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Matrix Calculator | Complex Matrices & Linear Systems of Equations

About the Matrix Calculator

Multiply, add, and subtract matrices, or evaluate matrix expressions involving multiple complex matrices simultaneously using our free online matrix calculator. In addition, our matrix solver efficiently solves systems of linear equations.

This matrix and linear system solver by Calculators Math™ supports matrix dimensions up to 30×30 (and more if your device is fast enough).

Matrix Operations

Beyond elementary matrix arithmetic, the calculator performs advanced operations on square matrices, such as finding the determinant, inverse, or adjoint. For matrices of any dimension, you can perform other advanced operations like finding the rank, upper/lower triangular forms, and RREF (reduced row echelon form).

Matrix Expression Handling

Our matrix calculator is capable of evaluating intricate matrix expressions involving up to eight compatible matrices. This unique capability allows you to evaluate and simplify expressions 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.

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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.

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:

Advanced Matrix Operations

Determinant, Inverse, and Adjugate

Calculate these properties for square matrices:

Rank, Triangular Forms, RREF, and Transpose

Compute these properties for matrices of any dimension: