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Question 4 The characteristic roots of the recurrence relation ax = 642-1 - lla,-2 + 60-3...
Question 1. A linear homogeneous recurrence relation of degree 2 with constant coefficients is a recurrence relation of the form an = Cian-1 + c2an-2, for real constants Ci and C2, and all n 2. Show that if an = r" for some constant r, then r must satisfy the characteristic equation, p2 - cir= c = 0. Question 2. Given a linear homogeneous recurrence relation of degree 2 with constant coefficients, the solutions of its characteristic equation are called...
2) [PI 1.2||PI 1.3]Use characteristic equation to solve the recurrence relation. ak= - 10ak-1 - 25ak-2, 20 = 1; a1 = -1 use the equation an= rom +2 nrm for repeated roots. ( 20 Points)
Question 9 4 pts Solve the recurrence relation an an-1+2 with a = 4 (Hint: This will telescope.)
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 21 subsequence. b) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 44 subsequence. Answer is a) an = an-1+ an-4 + an-2 - an-3, b) an = an-1 + an-2 + an-5 + an-6, please explain how to get it,...
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 21 subsequence. b) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 44 subsequence. Answer is a) an = an-1+ an-4 + an-2 - an-3, b) an = an-1 + an-2 + an-5 + an-6, please explain how to get it,...
ts) Find three linearly independent characteristic vectors and all characteristic roots of the matrix 3 2 -3 -3 -4 9 1-1 - 5
(1) (1) (a) (14 pts.) Solve the following recurrence relation with the method of the charac- teristic equation: T(n) = 4T(n/2) + (n/2), for n > 1, n a power of 2 T(1) = 1 Determine the coefficients. (b) (1 PT.) What is the big O) order of the solution as a function of n? (c) (5 PTS.) Verify your solution by substituting back in the recurrence relation. (ii) (10 PTS.) Solve using the method of the characteristic equation to...
Algorithm Question:
Problem 3. Solve the recurrence relation T(n) = 2T(n/2) + lg n, T(1) 0.
9) Solve the linear recurrence relation a, 8am-1 - 15a -2, a. =3, a, =11.
Find general solution for the recurrence relation: an = 6an−1−9an−2+ 2 × 3n + 4 × 2n