Gaussian Elimination

Learn the systematic approach to solving linear systems called Gaussian elimination.

Elimination

Elimination is a systematic process used for converting a matrix to one of its echelon forms. Depending on the form of this echelon matrix, the algorithm has a different variant. We’ll go through each variant one by one. We’ll use the following linear system as an example to explain the two variants of the elimination algorithm:

2x3y+7z=104x+8y4z=44x+9y3z=82x+5yz=6\begin{array}{rcr} -2x-3y+7z&=&10 \\ 4x+8y-4z&=&4 \\ 4x+9y-3z&=&8 \\ 2x+5y-z&=&6 \end{array} ...

(23710484449382516)\left(\begin{array}{rrr|r} -2 & -3 & 7 & 10\\ 4 & 8 & -4 & 4\\ 4 & 9 & -3 & 8\\ 2 & 5 & -1 & 6 \end{array}\right) ...