Matrix Calculator

Compute matrix operations, including addition, subtraction, multiplication, and inversion, with detailed step-by-step solutions!

Matrix Calculator

Embed Matrix Calculator Widget

About Matrix Calculator

Welcome to our Matrix Calculator, a powerful tool designed to perform matrix addition, subtraction, multiplication, and inversion with detailed step-by-step solutions. This calculator is ideal for students, teachers, and anyone working with linear algebra and matrix operations.

Features of the Matrix Calculator

Step-by-Step Solutions: Understand each step involved in matrix computations.
User-Friendly Interface: Input matrices easily and get instant results.
Accurate Computations: Utilizes numerical computation for precise results.

Understanding Matrix Operations

Matrices are a fundamental tool in linear algebra, representing linear transformations and systems of linear equations.

Addition and Subtraction

Two matrices of the same dimensions can be added or subtracted by adding or subtracting corresponding elements.

Multiplication

The product of two matrices is computed by taking the dot product of rows and columns. The number of columns in the first matrix must equal the number of rows in the second matrix.

Inversion

The inverse of a square matrix \( A \) is a matrix \( A^{-1} \) such that \( A A^{-1} = I \), where \( I \) is the identity matrix.

For a 2x2 matrix, the determinant is calculated as:

\[ \text{det}(A) = a \times d - b \times c \] \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \).

The inverse of matrix \( A \) is then calculated using the formula:

\[ A^{-1} = \frac{1}{\text{det}(A)} \times \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \]

How to Use the Matrix Calculator

Select the operation you wish to perform.
Enter Matrix A and, if required, Matrix B. Use new lines to separate rows and spaces or commas to separate elements.
Click on "Compute" to process your inputs.
View the result along with step-by-step solutions.

Uses of Matrix Operations

Engineering: Analyzing systems, transforming coordinates, and modeling electrical circuits.
Computer Graphics: Performing transformations such as scaling, rotating, and translating objects.
Economics: Modeling economic systems and solving systems of linear equations.
Physics: Representing and solving linear transformations in various physical systems.