Answered: 8. Consider the second-order… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 50EQ

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8. Consider the second-order homogeneous recurrence relation an =
3an-1 + 10an-2 with initial
conditions ao = 5, a1 = 11.
(a) Find the next three terms of the sequence.
(b) Find the general solution.
(c) Find the unique solution with the given initial conditions.

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2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
Consider the following recurrence relation and initial conditions. tk = 8tk − 1 − 16tk − 2, for each integer k ≥ 2 t0 = 1, t1 = 4 (a) Suppose a sequence of the form 1, t, t2, t3, , tn , where t ≠ 0, satisfies the given recurrence relation (but not necessarily the initial conditions). What is the characteristic equation of the recurrence relation?
an =8an-1 -15an-2 +4n/4 with boundary conditions as a0=−3 and a1=2. What is the final solution of the recurrence relation?
What is the solution of the linear homogeneous recurrence relation? an = an−1 + 2an−2 with a0 = 2 and a1 = 7 2. What is the solution of the linear homogeneous recurrence relation? an = 4an−1 - 4an−2 with a0 = 1 and a1 = 2
Solve the recurrence relation with the given initial conditions.Xo = 0, X1 = 1, Xn = 4Xn-I - 3Xn-2 for n >=2
Solve the recurrence relation subject to the initial conditions. F(1) = 8, F(2) = 18, and F(n) = 6F(n − 1) − 5F(n − 2) for n ≥ 3

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