Calculator for NxN equation systems

Gaussian elemination solver NxN

The calculator uses the Gaussian elemination to transform the matrix step-by-step in row echelon form. If the extended coefficient matrix brought to row echelon form by means of elementary transformations, the solution can be read directly.

( 1a12*a1n* 01a2n* 0001 | b1* b2* bn* )

Linear Equation System NxN

a11x1+a12x2++a1nxn=b1 a21x1+a22x2++a2nxn=b2 am1x1+am2x2++amnxn=bn

or in matrix notation

( a11a12a1n a21a22a2n am1am2amn ) ( x1 x2 xn ) = ( b1 b2 bn )

The schematic matrix form is used to show the transformations:

( A|b ) = ( a11a12a1n a21a22a2n am1am2amn | b1 b2 bn )

Dimension of the equation system N =

Enter the coefficients: a11, a12, ... und b1, ...

Solution with the Gauss algorithm

Step by step performing of the Gaussian elimination to get the row echelon form of the matrix.

The entered matrix is:

Calculation of the row echelon form (Gaussian elimination)

Calculation of the reduced row echelon form (Jordan-Algorithm)

The solution vector

The solution of the linear equation system is now given in the right column.

More Calculators

Here is a list of of further useful calculators and sites:

Index Linear Equations Linear Equation Systems Calculator 2x2 systems Calculator 3x3 systems Calculator NxN Cramer's rule Calculator NxN Gauss method Matrix Determinant