Science:Math Exam Resources/Courses/MATH307/December 2010/Question 05 (b)/Statement

Define a sequence x₀, x₁, ... by the initial conditions x₀ = a, x₁ = b and x₂ = c together with the recursion relation

$\displaystyle x_{n+3}=x_{n+2}+x_{n+1}+x_{n}$

for n = 0, 1, 2, ...

(b) If the matrix A from part (a) is defined in MATLAB/Octave, we can do the following calculations

>eig(A)
ans = 
     1.83929 + 0.00000i
    -0.41964 + 0.60629i
    -0.41964 - 0.60629i

>abs(eig(A))
ans =
     1.83929
     0.73735
     0.73735

Describe how you could make further use of the eig command and other MATLAB/Octave commands to determine all (possibly complex) initial values a, b and c for which $x_{n}\to 0$ as $n\to \infty$.