How to find matrix determinant by gauss method by column?

Question

Programming

Calculation of the matrix determinant by the Gaussian method with the choice of the main element by the column. For testing, find the determinant of a matrix of dimension 4.

Answer 1

void GetDeterminant(double **matrix, int size, double epsilon)
{
    //Предполагается, что матрица квадратная
    int pivot_index = -1;
    double pivot_value = 0;
    double determinant = 1;
    
    for(int i = 0; i < size; i++)
    {
        for(int j = i; j < size; j++)
        {
            if(abs(matrix[j][i]) > pivot_value)
            {
                pivot_index = j;
                pivot_value = abs(matrix[j][i]);
            }
        }
        
        //Если опорный элемент равен нулю (эпсилон для сброса погрешности)
        if(pivot_value < epsilon)
        {
            //Матрица вырождена
            return 0;
        }
        
        if(pivot_index != i)
        {
            //Обменяем строки местами
            SwapRows(matrix, pivot_index, i)
            determinant *= -1;
        }
        
        for(int j = i + 1; j < size; j++)
        {
            if(matrix[j][i] != 0)
            {
                multiplier = 1 / matrix[i][i] * matrix[j][i];
                
                for(int k = i; k < size; k++)
                {
                    matrix[j][k] -= matrix[i][k] * multiplier;
                }
            }
        }
        
        determinant *= matrix[i][i];
    }
    
    return determinant;
}

Haven't worked with sami for a hundred years, so syntax errors are guaranteed. Especially with types.
But I think the meaning is clear.

Answer 2

Using the Gauss method, you can bring the matrix to a triangular form, after which it turns out that its determinant is equal to the product of the elements of the main diagonal.