QUESTION 6 Consider a sequence Fo, F1, F2,... which satisfies the recurrence relation Fn = 2Fn-1+3Fn-2 for all n ≥ 2. (a

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Question 6 Consider A Sequence Fo F1 F2 Which Satisfies The Recurrence Relation Fn 2fn 1 3fn 2 For All N 2 A 1 (33.96 KiB) Viewed 10 times

QUESTION 6 Consider a sequence Fo, F1, F2,... which satisfies the recurrence relation Fn = 2Fn-1+3Fn-2 for all n ≥ 2. (a) This recurrence relation can equivalently be written as Xn = all n ≥ 2, where R is a matrix and Find R. (b) Diagonalise the matrix R. [TOTAL MARKS: 22] - (F). MS200A, Semester Two 2021/22 Xn = Rxn-1 for [3 marks] [10 marks] (c) Using your result from part (b), solve the recurrence relation if Fo = 1 and F₁ = 2. [9 marks] Page 4 of 5