1. (20 points) (a) (9 points) Show the following three facts, for b a constant vector in R", x a vector of variables in R", and M an n x n constant matrix: (i) V(b'x) = b, (ii) V(x'b) = b, x( W + W) = (xWx) (!) In your proof, feel free to demonstrate the details for the n = 2 case, so that b1 ar X = b = M = with Vf(x) = VS(x,y) = T121 17122 of (b) (11 points) Using the calculus results from part (a), show that the minimum of S(v) = lly - Av||2 occurs when V = Vo, where Vo is the solution to: A"Avo = Aly