(a) The gradient G = WRSS(W) is a k d matrix whose entries are Gi j = RSS(W)/Wi j, where RSS(W) is defined by Equation (1). Write two explicit formulas for WRSS(W). First, derive a formula for each Gi j using summations, simplified as much as possible. Use that result to find a simple formula for WRSS(W) in matrix notation with no summations. HW2: I r Math, UCB CS 189/289A, Spring 2024. All Rights Reserved. This may not be publicly shared without explicit permission. 7 (b) Directional derivatives are closely related to gradients. The notation RSS W(W) denotes the directional derivative of RSS(W) in the direction W, and the notation () denotes the directional derivative of () in the direction . 3 Informally speaking, the directional derivative RSS W(W) tells us how much RSS(W) changes if we increase W by an infinitesimal displacement W R kd . (However, any W we can actually specify is not actually infinitesimal; RSS W(W) is a local linearization of the relationship between W and RSS(W) at W. To a physicist, RSS W(W) tells us the initial velocity of change of RSS(W) if we start changing W with velocity W.)