Anzeige


Linear Algebra | Matrices | Determinants | Equation Systems | Vectors

Calculator for Systems of Linear Equations

A system of linear equations consists of equations of the form a11x1+a12x2+a13x3+...=b1, a21x1+a22x2+a23x3+...=b2, .... Such a system contains several unknowns. It is solvable for n unknowns and n linear independant equations. If two or more equations are linearly dependent, then there are several possible solutions and no solution can be determined here. The coefficients of the equations are written in the form of an n-dimensional matrix, the solutions as a one-dimensional matrix. The extended coefficient matrix used here separates the coefficient matrix from the solution matrix or solution column with a vertical line.


Size: | Decimal digits: |

(




  





)

Transformations:
* + *
Swap with
Determinants: =
x1= x2= x3= x4= x5=

The size indicates the size of the square matrix without the solution column. Together with this solution column, the matrix has one more column than rows. In a linear system of equations, whole rows with values ​​other than zero can be multiplied and one row can be added to another. The result of this transformation is entered in the row which is set first, the first multiplier should not be zero. For example, to double row 1, you can set 1 * row 1 + 1 * row 1, or 2 * row 1 + 0 * row 2. You can also swap two rows or columns.
The determinant D is that of the matrix without the solution column. For the determinants D1 to D5, the solution column is taken into calculation and instead the first column for D1, the second column for D2 and so on are omitted.
If the system of equations is solvable, then the solutions can be calculated here. In this case, a system with n unknowns also has n solutions.
The contents of the matrix without the solution column can be transferred to the data set and read out in its entirety. At Reading Data Set, data in text form can be transferred into a matrix. The solution column must still be filled in.


Last updated on 06/27/2025.



© Jumk.de Webprojects | Online Calculators | Imprint & Privacy | German: Lineare Algebra



Anzeige


Cite this page: Rechneronline (2025) - Calculator for Systems of Linear Equations.
Retrieved on 2026-08-18 from https://rechneronline.de/linear-algebra/equation-systems.php


Related articles and calculators:

Calculator for Determinants

Calculators for Linear Algebra

Calculator for Matrices

Draw and Calculate a Straight Line

Calculate Line through Two Points