Suppose the Leslie matrix is 6a 1/2 a > (). () 1/3 () The only reproductive age class is the third age class. (a) Find the characteristic equation, cigenvalucs, and inherent net reproductive number Ro of L. (b) Show that L is imprimitive. 1 and X (0) = (6, 0, 0)', find X (1), X (2), X (3); then describe the (c) For a = behavior of X (t) as t → ∞. (d) For a = 1 and X (0) = (12, 2. 1)", find X(1), X(2), X(3); then describe the behavior of X(t) as t→ ∞. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Can you please help with part (d) of question attached?

Suppose the Leslie matrix is
6a3
L.
1/2
1/3
u > ().
()
The only reproductive age class is the third age class.
(a) Find the characteristic equation, eigenvalues, and inherent net reproductive
number Ro of L.
(b) Show that L is imprimitive.
(c) For a =
behavior of X(t) as t → ,
1 and X (0) = (6, 0, 0)', find X (1), X (2), X (3); then describe the
1 and X(0) = (12, 2, 1)", find X(1), X(2), X(3); then describe the
(d) For a =
behavior of X(t) as t→ 0.
Transcribed Image Text:Suppose the Leslie matrix is 6a3 L. 1/2 1/3 u > (). () The only reproductive age class is the third age class. (a) Find the characteristic equation, eigenvalues, and inherent net reproductive number Ro of L. (b) Show that L is imprimitive. (c) For a = behavior of X(t) as t → , 1 and X (0) = (6, 0, 0)', find X (1), X (2), X (3); then describe the 1 and X(0) = (12, 2, 1)", find X(1), X(2), X(3); then describe the (d) For a = behavior of X(t) as t→ 0.
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