Soalan 15:
$$ \text { (a) Diberi bahawa }\left[\begin{array}{cc} 7 & -2 \\ x+3 & 4 \end{array}\right]=\left[\begin{array}{cc} 7 & 5 y \\ -1 & 4 \end{array}\right] \text {. } $$
Penyelesaian:
(a)
$$ \begin{aligned} {\left[\begin{array}{cc} 7 & -2 \\ x+3 & 4 \end{array}\right] } & =\left[\begin{array}{cc} 7 & 5 y \\ -1 & 4 \end{array}\right] \\ x+3 & =-1 \\ x & =-4 \\ 5 y & =-2 \\ y & =-\frac{2}{5} \end{aligned} $$
(b)(i)
$$ \begin{aligned} &3 x+2 y=55 \sim \text { (Lily) }\\ &\begin{aligned} & 4 x+3 y=55+20 \sim \text { (Kelly) } \\ & 4 x+3 y=75 \end{aligned} \end{aligned} $$
$$ \begin{aligned} & {\left[\begin{array}{ll} 3 & 2 \\ 4 & 3 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{l} 55 \\ 75 \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\frac{1}{(3)(3)-(2)(4)}\left[\begin{array}{cc} 3 & -2 \\ -4 & 3 \end{array}\right]\left[\begin{array}{l} 55 \\ 75 \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{l} (3 \times 55)+(-2 \times 75) \\ (-4 \times 55)+(3 \times 75) \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{c} 165-150 \\ -220+225 \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{c} 15 \\ 5 \end{array}\right]} \\ & \text { Harga sekotak sushi }=\text { RM15 } \\ & \text { Harga seketul ayam goreng = RM5 } \end{aligned} $$
(b)(ii)
$$ \text { sekotak sushi pada harga diskaun }=15 \times \frac{80}{100}=\text { RM12 } $$
$$ \text { seketul ayam goreng pada harga diskaun }=5 \times \frac{60}{100}=\text { RM3 } $$
$$ \begin{aligned} &2 \text { kotak sushi dan } 8 \text { ketul ayam goreng dengan menggunakan pendaraban matriks }\\ &\begin{aligned} & =\left[\begin{array}{ll} 2 & 8 \end{array}\right]\left[\begin{array}{c} 12 \\ 3 \end{array}\right] \\ & =[2 \times 12+8 \times 3] \\ & =[48] \end{aligned} \end{aligned} $$
$$ \text { Maka, Jane mempunyai wang cukup kerana hanya RM48 diperlukan. } $$
$$ \text { (a) Diberi bahawa }\left[\begin{array}{cc} 7 & -2 \\ x+3 & 4 \end{array}\right]=\left[\begin{array}{cc} 7 & 5 y \\ -1 & 4 \end{array}\right] \text {. } $$
Tentukan nilai dan nilai .[2 markah]
(b) Sebuah pasar raya menjual sushi dan ayam goreng.
(i) Lily membelaniakan RM55 untuk 3 kotak sushi dan 2 ketul ayam goreng. Kelly membelaniakan lebih RM20 berbanding Lily untuk 4 kotak sushi dan 3 ketul ayam goreng. Menggunakan kaedah matriks, hitung harga sekotak sushi dan seketul ayam goreng itu.
[5 markah]
(ii) Rajah 9 menuniukkan diskaun yang diberi oleh pasar raya itu pada satu hari tertentu.
Jane mempunyai RM50. Dia ingin membeli 2 kotak sushi dan 8 ketul ayam. Adakah dia mempunyai wang yang cukup untuk membeli makanan itu pada harga diskaun?
Justifikasikan jawapan anda dengan menggunakan pendaraban matriks.
[3 markah]
Penyelesaian:
(a)
$$ \begin{aligned} {\left[\begin{array}{cc} 7 & -2 \\ x+3 & 4 \end{array}\right] } & =\left[\begin{array}{cc} 7 & 5 y \\ -1 & 4 \end{array}\right] \\ x+3 & =-1 \\ x & =-4 \\ 5 y & =-2 \\ y & =-\frac{2}{5} \end{aligned} $$
(b)(i)
$$ \begin{aligned} &3 x+2 y=55 \sim \text { (Lily) }\\ &\begin{aligned} & 4 x+3 y=55+20 \sim \text { (Kelly) } \\ & 4 x+3 y=75 \end{aligned} \end{aligned} $$
$$ \begin{aligned} & {\left[\begin{array}{ll} 3 & 2 \\ 4 & 3 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{l} 55 \\ 75 \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\frac{1}{(3)(3)-(2)(4)}\left[\begin{array}{cc} 3 & -2 \\ -4 & 3 \end{array}\right]\left[\begin{array}{l} 55 \\ 75 \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{l} (3 \times 55)+(-2 \times 75) \\ (-4 \times 55)+(3 \times 75) \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{c} 165-150 \\ -220+225 \end{array}\right]} \\ & {\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{c} 15 \\ 5 \end{array}\right]} \\ & \text { Harga sekotak sushi }=\text { RM15 } \\ & \text { Harga seketul ayam goreng = RM5 } \end{aligned} $$
(b)(ii)
$$ \text { sekotak sushi pada harga diskaun }=15 \times \frac{80}{100}=\text { RM12 } $$
$$ \text { seketul ayam goreng pada harga diskaun }=5 \times \frac{60}{100}=\text { RM3 } $$
$$ \begin{aligned} &2 \text { kotak sushi dan } 8 \text { ketul ayam goreng dengan menggunakan pendaraban matriks }\\ &\begin{aligned} & =\left[\begin{array}{ll} 2 & 8 \end{array}\right]\left[\begin{array}{c} 12 \\ 3 \end{array}\right] \\ & =[2 \times 12+8 \times 3] \\ & =[48] \end{aligned} \end{aligned} $$
$$ \text { Maka, Jane mempunyai wang cukup kerana hanya RM48 diperlukan. } $$