Multi-Step Route Analysis Using Matrix Powers

00:00 5 marks

Consider the following 3×3 adjacency matrix \(A\) representing a directed network where the entry \(a_{ij}=1\) indicates a direct route from node \(i\) to node \(j\), and 0 indicates no direct route. \(A = \begin{pmatrix}0 & 1 & 1\\ 1 & 0 & 1\\ 0 & 1 & 0\end{pmatrix}\).

Determine the number of distinct routes of exactly three steps starting from node 1 and ending at node 3 by computing \(A^3\).

Hint Hint

Hint

Remember that the (1,3) entry of \(A^3\) gives the number of 3-step routes from node 1 to node 3.

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Common Errors Common Errors

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