Matrix Calculator with Step-by-Step Solutions

A set of detailed matrix calculation tools that allows you to do the following operations:

Addition, subtraction, division and product.
Rank of a matrix
Power of a matrix
Determinant calculation
Cofactors
Solving linear systems
Vectors and eigenvalues
Generation of random matrices

Matrix A:

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Matrices

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Complete Matrix Operations Suite

Choose from our comprehensive collection of matrix calculators, each providing detailed step-by-step solutions and mathematical explanations.

Basic Matrix Operations

Arithmetic Add, subtract, multiply or divide matrices with detailed step-by-step calculations Matrix Transpose Calculate the transpose of any matrix by interchanging rows and columns

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Advanced Calculations

Determinant Calculator Calculate determinants using cofactor expansion, row reduction, and other efficient methods Matrix Inverse Find the inverse of square matrices using Gauss-Jordan elimination with detailed steps Matrix Rank Determine the rank of matrices using row reduction and echelon form techniques Matrix Power Calculate matrix powers and exponentiation using efficient algorithms Cofactor Matrix Compute cofactor and adjugate matrices with step-by-step minor calculations

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Matrix Factorization

LU Factorization Decompose matrices into lower and upper triangular factors using various pivoting strategies QR Decomposition Factor matrices into orthogonal Q and upper triangular R components using Gram-Schmidt Cholesky Decomposition Decompose positive definite matrices efficiently for numerical computations Gram-Schmidt Process Orthogonalize vectors and create orthonormal bases with detailed calculations

Linear Algebra & Systems

Eigenvalues & Eigenvectors Find eigenvalues and eigenvectors using characteristic polynomial and various numerical methods RREF Calculator Reduce matrices to row echelon form and reduced row echelon form with step-by-step operations Gaussian Elimination Solve linear systems using forward elimination and back substitution methods Random Matrix Generator Generate random matrices with customizable dimensions and value ranges for testing

Why Choose Our Matrix Calculator?

Discover the features and applications that make our calculator the preferred choice for linear algebra computations.

Educational Excellence

Our matrix calculator is designed with education in mind, providing detailed step-by-step solutions that help students understand the underlying mathematical concepts.

Complete solution steps for every calculation
Mathematical explanations and formulas
Visual representation of matrix operations
Error checking and validation

Powerful Features

Access a comprehensive suite of matrix operations with advanced algorithms and numerical stability considerations.

Support for matrices of any reasonable size
Decimal, fraction, and complex number input
Multiple solution methods when applicable
High precision numerical computations

Real-World Applications

Matrix calculations are fundamental to numerous fields and have countless practical applications in modern science and technology.

Engineering: Structural analysis, control systems, signal processing
Computer Science: Machine learning, computer graphics, data analysis
Physics: Quantum mechanics, electromagnetic field calculations
Economics: Input-output models, optimization problems

How to Use

Getting started with our matrix calculator is simple and straightforward. Follow these easy steps to solve your linear algebra problems.

Select Operation: Choose the matrix operation you need from our comprehensive list
Input Matrix: Enter your matrix values using our intuitive interface
Calculate: Click the calculate button to get instant results
Review Steps: Study the detailed solution process and verify your understanding