Overview
The Gaussian eliminatoin method is a method for soliving systems of linear equations such asScaling
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('/code/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);