Task: Reduced row echelon form
C#: using System;

namespace rref
{
    class Program
    {
        static void Main(string[] args)
        {
            int[,] matrix = new int[3, 4]{
                {  1, 2, -1,  -4 },
                {  2, 3, -1, -11 },
                { -2, 0, -3,  22 }
            };
            matrix = rref(matrix);   
        }

        private static int[,] rref(int[,] matrix)
        {            
            int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
            for (int r = 0; r < rowCount; r++)
            {
                if (columnCount <= lead) break;
                int i = r;
                while (matrix[i, lead] == 0)
                {
                    i++;
                    if (i == rowCount)
                    {
                        i = r;
                        lead++;
                        if (columnCount == lead)
                        {
                        lead--;
                        break;
                        }
                    }
                }
                for (int j = 0; j < columnCount; j++)
                {
                    int temp = matrix[r, j];
                    matrix[r, j] = matrix[i, j];
                    matrix[i, j] = temp;
                }
                int div = matrix[r, lead];
                if(div != 0)
                    for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;                
                for (int j = 0; j < rowCount; j++)
                {
                    if (j != r)
                    {
                        int sub = matrix[j, lead];
                        for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
                    }
                }
                lead++;
            }
            return matrix;
        }
    }
}

VB: Private Function ToReducedRowEchelonForm(M As Variant) As Variant
    Dim lead As Integer: lead = 0
    Dim rowCount As Integer: rowCount = UBound(M)
    Dim columnCount As Integer: columnCount = UBound(M(0))
    Dim i As Integer
    For r = 0 To rowCount
        If lead >= columnCount Then
            Exit For
        End If
        i = r
        Do While M(i)(lead) = 0
            i = i + 1
            If i = rowCount Then
                i = r
                lead = lead + 1
                If lead = columnCount Then
                    Exit For
                End If
            End If
        Loop
        Dim tmp As Variant
        tmp = M(r)
        M(r) = M(i)
        M(i) = tmp
        If M(r)(lead) <> 0 Then
            div = M(r)(lead)
            For t = LBound(M(r)) To UBound(M(r))
                M(r)(t) = M(r)(t) / div
            Next t
        End If
        For j = 0 To rowCount
            If j <> r Then
                subt = M(j)(lead)
                For t = LBound(M(j)) To UBound(M(j))
                    M(j)(t) = M(j)(t) - subt * M(r)(t)
                Next t
            End If
        Next j
        lead = lead + 1
    Next r
    ToReducedRowEchelonForm = M
End Function
 
Public Sub main()
    r = ToReducedRowEchelonForm(Array( _
        Array(1, 2, -1, -4), _
        Array(2, 3, -1, -11), _
        Array(-2, 0, -3, 22)))
    For i = LBound(r) To UBound(r)
        Debug.Print Join(r(i), vbTab)
    Next i
End Sub