Use the age transition matrix $ L $ and age distribution vector $ \mathbf{x}_1 $ to find the age distribution vectors $ \mathbf{x}_2 $ and $ \mathbf{x}_3 $.\[L = \begin{bmatrix} 0 & 3 & 6 \\ 1 & 0 & 0 \\ 0 & \frac{1}{3} & 0 \end{bmatrix}, \quad \mathbf{x}_1 = \begin{bmatrix} 18 \\ 18 \\ 18 \end{bmatrix}\]\[\mathbf{x}_2 = \begin{bmatrix} \boxed{\phantom{0}} \\\boxed{\phantom{0}} \\\boxed{\phantom{0}} \end{bmatrix}\]\[\mathbf{x}_3 = \begin{bmatrix} \boxed{\phantom{0}} \\\boxed{\phantom{0}} \\\boxed{\phantom{0}} \end{bmatrix}\]Then find a stable age distribution vector.\[\mathbf{x} = t \begin{bmatrix} \boxed{\phantom{0}} \\\boxed{\phantom{0}} \\\boxed{\phantom{0}} \end{bmatrix}\]**Explanation of Diagram:**The provided matrix $ L $ is a 3x3 transition matrix used to model changes in age distribution over time.The vector $ \mathbf{x}_1 $ represents the initial age distribution with three equal age cohorts of size 18.The blank vector boxes for $ \mathbf{x}_2 $, $ \mathbf{x}_3 $, and a stable age distribution vector $ \mathbf{x} $, denoted as $ t \times $ the vector, represent places to calculate subsequent age distributions and a stable distribution after sufficient time has passed, presumably by iterating the matrix multiplication.

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Answered: Use the age transition matrix L and age…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Use the age transition matrix L and age distribution vector x₁ to find the age distribution vectors x₂ and X3. 0 36 1 00 X2 X3 || || L = x = t 0 000 ↓1 000 0 I X₁ = 18 18 18 Then find a stable age distribution vector. E