Mathematics-Online lexicon: Elimination of Variables in Linear Systems of Equations

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	Mathematics-Online lexicon:
	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

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:

automatically generated 9/18/2007