7. (Pencil-and-paper but mostly MATLAB. Note opportunity for extra credit in part (c).) Consider the following system of nonlinear equations. f2(1,2,3)32-0 In shorthand vector notation the system can be expressed as f(x) o where f and x are vectors defined by fi T1 T3 Consider solving the system by using Newton's method. Let denote the k-th iterate and A z(k+1)-Z(k) the increment from the k-th to the (k+ 1)-th iterate. (a) Find the Jacobian matrix J(x) of this system. (b) The Newton iteration can be written as where J)and ff( Write a MATLAB code based upon the above iteration to solve the system (1). Write the code in three modules, as indicated in section 6 of posted notes of Lesson 3. (c) Use your code to solve the system. Find as many solutions as you can. You will receive extra credit if you find more than one solution. (You should be able to find at least four real solutions.) 7. (Pencil-and-paper but mostly MATLAB. Note opportunity for extra credit in part (c).) Consider the following system of nonlinear equations. f2(1,2,3)32-0 In shorthand vector notation the system can be expressed as f(x) o where f and x are vectors defined by fi T1 T3 Consider solving the system by using Newton's method. Let denote the k-th iterate and A z(k+1)-Z(k) the increment from the k-th to the (k+ 1)-th iterate. (a) Find the Jacobian matrix J(x) of this system. (b) The Newton iteration can be written as where J)and ff( Write a MATLAB code based upon the above iteration to solve the system (1). Write the code in three modules, as indicated in section 6 of posted notes of Lesson 3. (c) Use your code to solve the system. Find as many solutions as you can. You will receive extra credit if you find more than one solution. (You should be able to find at least four real solutions.)