Page 16 - Focus SPM KSSM 2021 Tingkatan 5 - Maths DLP

Mathematics Form 5 Chapter 2 Matrices

26 2 Write the equations 3 a b 43 4 3 4 where
m
x
=
n
y
cd
Given that 3 –2 1 4 Q = 3 1 0 4 , find matrix Q. in the form of a, b, c, d, m and n are
–4 3
0 1
matrix,
Solution AX = B. constants, while x and y
are variables.
Given that the product of 3 –2 1 4 and Q is an identity
–4 3
matrix, therefore Q is the inverse matrix of 3 –2 1 4 . 3 Solve by multiplying
–4 3
Q = 1 3 3 –1 4 inverse matrix: x 1 d –b m Chapter 2
AX = B
3
[(–2) × 3] – [1 × (–4)] 4 –2 A AX = A B 3 4 = ad – bc –c a 43 4
n
y
–1
–1
3
Chapter 2
= – 1 3 –1 4 IX = A B
–1
2 4 –2 X = A B
–1
3
3 – 1 4
2
= –2 2 28
1
Write the following simultaneous linear equations in
Minion Pro 10pt = 1 27 the form of matrix.
2 4 5 2x = 4 – 3y
= 1 0 0 2 It is given that G = 3 –2 –3 4 and the inverse matrix of 3x + 4y = 5
0
0
3
G is 1 –3 n 4 . Find the value of m and of n. Solution
Arial 8.5 pt = 1 m 2 4 2x + 3y = 4
2 Solution 3x + 4y = 5
= 1 0 0 2 The inverse matrix of G Matrix form:
0
0
x
4
=
= 1 3 –3 –5 4 3 2 3 43 4 3 4
[4 × (–3)] – [5 × (–2)] 2 4 3 4 y 5
Kaedah Alternatif 1 –3 –5
= – 3 4 29
2 2 4
Compare with the inverse matrix given: Solve the following equation. 2
3 2
x
=
3
3
4
y
– 1 –3 –5 4 = 1 –3 n 4 3 8 6 43 4 3 4
2 2 4 m 2 4
Solution
Hence, m = –2 and n = –5 3 2
The inverse matrix of 3 8 6 4
Try Questions 18 – 22 in Try This! 2.2 1 6 –2
= 3 4
18 – 16 –8 3
3
F Using the matrix method to solve = 1 6 –2 4
simultaneous linear equations 2 –8 3
2
x
1. Simultaneous linear equations can be solved 3 4 = 1 6 –2 43 4
3
using matrix method in accordance to the steps y 2 –8 3 4
below: 1 12 + (–8)
= 3 4
1 Write simultaneous 2 –16 + 12
3 4
linear equations in ax + by = m = 1 4
the form of cx + dy = n 2 –4
2
ax + by = c. = 3 4
–2
Hence, x = 2 and y = –2.
28
02 Focus Math F5_E2021.indd 28 18/02/2021 2:32 PM