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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. 0.15 \(C\)
  2. 0.85 \(C\)
  3. 8.5 \(C\)
  4. 15 \(C\)
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\(B\)

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. Write down the value of the scalar `k`.  (1 mark)
       `k =`
     
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  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]]`

 

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`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]]`

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`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)]`
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`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)]`    
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`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)]`  
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`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`