Let A = Rmxn, b = R, D = Rn, and \ > 0. Consider the regularized least squares problem xRn min || Ax b|| + X||Dx||. Show that the problem has a unique solution iff null(A) null(D) = {0}, where the the null space of a linear map T, denoted by null (T), is the set of vectors x such that Tx = 0. A synonym for null space is kernel. Note that {0} is not the emptyset.