Tugas Fisika Komputasi

Soal.

1. Terdapat beberapa matrik sebagai berikut :

A=[4 6 19 0 3 ] ,

B=[4 68 −55 −1 ]

a. AxB

b. AxAT

c. BxBT

2. Hitung perkalian matrik dibawah ini :

a. [a11 a12 a13

a21 a22 a23

a31 a32 a33]×[a11 a12 a13

a21 a22 a23

a31 a32 a33]

b. Tentukan formula dan syarat perkalian matrik ( sebagai algoritma

pembuatan program perkalian matrik)

3. Buat program untuk menghitung perkalian dari 2 buah matrik dengan syarat

orde matrik bebas (minimal orde 3)

Jawab

1. a. A x B = [4 6 19 0 3 ]

x [4 68 −55 −1 ]

= [69 −751 51 ]

b. A x AT

AT = [4 96 01 3 ]

A x AT = [4 6 19 0 3 ]

x [4 96 01 3 ]

= [53 3939 90 ]

c. B x BT

BT = [4 8 56 −5 −1 ]

B x BT = [4 68 −55 −1 ]

x[4 8 56 −5 −1 ]

= [52 2 14

2 89 4514 45 26 ]

2. a. [a11 a12 a13

a21 a22 a23

a31 a32 a33]×[a11 a12 a13

a21 a22 a23

a31 a32 a33] =

[a1 a2 a3

a4 a5 a6

a7 a8 a9]

operasinya :

a1=[a11] [a11 ]+ [a12] [a21]+[a13 ] [a31 ]a2=[a11] [a12 ] + [a12 ] [a22 ]+ [a13 ] [a32 ]a3 = [a11] [a13 ] + [a12 ] [a23 ]+[a13 ] [a33 ]a4 =[a21 ] [a11] + [a22 ] [a21 ]+[a23 ] [a31 ]a5 =[a21 ] [a12 ]+ [a22 ] [a22 ]+[a23 ] [a32 ]a6 = [a21 ] [a13 ]+ [a22] [a23 ]+ [a23 ] [a33 ]a7 =[a31 ] [a11] + [a32 ] [a21 ]+[a33 ] [a31 ]a8 =[a31 ] [a12 ]+ [a32 ] [a22 ]+[a33 ] [a32 ]a9 = [a31 ] [a13 ]+ [a32 ] [a23 ]+ [a33 ] [a33 ]

b. formula :

1. A [ 0 ] [0 ]¿B [ 0 ] [0 ]+A [0 ] [ 1 ]¿B [ 1 ] [ 0 ]+A [ 0 ] [2 ]¿B [ 2 ] [ 0 ]

2. A [ 0 ] [0 ]¿B [ 0 ] [1 ]+A [ 0 ] [1 ]¿B [1 ] [ 1 ]+A [ 0 ] [ 2 ]¿B [ 2 ] [ 1 ]

3. A [ 0 ] [0 ]¿B [ 0 ] [2 ]+A [ 0 ] [1 ]¿B [1 ] [ 2 ]+A [0 ] [ 2 ]¿B [ 2 ] [2 ]

4. A [ 1 ] [ 0 ]¿B [ 0 ] [ 0 ]+A [ 1 ] [ 1 ]¿B [ 1 ] [0 ]+A [ 1 ] [2 ]¿B [2 ] [ 0 ]

5. A [ 1 ] [ 0 ]¿B [ 0 ] [ 1 ]+A [1 ] [ 1 ]¿B [ 1 ] [ 1 ]+A [1 ] [ 2 ]¿B [ 2 ] [ 1 ]

6. A [ 1 ] [ 0 ]¿B [ 0 ] [ 2 ]+A [1 ] [ 1 ]¿B [ 1 ] [ 2 ]+A [1 ] [ 2 ]¿B [ 2 ] [ 2 ]

7. A [ 2 ] [ 0 ]¿B [ 0 ] [ 0 ]+A [ 2 ] [1 ]¿B [1 ] [ 0 ]+A [2 ] [ 2 ]¿B [ 2 ] [ 0 ]

8. A [ 2 ] [ 0 ]¿B [ 0 ] [ 1 ]+A [ 2 ] [ 1 ]¿B [ 1 ] [ 1 ]+A [ 2 ] [ 2 ]¿B [ 2 ] [1 ]

9. A [ 2 ] [ 0 ]¿B [ 0 ] [ 2 ]+A [ 2 ] [ 1 ]¿B [ 1 ] [ 2 ]+A [ 2 ] [ 2 ]¿B [ 2 ] [2 ]Syarat Perkialan :

1. Orde sama untuk matrik terikat cD

matrik 3x3 x matrik 3x3.

2. Jumlah baris harus sama dengan jumlah kolom (untuk matrik bebas) cD

:

matrik 2x3 dikali matrik 3x2.

3. Listing Program

#include <cstdlib>#include <iostream>

using namespace std;

int main(int argc, char *argv[]){int a[3][3], b[3][3],c[3][3],j,k,i;//menampilkan matrik 1cout<<" Perkalian Matrik "<<endl;cout<<"-----------------------"<<endl<<endl;cout<<" KELPMPOK 4 "<<endl<<endl;cout<<"-----------------------"<<endl;cout<<" Masukan matrik 1 "<<endl;cout<<"-----------------------"<<endl;for (int i=0;i<3;i++){for (int j=0;j<3;j++){cout<<"Isi a["<<i<<"]["<<j<<"] : ";cin>>a[i][j];}}

cout<<endl;for (int i=0;i<3;i++){for (int j=0;j<3;j++){cout<<a[i][j]<<" ";}cout<<endl;}cout<<"-----------------------"<<endl;cout<<" Masukan matrik 2 "<<endl;cout<<"-----------------------"<<endl;for (int i=0;i<3;i++){for (int j=0;j<3;j++){cout<<"Isi b["<<i<<"]["<<j<<"] : ";cin>>b[i][j];}

}cout<<endl;for (int i=0;i<3;i++){for (int j=0;j<3;j++){cout<<a[i][j]<<" ";}cout<<endl;}cout<<"\n";

cout<<" matrik 1 * matrik 2 = ";cout<<"\n\n";

//proses perkalian matrikfor (i=0;i<3;i++) { for (j=0;j<3;j++) { c[i][j]=0; for (k=0;k<3;k++) c[i][j]=c[i][j]+a[i][k]*b[k][j]; cout<<c[i][j]<<" "; } cout<<endl; } system("PAUSE"); return EXIT_SUCCESS;}

Print Out Program