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private static double Determinante(double[,] matrix) {
	int n = matrix.GetLength (0);
	for (int i = 0; i < n; i++)
	{
		if (matrix[i, i] == 0)
		{
			for (int zeile=i; zeile<n; zeile++) {
				if (matrix [i, zeile] != 0) { //zeile tauschen
					for (int k = 0; k < n; k++) {
						double tmp = matrix [k, i];
						matrix [k, i] = matrix [k, zeile];
						matrix [k, zeile] = tmp;
					}
				}
			}
		}
		if (matrix[i, i] == 0) continue;
		for (int j = i + 1; j < n; j++)
		{
			//0er erzeugen durch Addition
			double faktor = -matrix[j, i] / matrix[i, i];
			for (int k = 0; k < n; k++) {
				matrix [j, k] += faktor * matrix [i, k];
			}
		}
	}
	double result = 1;
	for (int i = 0; i < n; i++) {
		result *= matrix [i, i];
	}
	return result;
}