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3. The Following System Of Equations Has A Few Different Roots: Xy – 22 = 1 Xyz + Y2 – X2 = 2 Et

3. The following system of equations has a few different roots: xy – 22 = 1 xyz + y2 – x2 = 2 et +2 -ey = 3 (a) (2 points) Let t = [x;y; z] so that we can write x1 for x, 2 for y and x3 for z. Write down the vector-valued function f that defines the root-finding problem f(a) = 0. Express the function in terms of 1. [1.7777] (b) (3 points) Let Pa = 1 and let Ij = (1.4240. One of these vectors is a root, and the 1.2375] other is not. Evaluate f(a) and f(F). Explain how these computations tell you which one is a root, and which one isn't a root. (c) (3 points) Write down the 3x3 Jacobian for the system in terms of . (d) (4 points) Find another root besides the one given in part (e) above. Try some initial guesses

%Matlab code for Newton method clear all close all %nonlinear function to be solved syms x y z f1(x,y,z)=x.*y-z.^2-1; f2(x,y,z)=x.*y.*z+y.^2-x.^2-2; f3(x,y,z)=exp(x)+z-exp(y)-3; %displaying the functi