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Matrices, GEN1 2025 VCAA 26 MC

Consider the matrices \(A, B\) and \(C\) where

\begin{align*}
A=\begin{bmatrix}
2 & 0 \\
1 & 6
\end{bmatrix}, B=\begin{bmatrix}
3 \\
5
\end{bmatrix} \ \text{and}\ \  C=AB.
\end{align*}

The calculation that correctly determines element \(c_{21}\) is

  1. \(2 \times 3+0 \times 5\)
  2. \(2 \times 5+3 \times 0\)
  3. \(1 \times 3+6 \times 5\)
  4. \(1 \times 5+6 \times 3\)
Show Answers Only

\(C\)

Show Worked Solution

\(AB=\begin{bmatrix}2 & 0 \\ 1 & 6\end{bmatrix}\begin{bmatrix}3 \\ 5\end{bmatrix}=\begin{bmatrix} 6 \\ 33\end{bmatrix}\)

\(c_{12}=1 \times 3+6 \times 5=33\)

\(\Rightarrow C\)

Matrices, GEN1 2024 VCAA 26 MC

A market stall sells three types of candles.

The cost of each type of candle is shown in matrix \(C\) below.

\begin{align}
C=\left[\begin{array}{lll}
25 & 32 & 43
\end{array}\right] \end{align}

Towards the end of the day, the cost of each item is discounted by 15%.

Which one of the following expressions can be used to determine each discounted price?

  1. \(0.15C\)
  2. \(0.85C\)
  3. \(8.5C\)
  4. \(15C\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Discounted price is 85}\%\ \text{of the original price.}\)

\(\therefore, 0.85 is the multiplier}\)

\(\Rightarrow B\)

MATRICES, FUR2 2021 VCAA 1

Elena imports three brands of olive oil: Carmani (`C`) Linelli (`L`) and Ohana (`O`).

The number of 1 litre bottles of these oils sold in January 2021 is shown in matrix `J` below.

`J = {:[(2800),(1700),(2400)]:} {:(C),(L),(O):}`

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

  2. Elena expected that in February 2021 the sales of all three brands of olive oil would increase by 5%.
  3. She multiplied matrix `J` by a scalar value, `k` , to determine the expected volume of sales for February.
  4. What is the value of the scalar `k`.   (1 mark)

Show Answers Only
  1. `3 xx 1`
  2. `1.05`
Show Worked Solution

a.      `3 xx 1`
 

b.     `text{All brands} \ ↑ 5%`

 `:. k = 1.05`

MATRICES, FUR1 2009 VCAA 2 MC

The matrix `[[12,15,3],[−6,0,24]]` can also be written as
 

A.   `[12,15,3] + [−6,0,24]`

B.   `[[12],[−6]] + [[15],[0] ]+ [[3],[24]]`

C.   `[[3],[6]] [[4,5,1],[−1,0,4]]`

D.   `1/3 × [[4,5,1],[−2,0,8]]`

E.   `3 × [[4,5,1],[−2,0,8]]`

 

Show Answers Only

`E`

Show Worked Solution

`=>  E`

MATRICES, FUR1 2009 VCAA 1 MC

`3[[2,1],[0,3]] + 2[[−1,0],[2,−7]]` equals
 

A.     `[[4,3],[4,−5]]`

 

B.   `6[[1,1],[2,−4]]`

 

C.     `[[4,3],[4,2]]`

 

D.   `5[[1,1],[2,−4]]`

 

E.     `[[3,6],[7,4]]`

Show Answers Only

`A`

Show Worked Solution

`3[(2,1),(0,3)] + 2[(−1,0),(2,−7)]`

`= [(6,3),(0,9)] + [(−2,0),(4,−14)]`

`= [(4,3),(4,−5)]`

`=>  A`

MATRICES, FUR1 2012 VCAA 1 MC

`2 xx [(2,8), (4, -1), (3,5)] -[(3,7), (4,2), (2,3)] quad text (equals)`

  1. `[(1,1), (0,-3), (4,2)]`
  2. `[(-2,2), (0,-6), (2,4)]`
  3. `[(1,9), (12,0), (8,13)]`
  4. `[(1,9), (4,-4), (4,7)]`
  5. `[(-1,1), (0,-3), (1,2)]`
Show Answers Only

`D`

Show Worked Solution

`2 xx [(2,8),(4,−1),(3,5)] – [(3,7),(4,2),(2,3)]`

`= [(4,16),(8,−2),(6,10)] – [(3,7),(4,2),(2,3)]`

`= [(1,9),(4,−4),(4,7)]`

`rArr D`

MATRICES, FUR1 2006 VCAA 1 MC

The matrix `[(12, 36), (0, 24)]` is equal to

A.    `12[(0,3),(0,2)]` B.    `12[(1,3),(0,2)]`
       
C.    `12[(0,24),(−12,12)]` D.    `12[(0,24),(0,12)]`
       
E.    `12[(1,3),(−12,2)]`    
Show Answers Only

`B`

Show Worked Solution
`12[(1,3),(0,2)]` `= [(12 xx 1, 12 xx 3),(12 xx 0,12 xx 2)]`
  `= [(12,36),(0,24)]`

`rArr B`

MATRICES, FUR1 2007 VCAA 1 MC

The matrix sum `[(0, -4), (2, 5)] + [(5, 4), (-2, 2)]` is equal to
 

A.   `[(5, 0), (0, 7)]` B.   `[(0, 0), (0, 7)]`
   
C.   `[(5, -4), (0, 7)]` D.   `[(0, 5, -4,4), (2, -2, 5, 2)]`
   
E.   `[(0, -4, 5, 4), (2, 5, -2, 2)]`  
Show Answers Only

`A`

Show Worked Solution

`[(0,−4),(2,5)] + [(5,4),(−2,2)]`

`= [(0 + 5,−4 + 4),(2 + −2,5 + 2)]`

`= [(5,0),(0,7)]`

`=>  A`