Problem 1 [60] Write a Matlab program that uses the Newton-Raphson method to solve the system of equations Select le-10 as the convergence threshold. Print the values of q and the number of iterations to the screen. Confirm that the solutions yield f(q) 0 Approach: Recall that the Newton-Raphson update for a system of equations is Xn+1 Xn J-1 f(%) = - where x is a vector and J is the Jacobian (matrix of partial derivatives). The matrix inversion can be accomplished in Matlab using: >>inv(J)*f (x) or J\f (x) Hint: Use [1;1;1 or -1:-1;-1] as useful initial guesses. The Jacobian will be a (3x 3) matrix Bonus [20 pts]: This system is highly nonlinear and sensitive to changes in initial guess Write a paragraph in your Output.doc/x explaining why different initial guesses can yield different viable solutions