4.2.1 Matriks Sama (Contoh Soalan)


4.2.1 Matriks Sama (Contoh Soalan)
Contoh 1:
( 1 x + 2 4 y 1 ) = ( 1 3 2 1 )

Penyelesaian:
( 1 x + 2 4 y 1 ) = ( 1 3 2 1 ) x + 2 = 3 x = 1 4 y = 2 y = 2 y = 2


Contoh 2:
Hitung nilai p dan nilai q dalam setiap persamaan matriks yang berikut:
(a) ( 3 2 p + q p 3 ) = ( 3 1 8 2 q 3 ) (b) ( 10 0 5 p 8 1 ) = ( p 2 q 0 4 q 1 )
 
Penyelesaian:
(a) ( 3 2 p + q p 3 ) = ( 3 1 8 2 q 3 )
2p + q = 1
= 1 – 2p ----(1)
= 8 – 2q ----(2)

Gantikan (1) ke dalam (2),
= 8 – 2 (1 – 2p)
= 8 – 2 +  4p
– 4p = 6
–3p = 6
= –2

Gantikan = –2 ke dalam (1),
= 1 – 2(–2)
= 5


(b) ( 10 0 5 p 8 1 ) = ( p 2 q 0 4 q 1 )
10 = p – 2q
= 10 + 2q ----(1)
5p – 8 = –4q ----(2)

Gantikan (1) ke dalam (2),
5 (10 + 2q) – 8 = –4q
50 + 10q – 8 = –4q
14q = –42
= –3

Gantikan = –3 ke dalam (1),
= 10 + 2(–3)
= 4

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