By default is shows a 4 * 4 matrix equation filled by the same values I use in my C# sample projects.
Pressing the “Solve” button solves the matrix equation and prints out the result in the fields at the very bottom and the result of the elimination in the matrix.
For the detailed description of the elimination algorithm by Gauss see The elimination algorithm by Gauss
Matrix solver by Gauss
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Demo Project matrix equation solver in Java script