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10. Let (Un) be a sequence of real numbers defined recursively by uj = 1, u2 = 2 and un+1 = 2 (un + Un-1) for all n 2 2. The goal of this problem is to find a formula that gives un explicitly in terms of n for all n 2 1. Let Un = [un Un+1] for all n 2 1. Fill in the missing information below. (a) Let n be a natural number. Then Un+ 1 = Un (b) Let A be the 2 x 2 matrix of (a). Find an invertible matrix P and a diagonal matrix D such that A = PDP-1. A = P = P-1 = D = (c) Let n be a natural number. By using (b), we get Un = PDn-1P-1v1. After performing the preceding matrix multiplications, we find that Un (d) Let n be a natural number. Find un from (c): Un = (e) lim un =