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Unformatted text preview: such that if g1 = αf1 + β f2 and g2 = γ f1 + δ f2
T
1
α
γ
then 0 g1 g2 =
.
β
δ 7. (a) Suppose two populations of animals follow the discrete dynamical
system
p(t + 1) = 1.7p(t) − .6q (t)
q (t + 1) = −.6p(t) + .8q (t).
You are told that the eigenvalues of the relevant matrix are 2 and
1
. Determine p(t) and q (t) in the case where p(0) = 100 and
2
q (0) = 200.
(b) Solve the system of diﬀerential equations
1.7 −0.6
=
x
x
−0.6 0.8
100
when x(0) =
.
200
8. Determine the steadystate behavior of the Markov chain with transition matrix given by the Markov matrix 0.3 0.2 0.7
0.4 0.5 0.2 .
0.3 0.3 0.1...
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This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell University (Engineering School).
 Fall '05
 HUI
 Math, Linear Algebra, Algebra

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