\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the directed graph \(H\) given by the following adjacency matrix (vertices are ordered alphabetically: P, Q, R):$$ \mathbf{M} = \begin{pmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 1 & 0\end{pmatrix} $$
  1. Draw the directed graph \(H\).
  2. Find the number of walks of length 2 from vertex P to vertex R.
  3. Find the number of walks of length 3 from vertex R to vertex Q.

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