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\(\frac{a}{b}\)
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In a region, people move between the City (C) and the Suburbs (S). The transition matrix representing the annual migration is given by \(\mathbf{T} = \begin{pmatrix} 0.9 & 0.2 \\ 0.1 & 0.8 \end{pmatrix}\).
Find the steady state vector \(\mathbf{s} = \begin{pmatrix} x \\ y \end{pmatrix}\) algebraically by solving the system \(\mathbf{T}\mathbf{s} = \mathbf{s}\).
Interpret the result in terms of the long-term population distribution.
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