smc-619-20-Matrix product from table

MATRICES, FUR1 2019 VCAA 2 MC

There are two rides called The Big Dipper and The Terror Train at a carnival.

The cost, in dollars, for a child to ride on each ride is shown in the table below.

	Ride	Cost ($)
	The Big Dipper	7
	The Terror Train	8

Six children ride once only on The Big Dipper and once only on The Terror Train.

The total cost of the rides, in dollars, for these six children can be determined by which one of the following calculations?

A.	`[6] xx [(7, 8)]`	B.	`[6] xx [(7), (8)]`
C.	`[(6, 6)] xx [(7, 8)]`	D.	`[(6, 6)] xx [(7), (8)]`
E.	`[(6), (6)] xx [(7, 8)]`

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`D`

Show Worked Solution

`text(Total Cost)`	`= 6 xx 7 + 6 xx 8`
	`= [(6, 6)] xx [(7), (8)]`

`=> D`

MATRICES, FUR2 2018 VCAA 2

The Westhorn Council must prepare roads for expected population changes in each of three locations: main town `(M)`, villages `(V)` and rural areas `(R)`.

The population of each of these locations in 2018 is shown in matrix `P_2018` below.

`P_2018 = [(2100),(1800),(1700)]{:(M),(V),(R):}`

The expected annual change in population in each location is shown in the table below.

Write down matrix `P_2019`, which shows the expected population in each location in 2019 (1 mark)
The expected population in each of the three locations in 2019 can be determined from the matrix product.

`qquad qquad P_2019 = F xx P_2018,` where `F` is a diagonal matrix.

Write down matrix `F`. (1 mark)

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`P_2019 = [(1.04 xx 2100),(0.99 xx 1800),(0.98 xx 1700)] = [(2184),(1782),(1666)]`
`F = [(1.04, 0, 0),(0, 0.99, 0),(0, 0, 0.98)]`

Show Worked Solution

a. `P_2019 = [(1.04 xx 2100),(0.99 xx 1800),(0.98 xx 1700)] = [(2184),(1782),(1666)]`

♦ Mean mark part (b) 40%.
COMMENT: Many students included 0.04, -0.01 and -0.02 in this matrix. Know why this is incorrect!

b. `F = [(1.04, 0, 0),(0, 0.99, 0),(0, 0, 0.98)]`

MATRICES, FUR1 2016 VCAA 4 MC

The table below shows the number of each type of coin saved in a moneybox.

The matrix product that displays the total number of coins and the total value of these coins is

A.	`[(5,10,20,50)][(15),(32),(48),(24)]`	B.	`[(15,32,48,24)][(1,5),(1,10),(1,20),(1,50)]`
C.	`[(5,10,20,50)][(1,15),(1,32),(1,48),(1,24)]`	D.	`[(15,32,48,24)][(5),(10),(20),(50)]`
E.	`[(5,10,20,50),(15,32,48,24)][(1),(1),(1),(1)]`

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`B`

Show Worked Solution

`[(15,32,48,24)]quad[(1,5),(1,10),(1,20),(1,50)]`

`qquadquad1xx4qquadqquadqquadqquadqquad\ 4xx2`

♦♦ Mean mark 34%.

`= [15 + 32 + 48 + 24qquadqquad15 xx 5 + 32 xx 10 + 48 xx 20 + 24 xx 50]`

`=[119 qquad 2555]`

`= {:[text(total number)qquadtext(total value)]:}`

`=> B`

MATRICES, FUR2 2009 VCAA 2

Tickets for the function are sold at the school office, the function hall and online.

Different prices are charged for students, teachers and parents.

Table 1 shows the number of tickets sold at each place and the total value of sales.

For this function

- student tickets cost `$x`
- teacher tickets cost `$y`
- parent tickets cost `$z`.

Use the information in Table 1 to complete the following matrix equation by inserting the missing values in the shaded boxes. (1 mark)
Use the matrix equation to find the cost of a teacher ticket to the school function. (2 marks)

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`text(35 and 2)`
`$32`

Show Worked Solution

a. `text(35 and 2)`

MARKER’S COMMENT: Simply writing the column matrix in part (b) did not earn full marks. Students must extract the required data.

b.	`[(x),(y),(z)]`	`= [(283,28,5),(35,4,2),(84,3,7)]^(-1)[(8712),(1143),(2609)]`
		`= [(27),(32),(35)]`

`:.\ text(C)text(ost of a teacher ticket = $32)`

MATRICES, FUR1 2008 VCAA 2 MC

Apples cost $3.50 per kg, bananas cost $4.20 per kg and carrots cost $1.89 per kg.

Ashley buys 3 kg of apples, 2 kg of bananas and 1 kg of carrots.

A matrix product to calculate the total cost of these items is

A. `[(3), (2), (1)] [(3.50), (4.20), (1.89)]`

B. `[(3, 2, 1)] [(3.50, 4.20, 1.89)]`

C. `[(3.50 xx 2, 4.20 xx 3, 1.89 xx 1)]`

D. `[(3), (2), (1)] [(3.50, 4.20, 1.89)]`

E. `[(3.50, 4.20, 1.89)] [(3), (2), (1)]`

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`E`

Show Worked Solution

`text(The “total” cost must be a 1 × 1 matrix,)`

`[(3.50, 4.20, 1.89)] [(3), (2), (1)]`

`= [3.50 xx 3 + 4.20 xx 2 + 1.89 xx 1]`

`= [20.79]`

`=> E`

MATRICES, FUR1 2012 VCAA 7 MC

A store has three outlets, A, B and C. These outlets sell dresses, jackets and skirts made by the fashion house Ocki.

The table below lists the number of Ocki dresses, jackets and skirts that are currently held at each outlet.

A matrix that shows the total number of Ocki dresses (D), jackets (J) and skirts (S) in each size held at the three outlets is given by

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`B`

Show Worked Solution

`text(By consolidating the 3 outlets for the)`

`text(same items in the same size.)`

`rArr B`

MATRICES, FUR1 2012 VCAA 6 MC

The table below shows the number of classes and the number of students in each class at each year level in a secondary school.

Let `F= [1 quad 1 quad 1 quad 1], \ G= [(1),(1),(1),(1)],\ M= [7 quad 5 quad 6 quad 4],\ N= [(7),(5),(6),(4)],\ P= [(22,0,0,0), (0,20,0,0), (0,0,18,0), (0,0,0,24)]`

A matrix product that displays the total number of students in Years 9 – 12 at this school is

A. `M xx P xx F`

B. `P xx G xx M`

C. `F xx P xx N`

D. `P xx N xx F`

E. `F xx N xx P`

Show Answers Only

`C`

Show Worked Solution

`text(Total student matrix will produce)`

`text(a 1 × 1 matrix.)`

`text(Consider)\ C,`

`F`	`xx`	`P`	`xx`	`N`	`=`	`FPN`
`1 xx 4`		`4 xx 4`		`4 xx 1`		`1 xx 1`

`A, B\ text(and)\ E\ text(produce undefined matrices)`

`text(and)\ D\ text(produces a 4 × 4.)`

`rArr C`