Perkalian+Matriks
Transcript of Perkalian+Matriks
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PERKALIAN PERKALIAN MATRIKSMATRIKS
04/12/23 1Padiya,S.Pd.
PERKALIAN MATRIKS
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04/12/23 Padiya,S.Pd. 2
Setelah menyaksikan tayangan ini diharapkan siswa dapat :
Melakukan perhitungan perkalian maktriks dengan skalar dan perkalian
dua buah matriks .
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04/12/23 Padiya,S.Pd. 3
A. Perkalian matriks dengan
bilangan (skalar)B. Perkalian matriks dengan
matriks
(Pilih/klik salah satu materi di atas)
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04/12/23 4Padiya,S.Pd.
A.Perkalian skalar dengan matriks
Jika k suatu bilangan (skalar)maka perkalian k dengan matriks A
ditulis k.A, adalah matriks yang elemennya diperoleh
dari hasil kali k dengan setiap elemenmatriks A
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04/12/23 Padiya,S.Pd. 5
Jika matriks A = a b
c d
maka matriks k.A = k.a k.b
k.c k.d
dengan k suatu bilangan (skalar)
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04/12/23 Padiya,S.Pd. 6
Diketahui Matriks A =
Tentukan elemen-elemen matriks :a. 5A b. -4A
1 2 -3
3 4 -1
Jawab:
a. 5A =
Contoh :
5 =5
15 20
10 -15
-5
1
3 4
2 -3
-1
5x15x25x(-3)5x35x45x(-1)
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04/12/23 Padiya,S.Pd. 7
b. -4A = -41 2 -3
3 4 -1
=
-4x1
-4
-4x2
-8
-4x(-3)
12
-4x3
-12
-4x4
-16
-4x(-1)
4
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EVALUASI1. Diketahui matriks-matriks :
2 3
1 6A
3 4,
1 2B
Tentukan matriks-matriks berikut :a.3A e. 6A b.5A f. Apakah 3A + 5A = 8A?c.8A g. Apakah 2(3A) = 6A ? d.2(3A)
04/12/23 8Padiya,S.Pd.
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EVALUASI2. Diketahui matriks-matriks :
2 3
1 6A
3 4,
1 2B
Tentukan matriks-matriks berikut :a.A + B d. 3A + 3B b.3A e. 3(A + B)c.3B f. Apakah 3A + 3B = 3(A+B)?
04/12/23 9Padiya,S.Pd.
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04/12/23 Padiya,S.Pd. 10
Perkalian dua matriks A dan B (ditulis A x B) adalah matriks yang didapat dengan
mengalikan elemen baris matriks A dengan elemen kolom matriks B, kemudian hasilnya
dijumlahkan
Matriks A dan matriks B dapat dijkalikan jika banyaknya kolom matriks A sama dengan
banyaknya baris matriks B.
Ordo matriks hasil perkalian AxB adalah banyak baris matriks A x banyak kolom matriks B
Amxn x Bnxp = Cmxp
B. Perkalian matriks dengan matriks
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04/12/23 Padiya,S.Pd. 11
PERHATIKAN ILUSTRASI BERIKUT
A4X3
Setelah digabung menghasilkan :
C4x2
x B3X2
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04/12/23 Padiya,S.Pd. 12
Contoh 1:
x
=1x5 + 2x6
1 2
3 4
5
6
7
8
1x7 + 2x8
3x5 + 4x6 3x7 + 4x8
=17 23
39 53
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04/12/23 Padiya,S.Pd. 13
Contoh 2:
2 1 3
-1 5 4X
3
1
-2
4
3
-1
=
2x3 + 1x1 + 3x(-2) 2x4 + 1x3 + 3x(-1)
-1x3 + 5x1 + 4x(-2) -1x3 + 5x3 + 4x(-2)
=1 8
-6 4
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04/12/23 Padiya,S.Pd. 14
Contoh 3:Diketahui matriks-matriks :
3 2
4 1A
2 4,
1 3B
Tentukan matriks-matriks berikut :
a. A2
b. B2
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04/12/23 Padiya,S.Pd. 15
Jawab :
a. A2 = A x A = 3 -2
4 1x
3
4
-2
1
=
=
3x3 + (-2)x4 3x(-2) + (-2)x1
4x3 + 1x4 4x(-2) + 1x1
1 -8
16 -7
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04/12/23 Padiya,S.Pd. 16
Jawab :
b. B2 = B x B = 2 4
-1 3x
2
-1
4
3
=
=
2x2 + 4x(-1) 2x4 + 4x3
-1x2 + 3x(-1) -1x4 + 3x3
0 20
-5 5
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EVALUASI1. Diketahui matriks-matriks :
2 3
1 6A
3 4,
1 2B
2 0,
5 7C
Tentukan matriks-matriks berikut :a.A x B e. Apakah A x B = B x A ?b.B x A f. Apakah A x C = C x A ?c.A x C g. Kesimpulan apa yang d.C x A dapat diambil ?
04/12/23 17Padiya,S.Pd.
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EVALUASI2. Diketahui matriks-matriks :
3 4
1 2A
2 0,
5 7B
Tentukan matriks-matriks berikut :a.At e. (A x B)t
b.Bt f. (B x A)t
c.At x Bt g. Apakah ada hasil yang sama?d.Bt x At h. Jika ada, apa pendapatmu?
04/12/23 18Padiya,S.Pd.
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04/12/23 19Padiya,S.Pd.
Thank YouGood Luck