SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Matrices, GEN1 2024 VCAA 32 MC

A large sporting event is held over a period of four consecutive days: Thursday, Friday, Saturday and Sunday.

People can watch the event at four different sites throughout the city: Botanical Gardens , City Square , Riverbank or Main Beach .

Let be the state matrix that shows the number of people at each location days after Thursday.

The expected number of people at each location can be determined by the matrix recurrence rule

 

the number of people watching the event at the Botanical Gardens from Thursday to Sunday has

  1. decreased by 162
  2. decreased by 212
  3. increased by 124
  4. increased by 696
Show Answers Only

Show Worked Solution
 
♦♦♦ Mean mark 33%.

  

  

 

  

MATRICES, FUR2 2020 VCAA 4

A second market research project also suggested that if the Westmall shopping centre were sold, each of the three centres (Westmall, Grandmall and Eastmall) would continue to have regular shoppers but would attract and lose shoppers on a weekly basis.

Let be the state matrix that shows the expected number of shoppers at each of the three centres weeks after Westmall is sold.

A matrix recurrence relation that generates values of is


 

The matrix is the state matrix that shows the expected number of shoppers at each of the three centres in the second week after Westmall is sold

  1. Determine the expected number of shoppers at Westmall in the third week after it is sold.   (1 mark)

  2. Determine the expected number of shoppers at Westmall in the first week after it is sold.   (1 mark)

Show Answers Only
Show Worked Solution

♦ Mean mark part (a) 50%.
a.  
   

 

 

♦♦♦ Mean mark part (b) 20%.
b.