\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Two internet service providers, FastNet and SpeedWeb, compete for subscribers. The transition matrix representing annual customer switching is \(\mathbf{T} = \begin{pmatrix} 0.8 & 0.1 \\ 0.2 & 0.9 \end{pmatrix}\).
Currently, FastNet has \(30\pourcent\) of the market and SpeedWeb has \(70\pourcent\).
Find the market share of each provider after 1 year.
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