Consider the function f(x) = α1x 2 1 + α2x 2 2 + · · · + αnx 2 n , where α1, αn are some constants. a) find all possible vectors [α1 α2 · · · αn] t for which f(x) is coercive. b) consider a vector [α1 α2 · · · αn] t for which f(x) is coercive. let us use the gradient algorithm with some initial point to minimize f(x). describe the convergence rate of the algorithm in terms of α1, α2, αn. c) consider a vector [α1 α2 · · · αn] t for which f(x) is coercive. find a matrix a such that when the problem is reformulated using the change of variables y = ax, the gradient algorithm has the fastest convergence rate.