# Worksheet: Applications on Representing Data Using Matrices

In this worksheet, we will practice using matrices to model some applications like the payoff matrix of a game and the incidence and adjacency matrices of a graph.

**Q1: **

Write down the adjacency matrix of the network shown.

- A
- B
- C
- D
- E

**Q2: **

When a connection in a network does not have an arrow, it is said to be ‘undirected’. An undirected connection between nodes and is equivalent to a directed connection from to together with a directed connection from to . Determine the adjacency matrix of the network shown.

- A
- B
- C
- D
- E

**Q3: **

Players and play a game in which they both call “heads” or “tails” at the same time. They use the payoff matrix , where the first row and column represent “heads” and the second row and column represent “tails.” Describe the payoff rules for this game.

- AIf both players call “heads,” player gets 1 point from player ; if both players call “tails,” player gets 2 points from player ; and if both players call different sides, player gets 2 points from player if he calls “heads” or 1 point if he calls “tails.”
- BIf both players call “heads,” player gets 2 points from player ; if both players call “tails,” player gets 1 point from player ; and if both players call different sides, player gets 2 points from player if he calls “heads” or 1 point if he calls “tails.”
- CIf both players call “heads,” player gets 2 points from player ; if both players call “tails,” player gets 1 point from player ; and if both players call different sides, player gets 1 point from player if he calls “heads” or 2 points if he calls “tails.”
- DIf both players call “heads,” player gets 1 point from player ; if both players call “tails,” player gets 2 points from player ; and if both players call different sides, player gets 1 point from player if he calls “heads” or 2 points if he calls “tails.”
- EIf both players call “heads,” player gets 2 points from player ; if both players call “tails,” player gets 2 points from player ; and if both players call different sides, player gets 1 point from player if he calls “heads” or 1 point if he calls “tails.”

**Q4: **

Players and play a game in which they both call “heads” or “tails” at the same time. If they both call the same thing, player wins one point from player . If they call different things, player wins one point from player . Write the payoff matrix for this game.

- A
- B
- C
- D
- E