Operasi Matrik (Penjumlahan, Pengurangan, Perkalian Dan Transpose Matrik) _ Harianja Uniks

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HARIANJA UNIKS

Situs Informatika,Elektronika Komputer

HOME UMUM SISTEM OPERASI OFFICE ELEKTRONIKA DASAR FISIKA

HANDPHONE LAPTOP

HomeAljabar Linear Operasi Matrik (Penjumlahan, Pengurangan, Perkalian

dan Transpose Matrik)

HARI ALMAKKY TUESDAY, JANUARY 13, 2015

ALJABAR LINEAR

A.

Penjumlahan dan Pengurangan Matriks

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Operasi Matrik (Penjumlahan, Pengurangan,

Perkalian dan Transpose Matrik)

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2/8



syarat kedua matriks tersebut harus

berorde sama. Jika kedua matriks

ordenya tidak sama maka mustahil

keduanya dapat dijumlahkan. Cara

penjumlahannya adalah dengan

menjumlahkan entri entri / elemen

elemen kedua matriks yang bersesuaian.

Contoh :

A = [1 2 3 4 5 6 7 8 9 ] 3 X 3

B = [ 5 2 -3 6 5 6 7 -1 3 ] 3 X 3

Carilah :

A + B

A B

Jawab :

A + B = [ 1+5 2+2 3+(-3) 4+6 5+5 6+6 7+7 8+

(-1) 9+3 ]

A + B = [ 6 4 0 10 10 12 14 7 12 ]

A - B = [ 1-5 2-2 3-(-3) 4-6 5-5 6-6 7-7 8-(-1) 9-3

]

A - B = [ -4 0 6 -2 0 0 0 9 6 ]

Penjumlahan matrik menggunakan matlab

>> A = [1 2 34 5 67 8 9]

A =

1 2 3

4 5 6

7 8 9

>> B =[5 2 -36 5 67 -1 3]

B =

5 2 -3

6 5 6

7 -1 3

>>C =[1 -2 37 5 9]

C =

1 -2 3

7 5 9

>> A+B

Ans =

Minor, Kofaktor, Matrik

Kofaktor dan Adjoin

Matrik

1

Penyelesaian Sistem

Persamaan Linear

Dengan Metode Cramer

2

Mengenal Matematika

Diskrit Atau Matematika

Informatika

3

Perkalian dan

Pembagian Bilangan

Biner

4

Penjumlahan dan

Pengurangan BilanganBiner

5

Operasi Matrik

(Penjumlahan,

Pengurangan, Perkalian

dan Transpose Matrik)

6

Usaha, Energi Kinetik,

Energi Potensial dan

Energi Mekanik

7

Cara Mengukur Nilai

Tahanan Resistor

Menggunakan

Multimeter

8

Konversi Rangkaian

AND OR NOT ke NAND

dan NOR

9

Soal Soal Latihan

Fisika Yang Berkaitan

Dengan Hukum Newton

10
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3/8



6 4 0

10 10 12

14 7 12

>> A + C

??? Error using == > +

Matrix dimensions must agree

Ini artinya dimensi atau ukuran dari kedua matrik yangingin dijumlahkan tidak sama (pesan kesalahan dari

matlab)

Dengan cara yang sama kita juga dapat lakukan untuk

mencari hasil pengurangan dari matrik.

B. perkalian matrik

Ada dua macam perkalian matrik, yaitu :

1. Perkalian skalar

2. Perkalian matrik dengan matrikPerkalian skalar : adalah perkalian matrik dengan

bilangan skalar. Caranya dengan mengalikan semua

elemen matriks dengan bilangan skalar tersebut.

Contoh :

A = [ -4 0 6 -2 0 0 0 9 6 ]

Maka 5 A adalah :

A = [ -20 0 30 -10 0 0 0 45 30 ]

Perkalian matriks dengan matriks.Dua buah matrik dapat diperkalikan satu sama lain

dengan syarat jumlah kolom pada matrik pertama sama

dengan jumlah baris pada matriks kedua. Jika syarat ini

tidak terpenuhi maka perkalian matriks dengan matrik

tidak dapat dilaksanakan.

Dalam perkalian matrik dengan matrik berlaku rumus:

(m x n ) ( n x p ) = (m x p)

Jadi kalau ada matriks ( 2 x 3 ) dikalikan denganmatriks (3 x 2 ) , maka akan dihasilkan sebuah matriks

baru dengan orde (2 x 2)

Contoh :

A= [ 1 -2 3 7 5 9 ]2x3

B= [ 5 2 6 5 7 -1 ]3x2

Hitunglah :

A.B

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B.A

Jawab :

A . B

A= [ 1 -2 3 7 5 9 ]2x3 X B= [ 5 2 6 5 7 -1

]3x2

A.B = [ (1x5) + (-2)6 + (3x7) (1x2)+ (-2)5+(3x1)

(7x5)+ (5x6)+ (9x7) (7x2)+(5x5)+ (9 x (-1) ]2x2A.B = [ (5)+(-12)+(21) (2)+ (-10)+(-3) (35)+

(30)+ (63) (14)+(25)+ (-9 ) ]2x2

A.B = [ 14 -11 128 30 ]2x2

B.A = (3 X 2) (2 X 3) = (3 X 3) Cobalah buktikan

sendiri

Perkalian matrik menggunakan matlab

>>C =[1 -2 37 5 9]

C =1 -2 3

7 5 9

>> D =[5 26 57 -1]

D =

5 2

6 5

7 -1

>> C * DAns =

14 -11

128 30

Jika kedua matrik tidak memenuhi syarat untuk

dikalikan maka matlab juga akan memberikan pesan

kesalahan sebagai berikut:

??? Error using == > *

Inner matrix dimensions must agreeUntuk perkalian skalar kita juga dapat lakukan sebagai

berikut

>> K = 5

K =

5

>> Q = [-4 0 6-2 0 00 9 6]

Q =


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-4 0 6

-2 0 0

0 9 6

>> K * Q

Ans =

-20 0 30

-10 0 00 45 30

C. TRANSPOSE MATRIKS

Jika baris dan kolom dari suatu matriks dipertukarkan,

maksudnya :

Baris pertama menjadi kolom pertama

Baris kedua menjadi kolom kedua

Baris ketiga menjadi kolom ketiga

Dan seterusnyaMaka kita akan mendapatkan sebuah matriks baru yang

dinamakan matrik transpose. Matriks transpose sering

diberi symbol AT , BT atau .

Contoh :

A= [ 1 -2 3 7 5 9 ]2x3

B= [ 5 2 6 5 7 -1 ]3x2

Carilah matriks transpose dari:

1. A Transpose2. B Transpose

3. (A . B) Transpose

Tranpose matrik dengan matlab

Pertama kita buat sebuah matrik A sebagai berikut:

>>A=[2 6 45 1 95 2 9]

A =

2 6 4

5 1 95 2 9

Cari transpose matrik A dengan perintah berikut:

>> A

Ans =

2 5 5

6 1 2

4 9 9


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3 Tweet

Jika transpose matrik A kita transpose kembali akan

menghasilkan matrik A

>> A

Ans =

2 6 4

5 1 9

5 2 9Jadi A = A

Baca juga: Transpose matriks dan determinan

matriks

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Operasi Matrik (Penjumlahan, Pengurangan, Perkalian Dan Transpose Matrik) _ Harianja Uniks