Exercise 7.  Observe that the subroutine Broyden involves vector functions and is not dependent on the dimension.
Use the subroutine Broyden to solve the nonlinear system in 4D space:  

           
          
           
          
    
Hint.  There is one real solutions.  A good starting vectors is   Solution 7.

First, enter the coordinate functions and construct the vector function    using Mathematica, and then find the Jacobian matrix .  

Use Broyden's method to find a numerical approximation to the solution near  .  

Use the subroutine to get the answer.

Do you think that there might be other solutions ?  We can use Mathematica to explore the situation.

Exploration

(c) John H. Mathews 2005