I really do not know how to even start with this problem!!! Gradient of vectors, getting confused as to what the dot product/cross product/manipulation of the vectors is doing and also how to start thinking about the gradient part.

f. I [3 points][3 points] Let's practice taking gradients, which is a key operation for being able to optimize continuous ' functions. For W 6 [Rd (represented as a column vector) and constants a,, hi 6 [Rd (also represented as column vectors) and A 6 IR, define the scalar-valued function f(W) = 2 2(a3w 1),wa + Allwug, i=1 j=1 where the vector is W = (W1, , wd)T and ||W||2 = V 2L1 w,% is known as the Lg norm. Compute the gradient Vf(w). Recall: the gradient is a d -dimensional vector of the partial derivatives with respect to each wi: af(W) 0f(W))T awl awd . Vf(W) = ( If you're not comfortable with vector calculus, first warm up by working out this problem using scalars in place of vectors and derivatives in place of gradients. Not everything for scalars goes through for vectors, but the two should at least be consistent with each other (when d = 1). Do not write out summation over dimensions, because that gets tedious