QCEVault

Matrices and applications — Question 200

Original QCE Vault practice · 7 marks

Q200 · Practice questionTechnology-activeComplex unfamiliar7 marks

QUESTION 200 (7 marks)

A three-stage insect model uses
L=(0040.50000.50).L=\begin{pmatrix}0&0&4\\0.5&0&0\\0&0.5&0\end{pmatrix}.
Counts are expected values and may be fractional.
Three insect stages J, S and A. Directed arrows J to S and S to A have factors 0.5, and the return from A to J is labelled 4 offspring.
a)
Starting at (70,0,0), find the next three vectors and totals.
[3 marks]
b)
Show that every initial vector returns after three steps.
[2 marks]
c)
Determine a positive ratio unchanged every step.
[2 marks]
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