(MATLAB) System of non-linear equations.

Write a MATLAB program to obtain the root of the following system of non-linear equations using Newton-Raphson method

u(x, y, z) = x(x + ay + bz 1) = 0

v(x, y, z) = y(bx + y + az 1) = 0

w(x, y, z) = z(ax + by + z 1) = 0

Where a = b = 0.5. Use an initial guess of x = 1, y = 0.8 , and z = 0.9.

How many iterations are needed for the approximate error to go below 0.1%?

Derive by hand all 9 solutions of the non-linear equations and try to generate these solutions using your code by changing the initial guesses.