Multidimensional Newton-Raphson method

Create a program that finds and outputs the root of a system of nonlinear equations using Newton-Raphson metod.

Multidimensional Newton-Raphson method
You are encouraged to solve this task according to the task description, using any language you may know.

Task

C#

For matrix inversion and matrix and vector definitions - see C# source from Gauss-Jordan matrix inversion <lang C#> </lang> <lang C#> using System;

namespace Rosetta {

   class Program
   {
       static void Main(string[] args)
       {
       }
   }

} </lang>

Output: