4.5.1 Pendaraban Dua Matriks (Contoh Soalan)


4.5.1 Pendaraban Dua Matriks (Contoh Soalan)
 
Soalan 1:
Cari hasil darab bagi setiap pasangan matriks yang berikut.
(a)  ( 1       5       2 ) ( 2 4 3 ) (b)  ( 2 8 3 1 ) ( 1 0 4 2 )
(c)  ( 3 5 ) ( 2     6 ) (d)  ( 0 4 1 3 ) ( 7 2 ) (e)  ( 7      4 ) ( 2 0 1 3 )

Penyelesaian:
(a)  ( 1       5       2 ) ( 2 4 3 ) Analisis  matriks 1 × 3   dan  3 × 1               =  matriks   1 × 1 = ( 1 × 2       5 × 4       2 × 3 ) = ( 2 + 20 + 6 ) = ( 28 )

(b)  ( 2 8 3 1 ) ( 1 0 4 2 ) Analisis  matriks 2 × 2   dan  2 × 2                = matriks  2 × 2 = ( 2 × 1 + 8 × 4     2 × 0 + 8 × 2 3 × 1 + 1 × 4     3 × 0 + 1 × 2 ) = ( 34 16 1 2 )

(c) ( 3 5 ) ( 2     6 ) Analisis  matriks 2 × 1   dan  1 × 2                 = matriks  2 × 2 = ( 3 × 2    3 × 6 5 × 2      5 × 6 ) = ( 6 18 10 30 )

(d) ( 0 4 1 3 ) ( 7 2 ) Analisis  matriks 2 × 2   dan  2 × 1                   = matriks   2 × 1 = ( 0 × 7 + 4 × 2 1 × 7 + 3 × 2 ) = ( 8 13 )

(e) ( 7      4 ) ( 2 0 1 3 ) Analisis  matriks 1 × 2   dan  2 × 2                 = matriks   1 × 2 = ( 7 × 2 + ( 4 × 1 )       7 × 0 + ( 4 × 3 ) ) = ( 14 + 4       0 12 ) = ( 10      12 )



Contoh 2:
Cari nilai mdan nilai n dalam setiap persamaan matriks yang berikut:
( a ) ( 3 m ) ( 1      n ) = ( 3 12 2 8 )
( b ) ( m 2 3 1 ) ( 2 n ) = ( 12 4 + 2 n )
( c ) ( m 3 1 1 ) ( 1 2 4 n ) = ( 14 11 5 3 )
 
Penyelesaian:
(a) ( 3 m ) ( 1     4 ) = ( 3 12 2 n ) ( 3 12 m 4 m ) = ( 3 12 2 n )
= –2,
4m = n
4 (–2) = n
= –8

(b) ( m 2 3 1 ) ( 2 n ) = ( 12 4 + 2 n ) ( 2 m + 2 n 6 + n ) = ( 12 4 + 2 n )  
–6 + n = 4 + 2n
= –10
2m + 2n = 12
2m + 2 (–10) = 12
2m – 20 = 12
2m = 32
m = 16

(c) ( m 3 1 1 ) ( 1 2 4 n ) = ( 14 11 5 3 ) ( m + ( 12 ) 2 m + ( 3 n ) 1 + 4 2 + n ) = ( 14 11 5 3 )
m – 12 = –14
m = –2
m = 2
–2 + n = 3
n = 5

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