Matrix Calculator

Do matrix operations with real or complex matrices & solve linear systems.

The free matrix calculator & linear system solver allows performing matrix algebra (addition, subtraction, multiplication, inverses, etc.) and calculating determinant, inverse, adjugate, rank, rref, and triangular forms of matrices of any size with real or complex entries.

Also solve systems of linear equations with real or complex augmented matrices.

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 conveniently set the number of rows or columns of a selected matrix by pressing the numbered buttons on the left of a row or above a column, respectively.

You can select and/or modify a matrix A, B, C, ..., H by first choosing them from the drop-down list on the right of the matrix calculator. These matrices are initially filled with 0's, except for the matrix A.

This complex matrix calculator allows you to use any numeric (constant) expression, e.g., 1/2+3sin(5π/4)i for a matrix element.

This matrix calculator remembers the dimensions and entries of all matrices that you enter and also remembers whether a matrix is augmented for solving systems of linear equations.

All the data are retained indefinitely. To clear the data and reset the matrix calculator type in reset in the matrix expression box at the bottom of the matrix entries and press Clear, or clear site data from your browser history.

Matrix Algebra

To calculate the determinant, inverse, reduced row echelon form, adjugate, rank, lower/upper triangular forms and transpose of a selected matrix (A is initially selected) press the relevant buttons at the top of the matrix calculator.

You can do similarly as above with other matrices A, B, C, ..., H by first selecting them from the drop-down list and setting its dimensions and entries.

Under the Quick Calculations drop-down-list you can calculate frequently used matrix expressions involving two or more matrices such as A + B, (A+B)(C+D), and many more.

If a matrix expression is not listed under the quick calculation menu, you can enter it in the expression box provided. Press the Calculate button to evaluate it.

This matrix expression 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.

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)

All 1 × 1 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 1 × 1 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 1×1 matrices. Assign numbers (or constant expressions) to the variables (i.e., 1×1 matrices) and press the Calculate button. The value of the function is given as a scalar.

Complete instruction is included in the app.