Elementary Operations

Overview


The Gaussian eliminatoin method is a method for soliving systems of linear equations such as

Scaling


Scale multiplies one row by a scalar, a.
\begin{bmatrix} 1 & 0 & 0 \\ 0 & a & 0\\ 0 & 0 & 1 \\ \end{bmatrix}

Addition


Addition adds a times one row to another column
\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0\\ a & 0 & 1 \\ \end{bmatrix}

Interchange


Interchange switches on row for another.
\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0\\ 0 & 0 & 1 \\ \end{bmatrix}

Example





let la = await import('/lib/linear-algebra/v1.0.0/linear-algebra.mjs');

let matrix = [[1,2,3],[4,5,6],[7,8,9]];

let a=10;
let interchange = [[0,1,0],[1,0,0],[0,0,1]];
let scale = [[1,0,0],[0,a,0],[0,0,1]];
let add = [[1,0,0],[0,1,0],[a,0,1]]

let result1 = la.multiply(interchange, matrix);
let result2 = la.multiply(scale, matrix);
let result3 = la.multiply(add, matrix);
Try it!


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