# Matrix A

Column
Row

## Introduction to Matrix Determinant Calculator

A matrix determinant calculator is an online tool that can calculate the determinant of the matrix to find the scalar value. It uses the expansion method to find a single value of a square matrix. It also uses the reduction method and finds the scalar value.

We usually apply addition, subtraction, and multiplications in matrix algebra on the matrices. The determinant is necessary to calculate the unique solution of the system of nonlinear equations. That’s why we introduce a tool that can easily calculate determinants using both methods of expansion and reduction.

## Formula used by Matrix Determinant Formula Calculator

This calculator uses two formulas to calculate the determinant of a matrix of order 2, 3 or 4. These are:

1. The determinant plays an important role to solve the system of linear equations and to find the inverse of matrix, then the determinant of 2×2 matrix is:

$$A \;=\; \begin{bmatrix} a & b \\ c & d \end{bmatrix}$$ $$|A| \;=\; \begin{vmatrix} a & b \\ c & d \end{vmatrix} \;=\; (a \times c) \;-\; (b \times d)$$
2. If A is the determinant of the matrix A than the determinant for 3×3 matrix.

$$\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix}$$ $$\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{vmatrix}$$ $$|A| \;=\; a \begin{vmatrix} e & f \\ h & i \end{vmatrix} \;-\; b \begin{vmatrix} d & f \\ g & i \end{vmatrix} \;-\; c \begin{vmatrix} d & e \\ g & h \end{vmatrix}$$
3. The determinant for 4-by-by matrix can be solved by reducing its row of a column or reducing the matrix to triangular form.

## How to use the Matrix 4x4 Determinant Calculator?

This tool can be used by following some steps which are:

1. In the first step, you need to enter the number of rows and columns for the matrix.
2. Now put the values of all elements of the matrix.
3. Or you can use the random button to select the random matrix.
4. Now click on the calculate button.

You will get the solution within a few seconds of clicking on the calculate button. It will give you a step-by-step solution so that you can understand it.

## Why use Determinant Matrix Calculator?

In mathematics, the matrix is important to solve the system of linear equations. S0me operations are applied to solve a system of linear equations. So, the determinant is an important operation. You can use the determinant solver to solve many problems.

While you are computing the determinant of the higher-order matrix, you cannot solve it with expansion only. You have to reduce the order of the matrix by using a reduced echelon form, which is a tricky procedure. So there is a need for a tool that can easily reduce the demand for the matrix. That’s why you need to use a determinant finder that is helpful for you to find the determinant of the 2x2 matrix.

## Benefits of using Determinant Calculator with steps

The determinant of a matrix is a scalar value calculated from a square matrix. It is helpful to find a unique solution to the system of equations. The matrix calculator is useful for finding this solution because it can handle higher-order matrices easily. Some other benefits of this tool are given as follows:

1. It provides a step-by-step explanation of the matrix determinant so that you can understand every single step to find the determinant of the 3x3 matrix.
2. It saves your time by computing determinants quickly and efficiently.
3. Matrix Determinant Formula Calculator is easy for you because of the simple and unique interface.
4. It allows you to choose random values for the matrix so that you can practice with random examples and find the determinant of the 4x4 matrix.
5. Matrix determinant calculator gives a step-by-step solution that helps understand every step.

### Hamza Haroon

Last Updated April 05, 2022

I am a Content writer & Content Creator. I like writing content on different topics. Besides writing, I am an SEO-ASO-SMM specialist and Football Lover.