QCE Vault / Specialist Maths Vectors and matrices — Question 4 QCAA 2023, Paper 1 · 1 mark
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QUESTION 4 The age-specific population distribution of a particular species of animal is shown.
Age (years) 0–1 1–2 2–3 3–4 Female population 94 82 37 6 Breeding rate 0 1.3 0.9 0.2 Survival rate 0.6 0.8 0.4 0
The Leslie matrix based on this data is
(A) [ 94 82 37 6 0.6 0 0 0 0 0.8 0 0 0 0 0.4 0 ] \begin{bmatrix}94&82&37&6\\0.6&0&0&0\\0&0.8&0&0\\0&0&0.4&0\end{bmatrix} 94 0.6 0 0 82 0 0.8 0 37 0 0 0.4 6 0 0 0 (B) [ 1 2 3 4 1.3 0 0 0 0 0.9 0 0 0 0 0.2 0 ] \begin{bmatrix}1&2&3&4\\1.3&0&0&0\\0&0.9&0&0\\0&0&0.2&0\end{bmatrix} 1 1.3 0 0 2 0 0.9 0 3 0 0 0.2 4 0 0 0 (C) [ 0.6 0.8 0.4 0 1.3 0 0 0 0 0.9 0 0 0 0 0.2 0 ] \begin{bmatrix}0.6&0.8&0.4&0\\1.3&0&0&0\\0&0.9&0&0\\0&0&0.2&0\end{bmatrix} 0.6 1.3 0 0 0.8 0 0.9 0 0.4 0 0 0.2 0 0 0 0 (D) [ 0 1.3 0.9 0.2 0.6 0 0 0 0 0.8 0 0 0 0 0.4 0 ] \begin{bmatrix}0&1.3&0.9&0.2\\0.6&0&0&0\\0&0.8&0&0\\0&0&0.4&0\end{bmatrix} 0 0.6 0 0 1.3 0 0.8 0 0.9 0 0 0.4 0.2 0 0 0 WORKED SOLUTION
Answer D 1 mark Worked solution
A Leslie matrix places breeding rates in the first row and successive survival rates on the subdiagonal. This gives [ 0 1.3 0.9 0.2 0.6 0 0 0 0 0.8 0 0 0 0 0.4 0 ] \begin{bmatrix}0&1.3&0.9&0.2\\0.6&0&0&0\\0&0.8&0&0\\0&0&0.4&0\end{bmatrix} 0 0.6 0 0 1.3 0 0.8 0 0.9 0 0 0.4 0.2 0 0 0 . Worked explanation by QCE Vault; correct option verified against the QCAA answer key.
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