all numbers have a pattern

Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id

all patterns contain a message

all messages reveal a destiny (number23

movies)

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BUDI DARMA SETIAWAN, S.Kom., M.CSs.budidarma@ub.ac.id

WIBISONO SUKMO WARDHONO, ST, MT

wibiwardhono@ub.ac.id

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BISONWIBI

wibiwardhono.lecture. .ac.id

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refference’s keyword(s)

Linear AlgebraAljabar Linier

Aljabar Linier ElementerMatematika Teknik

Aljabar Linier & Matriks

Aljabar Linear

refference’s keyword(s)

MatriksDeterminan

Sistem Persamaan LinierTransformasi Linier

Aljabar Linier & Matriks

Vektor

by subject

Ruang 2 & Ruang 3Ruang-ruang vektor

Nilai & faktor Eigen

First sight ...PendahuluanAljabar Linier

Matriks Invers

Pangkat Matriks,Matriks Elementer

& Metode mencari A-1

kuis1MATRIKS

Sistem Persamaan LinierOperasi Baris Elementer

Eliminasi Gauss & Gauss-Jordan

- SPL (Lanjutan)- Determinan

Determinan(Lanjutan)

Ujian Tengah Semester

Vektor (Refreshing)Operasi Vektor di R2 & R3

Ruang-ruang Vektor

Ruang-ruang Vektor(lanjutan)

kuis2VEKTOR

Transformasi Linier

Nilai & Vektor Eigen

kuis3TransLin & Eigen

Ujian Akhir Semester

N1 = Kehadiran, Tugas & Keaktifan

N2 = Nilai Q1 N3 = Nilai UTS N4 = Nilai Q2 N5 = Nilai Q3

NA = average(N1:N5)

PENILAIAN

Read:NA

NA > 80 ?

Nilai = “A”

Write:Nilai

Read:UAS

NA > UAS ?

NA = 0,8 NA + 0,2 UAS

NA = 0,5 NA + 0,5 UAS

Nilai NA

Syarat Mutlak

MatriksKomputasi

Sekumpulan elemen berupa

angka/ simbol yang tersusun dalam

baris dan kolom

Matriks

p q rs t uv w x

Matriks

A i jjumlah barisjumlah kolom

Matriks

p q rs t uv w x

a11 a12 a13

a21 a22 a23

a31 a32 a33

Ordo Matriks: 3 x 3

MatriksBerdasarkan ordonya

Matriks Persegi

Ordo Matriks: n x n

15 4 8 3

12 7 9 10

11 1 16 6

14 5 2 13

Matriks Kolom

Ordo Matriks: n x 11

Matriks Baris

Ordo Matriks: 1 x n

Matriks Tegak

Ordo Matriks: m x nUntuk m > n8 1

Matriks Datar

Ordo Matriks: m x nUntuk m < n

MatriksBerdasarkan elemennya

Matriks DiagonalMatriks Persegi dengansemua elemen bernilai 0

Kecuali unsur-unsur pada diagonal utama

-1 0 0

Matriks SegitigaMatriks Persegi dengan

semua elemen bernilai 0 padaunsur-unsur di bawah/ di atas diagonal utama

-1 5 4 9

0 2 3 -6

0 0 -7 1

0 0 0 8

7 0 0 0

-2 3 0 0

-4 -1 6 0

9 -5 1 8

Matriks SkalarMatriks Persegi

Dengan semua elemenbernilai sama pada diagonal utama

Matriks SimetriMatriks Persegi dengan

elemen

amn = anm3 5 -2

-2 4 -6

a11 = a11a12 = a21a22 = a22a13 = a31a32 = a23a33 = a33

TRANSPOSE

Matriks

Transpose matriks

AT = Aji

Matriks Setangkup

3 5 -2

-2 4 -6

A = AT

OPERASI

Matriks

Penjumlahan & Pengurangan Matriks

A=a11 a12 a13

a21 a22 a23

a31 a32 a33

B=b11 b12 b13

b21 b22 b23

b31 b32 b33

Ordo matriks harus sama

A+B : aij+bij A-B : aij-bij

int i,j,m=3,n=3,a[m][n],b[m][n],c[m][n];main(){

for(i=0;i<m;i++)for(j=0;j<n;j++){

cin>>a[i][j];cin>>b[i][j];c[i][j]=a[i][j]+b[i][j];

Perkalian skalar dengan matriks

A’=kA=ka11 ka12 ka13

ka21 ka22 ka23

ka31 ka32 ka33

Perkalian Matriks

A32=a11 a12

a21 a22

a31 a32

B21=b11

Aij dengan Bjk menghasilkan matriks Cik

C31=a11*b11 + a12*b21

a21*b11 + a22*b21

a31*b11 + a32*b21

LATIHAN

-2 8 103 -1 46 -5 7

A =8 1 97 -3 511 4 -2

Tentukan: 1. A+BT

2. 2A*B3. Algoritma 2AT

all numbers have a pattern

Documents

The Chicago Guide to Writing about Numbers, 2 nd edition. Summarizing a pattern involving many numbers: Generalization, example, exception (“GEE”) Jane

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