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Problem 6 Let A € Rmx, beR", DE RP, and > 0. Consider the regularized least squares problem min||Ar – b|| +X||Dr||. ZER" 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(7), is the set of vectors a such that Tr = 0. A synonym for null space is kernel. Note that {0} is not the emptyset.

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