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).