unexpected examples.
5. Row echelon form calculator has an amazing feature of a random button that selects random values of the matrix. ### Hamza Haroon

Last Updated April 05, 2022

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