Page 26 - Top Class F5 - Mathematics (Chapter 2)

Mathematics Form 5 Chapter 2 Matrices

     Answer / Jawapan:
8
4 5 x
(b) 2 3 y = 5 (a) Inverse matrix of  2 –10 
1 –4

3 –5 8
1
  = 4(3) – 5(2) –2 4 5 Matriks songsang bagi  2 –10 
x
 
y
1 –1 1 –4

=   1 –4 10
2 4 = 2(–4) – (–10)(1) –1 2 
  1 –4 10 
1
–

= 2 =
2 2 –1 2
–4 10
1 = m  
Hence / Maka, x = – , y = 2 n 2
2
1
Hence / Maka, m = , n = –1
4. Theme Park Ria sells two types of tickets, theme park and 2
water park. Mr Watson paid RM435 to buy 5 theme park
   
tickets and 6 water park tickets while Mr Ho paid RM195 (b)  2 –10 x = 1
to buy 2 theme park tickets and 3 water park tickets. Using 1 –4 y 2
matrix method, calculate the price, in RM, of a theme park   1  –4 10 1
 
x
ticket and of a water park ticket. y = 2(–4) – (–10)(1) –1 2 2
Taman Tema Ria menjual dua jenis tiket, taman tema dan 1 16
taman tema air. Encik Watson membayar RM435 untuk =  
membeli 5 keping tiket taman tema dan 6 keping tiket taman 2 3
8
tema air manakala Encik Ho membayar RM195 untuk membeli =  
2 keping tiket taman tema dan 3 keping tiket taman tema air. 1.5
Menggunakan kaedah matriks, hitung harga sekeping tiket
taman tema dan sekeping tiket taman tema air. Hence / Maka, x = 8, y = 1.5
Answer / Jawapan: 6. Ali, Osman and Tan went to a market to buy fruits. Ali
Let / Katakan SPM paid RM13 to buy 2 kg of banana and 1 kg of watermelon.
x = the price of a theme park ticket 2019 Osman bought 4 kg of banana while Tan bought 3 kg
harga sekeping tiket taman tema of watermelon. The difference in price between 4 kg of
y = the price of a water park ticket banana and 3 kg of watermelon is RM11. The price of a
harga sekeping tiket taman tema air kilogram of banana is higher than the price of a kilogram
5x + 6y = 435 of watermelon. Using matrix method, calculate the prices
2x + 3y = 195 of a kilogram of banana and a kilogram of watermelon.
435
     Ali, Osman dan Tan pergi ke pasar untuk membeli buah-buahan.
5 6 x

=
Ali membayar RM13 untuk 2 kg pisang dan 1 kg tembikai.
195
2 3 y
  1  3 –6 435 Osman membeli 4 kg pisang manakala Tan membeli 3 kg
 
x
y = 5(3) – 6(2) –2 5 195 tembikai. Beza harga antara 4 kg pisang dan 3 kg tembikai ialah
1 135 RM11. Harga sekilogram pisang adalah lebih tinggi daripada
=   harga sekilogram tembikai. Menggunakan kaedah matriks,
3 105 hitung harga sekilogram pisang dan sekilogram tembikai.
45
 
= 35 Answer / Jawapan:
Hence, x = 45 and y = 35. The price of a theme park ticket Let / Katakan
is RM45 and the price of a water park ticket is RM35. x = the price of a kilogram of banana
Maka, x = 45 dan y = 35. Harga sekeping tiket taman tema ialah harga sekilogram pisang
RM45 dan harga sekeping tiket taman tema air ialah RM35. y = the price of a kilogram of watermelon
harga sekilogram tembikai
1 0
5. It is given that R =  2 –10  , S = m  –4 10  and I =   . 2x + y = 13
SPM 1 –4 n 2 0 1 4x – 3y = 11
2018 2 –10 –4 10 1 0
Diberi R =  1 –4  , S = m  n 2  dan I =   . 2 1 x 13
0 1
   
(a) Find the value of m and of n if RS = I.  4 –3 y = 11
Cari nilai m dan nilai n jika RS = I. x 1 –3 –1 13
 
(b) Write the following simultaneous linear equations in   = 2(–3) – 1(4)  –4 2 11
y
the form of matrix:
 
Tuliskan persamaan linear serentak berikut dalam bentuk = – 1 –50
matriks: 10 –30
5
2x – 10y = 1  
x – 4y = 2 = 3
Hence, by using matrix method, calculate the value of
x and of y. Hence, x = 5, y = 3. The price of a kilogram of banana is
Seterusnya, menggunakan kaedah matriks, hitung nilai x RM5 and the price of a kilogram of watermelon is RM3.
dan nilai y. Maka, x = 5, y = 3. Harga sekilogram pisang ialah RM5 dan
harga sekilogram tembikai ialah RM3.
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