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1 of 8 0-day streak

Count routes using powers of a connection matrix

Question 1 of 8

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Consider this network of teams linked by recorded matches. Each line records one match between the teams

Network. Vertices: [Hawks | Blues | Tigers]. Connections: Blues -- Tigers; Hawks -- Tigers; Hawks -- Blues.HawksBluesTigers

Use the order Hawks, Blues, Tigers for the rows and columns of connection matrix \(C\). Rows name the starting vertex and columns name the ending vertex

\[C = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix}\]
(a)9 marks

Construct the matrix of two-step route counts, \(C^2\)

\(C^2\)
(b)1 mark

Find the entry \((C^2)_{33}\), which counts two-step routes from Tigers to Tigers