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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 of a matrix 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