Question: Question 3 (20 points) Let (fn)n be a real sequence with the property that for all integer numbers n > 0 we have 2fn+3 =

Question 3 (20 points) Let (fn)n be a real

Question 3 (20 points) Let (fn)n be a real sequence with the property that for all integer numbers n > 0 we have 2fn+3 = fn+2+2fn+1 - fn. (a) Let In = [fn+2 fn+1 fn), for all integer numbers n > 0. Find the transition matrix A of the sequence (In)n of vectors in R3, that is, Xn+1 = Axn for all n > 0. (b) Find the explicit formula for fn, in terms of fo, fi, and f2, for n > 0

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