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The problem asks you to find the steady-state distribution vector for the given transition matrix \( P \).

The transition matrix is:

\[
P = \begin{pmatrix} 
1 & 1 \\
\frac{1}{2} & 2 \\
1 & 0
\end{pmatrix}
\]

### Steps

You are given a transition matrix P. Find the steady-state distribution vector.

Learn how to find the steady-state distribution vector for the given transition matrix. This problem involves key concepts in linear algebra, including Markov chains and the steady-state distribution theorem. Suitable for college-level students.

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