resolver un sistema de ecuaciones de gauss jordan

public void GaussJordanElimination()
{
    //a[][] is the coefficient matrix
    //b[] is the constant vector
    //x[] is the solution vector
    int num_equations = a.GetLength(0);
    int num_unknowns = a.GetLength(1);

    //Create augmented matrix
    var matrix = new double[num_equations, num_unknowns + num_equations];
    for (int i = 0; i < num_equations; i++)
    {
        for (int j = 0; j < num_unknowns; j++)
        {
            matrix[i, j] = a[i, j];
        }
        matrix[i, num_unknowns + i] = 1;
    }

    //Reduce it to r.e.f.
    for (int i = 0; i < num_equations; i++)
    {
        for (int j = 0; j < num_equations; j++)
        {
            if (i != j)
            {
                var mult