Mathematics-Online lexicon: Solving a Linear System Given in Triangular Form

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Solving a Linear System Given in Triangular Form

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 system of equations given in triangular form

$\begin{displaymath} \begin{array}{rcrcrcccccl} a_{11}x_1 &+& a_{12}x_2 &+& a_{13... ...ots \\ & & & & & & & & a_{nn}x_n &=& f_n \\ \par \end{array}\end{displaymath}$

can be uniquely solved, if $a_{ii}\neq 0$ für $i=1,2,3,\dots,n$ .

The solution can be determined by back substitution. So from the last line it follows that $x_n=f_n/a_{nn}$ . Inserting that into the second but last line allows to calculate $x_{n-1}$ . Successively moving upwards, one finally obtains from the first line.

(Authors: Wipper/Abele)

[Links]

automatically generated 5/12/2006