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The steady state of a chain with matrix \(\mathbf{M} = \begin{pmatrix} 0.9 & 0.1 \\ 0.4 & 0.6 \end{pmatrix}\) satisfies \(x = 4y\). Given \(x+y=1\), what is \(\pi\)?
\(\begin{pmatrix} 0.2 & 0.8 \end{pmatrix}\)
\(\begin{pmatrix} 0.5 & 0.5 \end{pmatrix}\)
\(\begin{pmatrix} 0.8 & 0.2 \end{pmatrix}\)
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