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# Solution of nonhomogeneous system of linear equations using matrix inverse

Solution of nonhomogeneous system of linear equations using matrix inverse

Calculator Inverse matrix calculator can be used to solve 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 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

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