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**.

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 **matrix** **A** (initially selected).

You can do similarly as above with other **matrices** by first selecting them from the 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 **matrix** by pressing the buttons on the left or above the selected **matrix**, respectively. You can also **add rows** or **add columns**by pressing the relevant **+** button.

This **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** 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 **Calculate**.

The **matrix expression** 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 **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 **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 **Calculate**. 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)**

**A/B** is the same as **Ainv(B)**

Enter the **augmented matrix** and press **RREF** (**Reduced Row Echelon Form)**. If the **coefficient matrix** is a *square matrix* and the system has a unique solution, the right-hand-side column will be the solution to the given linear system of equations.

*The following, which is a more proper way of solving linear systems, will be available in the future*.

To solve a **system of linear equations** with **coefficient matrix**, say **A**, first select the **Linear System** check-box. Then enter the associated **column vector** (the right hand side of the equation) in the highlighted column adjacent to A to form the associated **augmented matrix** and press **Solve**.

The **reduced row echelon form** of the **augmented matrix** will be displayed on a separate window. If the **coefficient Matrix** is a *square matrix* and the system has a unique solution, the vector representing the unique solution will also be displayed.