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Solve the nonlinear system using Newton's method with the given initial vector. Terminate the process when the maximum norm of the difference between successive iterates is less than 5 x 10-6. 2 = = f(x, y, z) 2. g(x, y, z) h(x, y, z) = x2 + y2 + 22 – 10 x + 2y – 2 X + 3z – 9 = 0 0 0 x(0) = [2 0 2)". 2 = niin I 2,4 ! 2 Inn 3 У Implement Gaussian elimination with partial pivoting to solve the linear system in each step. Use numerical differentiation to compute the Jacobian matrix at each step of the method.