2) [PI 1.2||PI 1.3]Use characteristic equation to solve the recurrence relation. ak= - 10ak-1 - 25ak-2,...
The sequence { ak } is defined by the recurrence relation ak+2 = 3ak+1 + 4ak with initial conditions do = 0, Q1 = 1. (a) Express the recurrence relation as a matrix difference equation Uk+1 = Auk (b) Find the general formula for ak. (Advise: You can check your answer by comput- ing the first few terms.)
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...
Solve the recurrence relation; an=an-1 + an-2 a1=2 a2=1
Question 4 The characteristic roots of the recurrence relation ax = 642-1 - lla,-2 + 60-3 are ar = 2,7 = 1,7 = -3 bir-2,= -1,7 = 3 cr=-2, r = -1, r = 3 d. r = 2,7 = 1,7 - 3
6. Solve the following recurrence relations: (a) An+1 ,00 = 2 (b) n-1 an+1 =1+ ak , 0o = a1 = 1 ,n> 1 k=0
(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...
Solve the nonhomogeneous recurrence relation A 47. ho 1 h1 2 Solve the nonhomogeneous recurrence relation A 47. ho 1 h1 2
Solve the recurrence relation: a subn = 5a subn-1 - 6 a subn-2 n is greater than or equal to 2 given: ao = 1, a1 = 0
6. Use the generating function method to solve the following recurrence relation: with ao 2, a6 6. Use the generating function method to solve the following recurrence relation: with ao 2, a6
) Solve the following recurrence relation with the given initial conditions: an=10an-1-21an-2 a0=-3 a1=5