Page 17 - Focus SPM KSSM 2021 Tingkatan 5 - Maths DLP

Mathematics Form 5 Chapter 2 Matrices

30 In matrix form,
43 4 3 4
Solve the following simultaneous linear equations 3 26 30 x y = 125
5
6
25
using matrix method.
x
43 4
x + 2y = 4 3 4 = 1 3 5 –30 125
3x + 4y = 6 y 130 – 180 –6 26 25
1 625 + (–750)
3
Solution = – 50 –750 + 650 4
x
4
1 –125
3
3 1 2 43 4 3 4 = – 50 –100 4 Chapter 2
=
6
3 4
y
2.5
1
4 –2
4
x
3
3 4 = 4 – 6 –3 1 43 4 = 3 4
2
Chapter 2
y
6
Hence, x = 2.50 and y = 2.00.
3
= – 1 16 + (–12) 4
2 –12 + 6 Try Questions 26 – 27 in Try This! 2.2
3 4
= – 1 4 SPM Highlights
2 –6
–2
= 3 4 Haris, Jimmy and Lim sold cakes and burgers on
school canteen day. Haris gained a profit of RM61.20
3
Hence, x = –2 and y = 3. from selling 12 cakes and 36 burgers. Jimmy sold 25
cakes while Lim sold 15 burgers. The profit difference
between selling 25 cakes and 15 burgers is RM19.50.
Calculate the profit, RMx, of selling a cake, and the
REMEMBER! profit, RMy, of selling a burger.
–2
Do not leave the answer in matrix form, 3 4 .
3
Write the answer as x = –2 and y = 3. Solution
12x + 36y = 61.20 ⇒ x + 3y = 5.10
25x – 15y = 19.50 ⇒ 5x – 3y = 3.90
Try Questions 23 – 25 in Try This! 2.2 1 3 x 5.10
3 5 –3 43 4 3 3.90 4
=
y
–3 –3 5.10
G Solving problems involving matrices 3 4 = 1(–3) – 3(5) –5 1 43 3.90 4
x
3
1
y
1 –15.30 – 11.70
3
31 = – 18 –25.50 + 3.90 4
Mr Salleh has stalls in market A and market B. The = – 1 –27.00 4
3
table below shows the number of packets of nasi lemak 18 –21.60
and mi goreng sold in both markets in a day. = 3 1.50 4
1.20
Market Nasi lemak Mi goreng Hence, x = 1.50, y = 1.20.
A 52 60
B 48 40
Try This! 2.2
It is given that Mr Salleh earned RM250 in market
A and RM200 in Market B on that day. Calculate the 1. Determine whether the following pairs of matrices
profit RMx of selling a packet of nasi lemak, and the can be added and subtracted.
profit, RMy, of selling a packet of mi goreng. (a) 3 0 –3 1 4 3 5 6 –1 4
,
8
9
7
2 10 4
Solution (b) 3 –2 5 4 3 4
3
,
52x + 60y = 250 ⇒ 26x + 30y = 125 1 6 8
48x + 40y = 200 ⇒ 6x + 5y = 25 (c) [11 4], [7 2]
29
02 Focus Math F5_E2021.indd 29 18/02/2021 2:32 PM