A tennis team consists of five players: Quinn, Rosie, Siobhan, Trinh and Ursula.
When the team competes, players compete in the order of first, then second, then third, then fourth.
The fifth player has a bye (does not compete).
On week 1 of the competition, the players competed in the following order.
\begin{array}{|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \quad\textbf{First} \quad\rule[-1ex]{0pt}{0pt}& \quad \textbf{Second} \quad& \quad\textbf{Third} \quad& \quad\textbf{Fourth}\quad & \quad\textbf{Bye} \quad\\
\hline
\rule{0pt}{2.5ex} \text{Quinn} \rule[-1ex]{0pt}{0pt}& \text {Rosie} & \text {Siobhan} & \text { Trinh } & \text {Ursula} \\
\hline
\end{array}
This information can be represented by matrix \(G_1\), shown below.
\(G_1=\begin{bmatrix} Q & R & S & T & U \end{bmatrix}\)
Let \(G_n\) be the order of play in week \(n\).
The playing order changes each week and can be determined by the rule \(G_{n+1}=G_n \times P\)
\(\text{where}\quad \\P=\begin{bmatrix}
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \end{bmatrix}\)
Which player has a bye in week 4 ?
- Quinn
- Rosie
- Siobhan
- Trinh