Page 8 - Focus SPM KSSM 2021 Tingkatan 5 - Maths DLP

Mathematics Form 5 Chapter 2 Matrices

(b) Ali’s year-end exam scores for English, 2. The corresponding elements can be added or
Mathematics and Science are 76, 83 and 80 subtracted to obtain a single matrix of the same
respectively. order. For example,
(c) The table below shows the selling prices of rice a b p q a ± p b ± q
±
=
by brand. 3 c d 4 3 r s 4 3 c ± r d ± s 4
Selling price
Rice
5 kg 10 kg 6
Brand A RM26 RM45 Determine whether the following pairs of matrices
Brand B RM18 RM32 can be added and subtracted. Chapter 2
–7
Brand C RM13 RM20 (a) [1 2], 3 4
5
2. Determine the order of the following matrices. 0 4 8 9
Chapter 2
,
(a) [–3 11] (b) 3 1 –3 4 3 11 6 4
(b) 3 3 –7 2 4 Solution
19
8
6
(c) 3 1 4 4 (a) Cannot. It is because both matrices are of
different orders.
2
5
(b) Can. It is because both matrices are of the same
3 5 0 1 4 order.
3. Given that matrix A = 13 8 –4 , determine
–1 2 9 7
(a) the element at the first row and 3 column.
rd
(b) a 22 . Express each of the following as a single matrix.
(c) a 31 . (a) [7 5] + [2 –11]
–
4. Determine whether each of the following pairs of (b) 3 2 3 4 3 1 9 4
matrices is equal. 1 –2 6 –5
(a) 3 10 –2 1 4 3 10 2 1 4 Solution
,
5
8
7
5
7
8
(a) [7 5] + [2 –11] = 37 + 2 5 + (–11)4
3 4 = [9 –6]
3
(b) [3 4 9], 4
3 – 9
3
9 (b) 3 2 1 –2 4 3 1 9 4 3 2 – 1 (–2) – (–5) 4
=
–
1 – 6
6 –5
0.5 3 4
7
(c) 3 4 , 1 7 1 –6
2 = 3 –5 3 4
5. It is given that matrix P = 3 8 x 4 and matrix 8
–7 9
8
Q = 3 2x + y –2 4 . Determine the values of x and y 12 7 2 3
9
if P = Q. Given that matrices M = 3 –3 5 4 , N = 3 9 –4 4 and
P = 3 1 6 4 , calculate
–10 8
1
3 2 4 x + 3 4 2 0.25 2
6. It is given that 0 2y 4z – x = 3 0 7 5 4 . (a) M + N
Determine the values of x, y and z. (b) N – P
Solution
2.2 Basic Operation on Matrices (a) M + N = 3 12 7 4 3 2 3 4
+
9 –4
–3 5
= 3 12 + 2 7 + 3 4
A Adding and subtracting matrices –3 + 9 5 + (–4)
1. Addition and subtraction can only be performed = 3 14 10 4
1
6
on matrices that have the same order.
20
02 Focus Math F5_E2021.indd 20 18/02/2021 2:32 PM