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

MATH307 December 2010
Other MATH307 Exams

### Question 05 (b)

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

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

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 ${\displaystyle x_{n}\to 0}$ as ${\displaystyle n\to \infty }$.

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