Can this calculator solve complex systems of equations?

Yes, it uses Gauss-Jordan elimination to solve augmented matrices with both real and imaginary entries.

Does it support 10x10 matrices?

Yes, the calculator supports matrices up to a maximum dimension of 10x10.

Complex Matrix Calculator | Augmented Matrix & Linear System Solver

Evaluate matrix expressions containing up to 8 complex matrices. Solve systems of linear equations using Gauss-Jordan elimination.

Perform multiplication, addition, subtraction, or evaluate matrix expressions using our free online complex matrix calculator. It supports matrices up to 10×10 with real or complex entries. Our Calculators Math™ matrix algebra calculator easily solves systems of linear equations using Gauss-Jordan elimination on complex augmented matrices. It also handles advanced tasks like calculating the determinant, inverse, and rank of complex matrices, as well as converting to reduced row echelon form (RREF).

Quick Start

Select a matrix (A–H) from the drop-down list to fill or edit its entries (Matrix A is selected by default).
If desired, add rows or columns to the selected matrix by pressing the ＋ buttons.
You can also resize a selected matrix by entering the number of rows or columns in the text boxes provided, or by clicking the numbered buttons located to the left of a row or above a column.

Note: The matrix calculator retains the dimensions and entries of all matrices, as well as whether a matrix is augmented for solving systems of linear equations.

About the Matrix Calculator

Our advanced matrix calculator is designed to efficiently perform operations on matrices up to 10×10. It offers full support for complex matrices—those containing real, imaginary, or complex entries.

Matrix Operations

Beyond elementary matrix operations, the calculator performs advanced operations on square matrices, such as finding the determinant or the inverse. For matrices of any dimension, you can perform other advanced operations like finding the rank and RREF.

Matrix Expression Handling

What sets our matrix calculator apart is its ability to evaluate intricate matrix expressions involving up to eight compatible matrices, such as: A+BCD-inv(E)

Solve Systems of Linear Equations

Our linear system solver uses Gauss-Jordan elimination to solve systems of linear equations by performing row operations on augmented matrices. As a complex augmented matrix calculator, it fully supports systems involving a complex coefficient matrix and a complex column vector representing the right-hand side of the system.

Linear System

Results

Instructions for Using Our Matrix Calculator

Elementary & Advanced Matrix Algebra

Suitable for all levels, this intuitive yet powerful complex matrix calculator evaluates expressions involving complex matrices, performing operations ranging from basic arithmetic to advanced linear algebra.

Basic Matrix Operations

Perform fundamental matrix algebra with our online calculator:

Addition — Add matrices
Subtraction — Subtract matrices
Multiplication — Matrix multiplication calculator
Division—Matrix division calculator (While not a standard operation, A/B is computed as AB^-1.)

Advanced Matrix Operations

Determinant, Inverse, and Adjugate

Calculate these properties for square matrices:

Determinant — Matrix determinant calculator
Inverse — Matrix inverse calculator
Adjugate — Matrix adjugate calculator

Rank, Triangular Forms, RREF, and Transpose

Compute these properties for matrices of any dimension:

Rank — Matrix rank calculator
RREF — Convert to Reduced Row Echelon Form
Triangular Forms — Find lower and upper triangular forms
Transpose — Calculate the transpose