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Further matrices — Question 275

Original QCE Vault practice · 6 marks

Q275 · Practice questionTechnology-freeComplex unfamiliar6 marks

QUESTION 275 (6 marks)

A two-stage population follows
(Jn+1An+1)=(f2fs0)(JnAn),f>0,0<s≤1.\binom{J_{n+1}}{A_{n+1}}=\begin{pmatrix}f&2f\\s&0\end{pmatrix}\binom{J_n}{A_n},\quad f>0,\quad0<s\le1.
The initial vector is (40,20)T(40,20)^T and the vector after one step is (32,20)T(32,20)^T.
a)
Determine f and s and interpret their roles.
[3 marks]
b)
Determine the vector after three steps from the start. A student instead uses (32,20)T(32,20)^T as the initial vector and applies the matrix three times. Explain the timing error.
[3 marks]
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