problem 5 system of nonlinear equations matlab given a system of nonli

Question

Problem 5: System of Nonlinear Equations (MATLAB)
Given a system of nonlinear equations:
u(x, y, z) = x(x + 2y + 5z - 4) = 0,
v(x, y, z) = y(5x + y + 2z - 4) = 0,
w(x, y, z) = 2(2x + 5y +z - 4) = 0,
(5)
(6)
(7)
1. Derive all real solutions to this system of equations by hand. Clearly show your work.
2. Write a MATLAB script to obtain the root of this system of non-linear equations
using the Newton-Raphson method. Use an initial guess of (x, y, z) = (4.4,-0.8,0.4).
How many iterations are needed for the approximate error ca to go below € = 0.1%?
3. Use your solution to Problem 5.2 to generate all the analytical solutions from Problem
5.1 by modifying your initial guesses for (x, y, z).