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Elimination of Variables in Linear Systems of Equations


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

A linear equation

$\displaystyle a_1x_1+a_2x_2+\dots=f
$

with $ a_1\neq 0$ can be tranformed into

$\displaystyle x_1=(f-a_2x_2-\cdots)/a_1\,.
$

By inserting such expressions into the remaining equations, linear systems can thus successively be reduced into systems in fewer variables.
(Authors: Höllig/Abele)

Example:


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  automatically generated 9/18/2007