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Gaussian Elimination

Explore Gaussian elimination and Gauss-Jordan elimination to convert matrices into row echelon and reduced row echelon forms. This lesson helps you solve linear systems effectively and understand matrix transformations with practical Python coding demonstrations.

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) ...