2. Show that the cost function for (1-regularized least squares. J,(w) & X'w (where ) > 0), can be rewritten as /,(w) = [) + ), /(x.. w) where /() is a suitable function whose first argument is a vector and second argument is a scalar. 3. Using your solution to part 2, derive necessary and sufficient conditions for the " component of the optimizer w* of / () to satisfy each of these three properties: w. > 0, w = 0. and 4. For the optimizer w of the 6-regularized least squares cost function J,(w) & w - Awif (where a > 0), derive a necessary and sufficient condition for w, = 0, where w. is the ith component of w. 5, A vector is called sparse if most of its components are 0. From your solution to part 3 and 4. which of w' and w is more likely to be sparse? Why