QCEVault

Matrices and applications — Question 201

Original QCE Vault practice · 5 marks

Q201 · Practice questionTechnology-freeComplex unfamiliar5 marks

QUESTION 201 (5 marks)

A population first undergoes transition (020.50.5)\begin{pmatrix}0&2\\0.5&0.5\end{pmatrix}. After each transition a fraction q of the new adults is removed, 0≤q<10\le q<1. Juveniles are not removed.
a)
Write the effective complete-step matrix.
[2 marks]
b)
Find q permitting a positive unchanged stage vector, and its stage ratio.
[3 marks]
Question linkSyllabus coverage

Related questions

  1. Q197 · Original practice · 5 marks
    In a tournament A beats B, B beats C and C beats A. Define Dij=1D_{ij}=1 if i beats j and 0 otherwise, in order A,B,C. There are no draws.
    Matrices and applications
  2. Q198 · Original practice · 5 marks
    A dominance matrix in order A,B,C,D is
    M=(0110001100011000).M=\begin{pmatrix}0&1&1&0\\0&0&1&1\\0&0&0&1\\1&0&0&0\end{pmatrix}.
    A score is the row sum of M+M2M+M^2.
    Matrices and applications
  3. Q199 · Original practice · 5 marks
    A population follows (Jn+1An+1)=(0f0.40.6)(JnAn)\binom{J_{n+1}}{A_{n+1}}=\begin{pmatrix}0&f\\0.4&0.6\end{pmatrix}\binom{J_n}{A_n} with f>0.
    Matrices and applications
  4. Q200 · Original practice · 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.
    Matrices and applications