Given a (full rank) matrix of n data points XRxd and labels y € R". Consider the minimization problem of f: Rd R defined as → == min [f(w) = xw-yl] 1. Calculate the Hessian V2f(w) of f(w) w.r.t. w. 2. Is f(w) a convex function on Rd? 3. Prove or disprove the following statement: f(w) has L-Lipschitz-continuous gradients. 4. Assuming the Hessian of f(w) is invertible and that the iterates are initialized at some wo € Rd, derive the update rule for Undamped Newton's method in terms of X and y for minimizing f(w). 5. Write the exact form of the minimizer that Newton's method leads to. How many iterations does it take to reach such a solution? 6. Now assume we change the initialization to 2wo. How does it affect your answer in part (5)?