# Solution of nonhomogeneous system of linear equations using matrix inverse

The solution of a nonhomogeneous system of linear equations using matrix inverse

### This page exists due to the efforts of the following people:

#### Michele

Created: 2011-05-15 09:56:11, Last updated: 2020-12-11 13:34:39

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/1436/. Also, please do not modify any references to the original work (if any) contained in this content.

Calculator Inverse matrix calculator can be used to solve the system of linear equations.
This method can be illustrated with the following formulae:
Let us have linear system represented in matrix form as matrix equation
$AX=B$
If we multiply both parts by matrix inverse we will get
$A^{-1}(AX)=A^{-1}B$
$(A^{-1}A)X=A^{-1}B$
$EX=A^{-1}B$
$X=A^{-1}B$
This means that to find out column vector of variables we need to multiply matrix inverse by column vector of solutions.

This method can be used only if matrix A is nonsingular, thus has an inverse, and column B is not a zero vector (nonhomogeneous system).

Calculator below uses this method to solve linear systems. Default values are taken from the following equations:
${ \begin{cases}3x+2y-z=4; \\2x-y+5z=23;\\x+7y-z=5;\end{cases} }$
thus elements of B are entered as last elements of a row

#### Solution of nonhomogeneous system of linear equations using matrix inverse

Digits after the decimal point: 2
Column X

URL copied to clipboard

#### Similar calculators

PLANETCALC, Solution of nonhomogeneous system of linear equations using matrix inverse