Dominance matrices
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The following dominance matrix \(M\), gives the results of a series of tennis matches between four friends, where \( m_{ij} = 1 \) if player \(i\) beat player \(j\).
\( A = \) Alan, \( B = \) Ben, \( C = \) Christine, \( D = \) Deborah
\[\begin{aligned}
&\qquad A\quad B\;\;\; C\;\;\; D\\
&\begin{array}{l|llll|}
A & 0 & 1 & 0 & 0 \\
B & 0 & 0 & 1 & 1 \\
C & 1 & 0 & 0 & 0 \\
D & 1 & 0 & 1 & 0
\end{array}
\end{aligned}
\]
i) How many matches are there?
ii) Use the dominance scores from the matrix \(M\) to give a ranking of the players.
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