Mathematics-Online lexicon: Linear System of Equations in Three Variables

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	Mathematics-Online lexicon:
	Linear System of Equations in Three Variables

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overview

A linear sytem of equations in three variables

has the form

$\begin{displaymath} \begin{array}{rcrcrcl} a_{11}x_1 &+& a_{12}x_2 &+& a_{13}x_3... ... a_{31}x_1 &+& a_{32}x_2 &+& a_{33}x_3 &=& f_3 \,. \end{array}\end{displaymath}$

The set of all solutions of such a system can be geometrically interpreted as the intersection of the three planes given by the system's equations. The following situations may occur:

Exactly one solution: The three planes concur at one point only.
No solution: The three planes have no common points.
Infinitely many solutions: All three planes concur at a line or coincide with each other.

Such a linear system can be solved by elimination of variables or by Gaussian transformation with subsequent back substitution, for instance.

(Authors: Wipper/Abele)

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automatically generated 5/12/2006