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Matrices, GEN1 2024 VCAA 29 MC

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.

This information can be represented by matrix , shown below.

Let be the order of play in week .

The playing order changes each week and can be determined by the rule 

Which player has a bye in week 4 ?

  1. Quinn
  2. Rosie
  3. Siobhan
  4. Trinh
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♦ Mean mark 49%.

MATRICES, FUR2 2019 VCAA 2

The theme park has four locations, Air World , Food World , Ground World and Water World .

The number of visitors at each of the four locations is counted every hour.

By 10 am on Saturday the park had reached its capacity of 2000 visitors and could take no more visitors.

The park stayed at capacity until the end of the day

The state matrix, , below, shows the number of visitors at each location at 10 am on Saturday.
 


 

  1. What percentage of the park’s visitors were at Water World at 10 am on Saturday?   (1 mark)

Let be the state matrix that shows the number of visitors expected at each location hours after 10 am on Saturday.

The number of visitors expected at each location hours after 10 am on Saturday can be determined by the matrix recurrence relation below.
 


 

  1. Complete the state matrix, , below to show the number of visitors expected at each location at 11 am on Saturday.   (1 mark)

 

 

  1. Of the 300 visitors expected at Ground World at 11 am, what percentage was at either Air World or Food World at 10 am?   (1 mark)

  2. The proportion of visitors moving from one location to another each hour on Sunday is different from Saturday.

     

    Matrix , below, shows the proportion of visitors moving from one location to another each hour after 10 am on Sunday.

     

     

     
    Matrix is similar to matrix but has the first two rows of matrix interchanged.

     

  3. The matrix product that will generate matrix from matrix is
  5. where matrix is a binary matrix.
  6. Write down matrix .   (1 mark)
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a.   

 

b.  
   

 

c. 


 

d.