**Note**: One interface for all **matrices** including **augmented matrices** representing **systems of linear equations**! The **matrix calculator** remembers the **dimensions** and entries of all matrices and whether a matrix is **augmented** or not. Just select a named matrix from the drop-down list and set its dimensions and fill the matrix with real or complex numbers.
You can increase the dimensions of a *selected* **matrix** by adding **rows** or **columns** to it by pressing the **+** (*insert row* or *insert column*) buttons provided. You can also set the dimensions of a selected matrix by entering the number of its **rows** or **columns** in the text boxes provided or, conveniently, by pressing the numbered buttons on the left of a row or above a column, respectively.

Try Graphing Calculator

This elegant **matrix calculator** deploys one single interface which can be used to enter multiple **matrices** including **augmented matrices** representing **systems of linear equations**!

In addition to **adding**, **multiplying** matrices, you can use this **matrix calculator** to calculate **determinant**, **inverse** and **adjugate** of *square matrices* and find the **rank** of any matrix. Also transform matrices to **lower triangular**, **upper triangular** and **reduced row echelon form**s.

You can also solve **systems of linear equation**s. The **linear equation solver** can solve any m × n linear equations.

Matrices can have **real**, **imaginary** and, in general, **complex numbers** as their elements. This **complex matrix calculator** can perform **matrix algebra**, all the previously mentioned **matrix operation**s and **solving linear system**s with **complex matrices** too.

Furthermore, this **matrix calculator** evaluates **matrix expressions** containing up to eight **real** or **complex matrices** and shows work.

## How to Use The Online Matrix Calculator

The matrix calculator allows you to do **matrix algebra** (**matrix addition**, **matrix multiplication**, **matrix inverses**, etc.) with *Real* or **Complex Matrices** and **solve systems of linear equations simultaneously**.

### Matrix Algebra

Press the relevant buttons at the top of the **Matrix Calculator** to calculate the **determinant**, **inverse**, **reduced row echelon form**, **adjugate**, **lower/upper triangular forms** and **transpose** of the real or complex matrix **A** (initially selected).

You can do similarly as above with other matrices by first selecting them from the drop-down list on right side of the Matrix Calculator.

The matrices (A, B, C, ..., H ) are initially filled with 0's.

You can set the numbers of **rows** and **columns** of a selected matrix by pressing the buttons on the left or above the selected matrix, respectively. You can also add rows or columns by pressing the relevant **+** button.

This Online Matrix Calculator allows you to use any numeric (constant) expression, e.g., 1/2+3i2sin(3pi/2) for a matrix element.

Under the Quick Calculations menu you can calculate frequently used **matrix expressions** involving two or more matrices.

If a matrix expression is not listed under the quick calculation menu, you can enter it in the expression box provided and press the **Calculate** button.

This Matrix Calculator allows you to use any matrix expression which can be in the most general form, such as (2+sin(π/3))A + inv(A+B/det(A))(B/2 + BC^4)/D^(3+2^5)

If the matrix expression is a valid expression and contains no operations of incompatible matrices, the result will be displayed. Otherwise an error message is displayed.

All 1x1 matrices are treated as scalars by this Online Matrix Calculator. They can be multiplied by any matrix (on either side) regardless of its dimension. Also if, for example, A = [1/2], then sin(A) is treated as sin(1/2). Conversely, whenever appropriate, scalars are treated as 1x1 matrices. For example, inv(2) is treated as inv([2]) which will be given as 0.5.

You can also use this Online Matrix Calculator as a *multi-variable function evaluator*. Type in a function expression containing up to 8 variables (use A, B, C, ... as variables, instead of x,y,z, ...). Set all matrices involved as 1x1 matrices. Assign numbers (or constant expressions) to the variables (i.e., 1x1 matrices) and press the **Calculate** button. The value of the function is given as a scalar.

You can use the following in your expressions:
**inv(), adj(), trans(), rref(), ut(), lt(), det()**

1/A is the same as inv(A) and A/B is the same as A*inv(B)

### Solving Linear Systems

The **system of linear equations solver** allows two different ways to solve **simultaneous system of linear equations**.

With the first method, which is a neat way to solve a single linear system, select the **Linear System** checkbox provided. Set the dimensions of the **coefficient matrix** and fill the **augmented matrix** with real or complex numbers (or expressions of them) noting the last column highlights the rhs (right hand side) of the system. Now press the **Solve** button.
If the system is **consistent** and has a unique solution, the vector representing the unique solution will be displayed together with the RREF (**reduced row echelon form**) of the **augmented matrix**. If there are more than one solutions, the general solution is given. If the system is **inconsistent** a message stating so and the RREF will be displayed.

With the second method you can solve more than one linear system at once, all having the same *square matrix* m × m as their **coefficient matrix**. Do **not** select **Linear System** but set the number of columns more than the number of rows. Fill each column after the m^{th} column with the right hand side of the corresponding system (with the same *coefficient matrix*) and press the **RREF** button.
If you see the entries of the m × m matrix on the left of the reduced row echelon form, then each system has a unique solution with the corresponding solution vector appearing on the right hand side.