dsc 140 Problem 1. In this problem, we'll show that the gradient of f(~x) = ~xT A~x is 2A~x, where A is a symmetric n n matrix and ~x R n. This is a useful result, but it's also a good exercise for reviewing topics in matrix-vector algebra and multivariate calculus. a) To compute the gradient, we need to compute f /x1, f /x2, and so on. To do this, we'll start by expanding ~xT A~x until we see the coordinates of ~x. Let the entries of A be a11 a12 a1n a21 a22 a2n . . . . . . . . . . . . an1 an2 a