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Matrices, GEN2 2024 VCAA 9

Vince works on a construction site.

The amount Vince gets paid depends on the type of shift he works, as shown in the table below.

This information is shown in matrix below.

  1. Matrix is the transpose of matrix .
  2. Determine the matrix .   (1 mark)

During one week, Vince works 28 hours at the normal rate of pay, 6 hours at the overtime rate of pay, and 8 hours at the weekend rate of pay.

  1. Complete the following matrix calculation showing the total amount Vince has been paid for this week.  (1 mark)

  

Vince will receive $90 per hour if he works a public holiday shift.

Matrix , as calculated below, can be used to show Vince's hourly rate for each type of shift.

  1. Write the values of and .  (1 mark)

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a.   

b.    

c.    

Show Worked Solution

a.   

 
b.   

 
c.   

MATRICES, FUR2 2019 VCAA 1

The car park at a theme park has three areas, and .

The number of empty and full parking spaces in each of the three areas at 1 pm on Friday are shown in matrix   below.
 


 

  1. What is the order of matrix ?   (1 mark)

  2. Write down a calculation to show that 110 parking spaces are full at 1 pm.   (1 mark)

Drivers must pay a parking fee for each hour of parking.

Matrix , below, shows the hourly fee, in dollars, for a car parked in each of the three areas.
 


 

  1. The total parking fee, in dollars, collected from these 110 parked cars if they were parked for one hour is calculated as follows.  

     

     

     

    where matrix    is a    matrix.

     

    Write down matrix  .   (1 mark)

The number of whole hours that each of the 110 cars had been parked was recorded at 1 pm. Matrix , below, shows the number of cars parked for one, two, three or four hours in each of the areas and .


 

  1. Matrix    is the transpose of matrix  .

      

    Complete the matrix    below.   (1 mark)

      


     

  2. Explain what the element in row 3, column 2 of matrix    represents.   (1 mark)

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Show Worked Solution

a. 
 

b. 
 

c. 
 

d. 
 

e.