Page 12 - Focus SPM KSSM 2021 Tingkatan 5 - Maths DLP

Mathematics Form 5 Chapter 2 Matrices

–1
C Multiplying two matrices (b) 3 10 3 43 4
6
–4 7
1. To multiply two matrices, A and B, the number Order: 2 × 2 2 × 1
of columns in matrix A must be the same as the
number of rows in matrix B, which is Same
A × B = AB Hence, the pair of matrices can be multiplied
Order: m × n n × p m × p and the order of the product is 2 × 1.
5
3 4
Number of = Number of (c) [12 4 7] 0 Chapter 2
columns in A rows in B 9

The order of AB is m × p Order: 1 × 3 3 × 1
Chapter 2
2. In multiplication of two matrices, each element Same
in the rows of the first matrix is multiplied by Hence, the pair of matrices can be multiplied
corresponding element in the columns of the and the order of the product is 1 × 1.
Minion Pro 10pt = 1 second matrix. Then, sum up the results of –2
2 multiplication of these elements. (d) 3 4 [6 1]
3
p
(a) [a b] 3 4 = [ap + bq] Order: 2 × 1 1 × 2
1 q
Arial 8.5 pt =
2 1 × 2 2 × 1 1 × 1 Same
Hence, the pair of matrices can be multiplied
(b) 3 a b 43 p q s 4 3 ap + br aq + bs 4 and the order of the product is 2 × 2.
=
c d
cp + dr cq + ds
r
2 × 2 2 × 2 2 × 2 17
Find the product of each of the following.
a b
3 4 q 3 4 5
ap + bq
p
(c) c d 3 4 = cp + dp (a) 3 4 [1 2]
e f ep + fq –4
43
3 × 2 2 × 1 3 × 1 8 –1 6 0
1
(b) 3 2 3 –2 4
16 9 4
Determine whether the following pairs of matrices (c) [3 –4] 3 4
12
can be multiplied. If yes, state the order of the Solution
product. 5
7
–1
–4
(a) 3 43 9 11 4 (b) 3 10 3 43 4 (a) 3 4 [1 2]
6
–4 7
0 8
2
= 3 5 × 1 5 × 2 4
–4 × 1 –4 × 2
3 4 –2
5
(c) [12 4 7] 0 (d) 3 4 [6 1] = 3 5 10 4
9 3 –4 –8
Solution 8 –1 6 43 0
1
7
(a) 3 43 9 11 4 (b) 3 2 3 –2 4
4
0 8
2
Order: 2 × 1 2 × 2 = 3 (8 × 0) + (–1 × 1) + (6 × 4) 4
(2 × 0) + (3 × 1) + (–2 × 4)
Not the same = 3 0 – 1 + 24 4
0 + 3 – 8
Hence, the pair of matrices cannot be multiplied. 23
= 3 4
–5
24

02 Focus Math F5_E2021.indd 24 18/02/2021 2:32 PM