solve part B only

3. Gradient depends on inner product. Therefore, one variant of gradient descent is obtained by choosing a weighted inner product of R" rather than the standard one. In particular, given a symmetric positive definite matrix W e Roxn, we know that (x, y)w :=x Wy defines an inner product of R". (a) Express Vwf (the gradient of f in R" with the weighted inner product (, .)w ) in terms of W and Vf (the gradient of f in R" with the standard inner product). (b) Give the gradient descent algorithm for solving (1) under the weighted inner product (, .)w (i.e., find an explicit formula of a(*+1) when we replace (., .) and | . |? in (2) by (, .)w and I| . Ili respectively). (By choosing a suitable W, we may obtain faster algorithms than the standard gradient descent. This technique is known as preconditioning.)