Page 9 - Focus SPM KSSM 2021 Tingkatan 5 - Maths DLP

Mathematics Form 5 Chapter 2 Matrices

(b) N – P = 3 2 3 4 3 1 6 4 Solution:
–
9 –4
8
–10
[98 92] – [45 50] + [50 45]
= 3 2 – 1 3 – 6 4 = [103 87]
The final stocks of flour and sugar are 103 and 87
9 – (–10)
–4 – 8
respectively.
= 3 1 –3 4 Try this HOTS Question
19 –12
The table below shows the scores of two teams in
9 a competition.
2
16
8
=
Given that 3 4 + S – 3 4 3 4 , find matrix S. First Second Chapter 2
3
4
–5
Team
round round Penalty
Solution A 15 17 2
Chapter 2
8
16
2
3 4 + S – 3 4 3 4 B 15 19 3
=
–5
4
3
16
8
2
+
S = 3 4 3 4 3 4 It is given that the penalty will be deducted from
–
–5
4
3
the total score of both rounds, and the team with
8 – 16 + 2
= 3 3 – (–5) + 4 4 a total score above 30 will be eligible for final
round. Which team will proceed to final round?
–6
= 3 4 Find your answer using matrix method.
12
Answer: Team B
10
–
=
Given that 3 3 x 4 3 1 2x 4 3 2 –1 4 , find
y 8
7 0
4y + 1 8
the value of x and of y. B Multiplying a matrix by a number
Solution 1. Multiplying a matrix by a number is known as
3 3 x 4 3 1 2x 4 3 2 –1 4 scalar multiplication.
=
–
7 0
4y + 1 8
y 8
Compare the corresponding elements: 2. The process of multiplying matrix A by a number
x – 2x = –1 n is a repeated addition.
–x = –1 nA = A + A + A + … + A
x = 1 n times
4y + 1 – y = 7 3. To multiply a matrix by a number, we multiply
3y = 6 each element in the matrix by the number.
y = 2 a b na nb
n 3 4 3 4
=
Try Questions 1 – 4 in Try This! 2.2 c d nc nd
Example of HOTS 4. Addition of matrices obeys the:
HOTS Question
(a) Commutative Law
The table below shows the stock records of flour and A + B = B + A
sugar sold at Ismail’s shop.
(b) Associative Law
Number of packets (A + B) + C = A + (B + C)
Flour Sugar 5. Addition and subtraction of matrices obey the
Stock 98 92 Distributive Law:
Sold 45 50 n(A + B) = nA + nB
Received 50 45 n(A – B) = nA – nB
Calculate the final stock for flour and sugar.
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