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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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A network of teams linked by recorded matches is shown. Each line records one match between the teams

Network. Vertices: [Orbits | Falcons | Comets]. Connections: Orbits -- Comets; Falcons -- Comets; Falcons -- Comets.OrbitsFalconsComets

Use the order Orbits, Falcons, Comets for the rows and columns of connection matrix \(C\). Rows name the starting vertex and columns name the ending vertex

\[C = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 2 \\ 1 & 2 & 0 \end{bmatrix}\]
(a)9 marks

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

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

Find the entry \((C^2)_{12}\), which counts two-step routes from Orbits to Falcons