1. [25 pts] Remember that for the trace operation tr (v . v ) = Z, v. = v v where v is a vector, and if a square matrix P is orthonormal then P TP = I (the identity). Given that v = [1 0 2] , and R is an orthonormal matrix, what is tr(Rvv RT) equal to? 2. [25 pts] Given that the A12, A21 and Azz E R3x3 are invertible, and b1, b2, X1, X2 E R3, then solve for x1 and X2 from 0 A21 3. [25 pts] Remember that the sigmoid function is given by o (u) = 1 1te-u Given the vector X = [x), What is the derivative do(2x1+4x2) equal to when evaluated at x = ? ? Hint : dx Remember that o' (u) = o(u) . (1 - o(u)). 4. [25 pts] Use the chain rule to compute the derivative of fog(x) with respect to x given that f (x) = x1x2 + X2 and g(x) = 3x2 2x1 Other techniques will result in partial credit