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all numbers have a pattern. all patterns contain a message. all messages reveal a destiny. (number 23 movies). TIF 4001. aljabar linier. aljabar linier. Any question?. Lecturer. BUDI DARMA SETIAWAN , S.Kom., M.CS s.budidarma @ub.ac.id WIBISONO SUKMO WARDHONO , ST, MT - PowerPoint PPT Presentation
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Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
all numbers have a pattern
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
all patterns contain a message
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
all messages reveal a destiny (number23
movies)
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
TIF4001aljabarlinieraljabarlinier
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Any question?
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
BUDI DARMA SETIAWAN, S.Kom., [email protected]
WIBISONO SUKMO WARDHONO, ST, MT
LecturerLecturer
BISONWIBI
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
wibiwardhono.lecture. .ac.id
Visit ...
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
refference’s keyword(s)
Linear AlgebraAljabar Linier
Aljabar Linier ElementerMatematika Teknik
Aljabar Linier & Matriks
Aljabar Linear
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
refference’s keyword(s)
MatriksDeterminan
Sistem Persamaan LinierTransformasi Linier
Aljabar Linier & Matriks
Vektor
by subject
Ruang 2 & Ruang 3Ruang-ruang vektor
Nilai & faktor Eigen
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
1
First sight ...PendahuluanAljabar Linier
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
2
Matriks Invers
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
3
Pangkat Matriks,Matriks Elementer
& Metode mencari A-1
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
4
kuis1MATRIKS
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
5
Sistem Persamaan LinierOperasi Baris Elementer
Eliminasi Gauss & Gauss-Jordan
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
6
- SPL (Lanjutan)- Determinan
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
7
Determinan(Lanjutan)
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
8
Ujian Tengah Semester
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
9
Vektor (Refreshing)Operasi Vektor di R2 & R3
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
10
Ruang-ruang Vektor
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
11
Ruang-ruang Vektor(lanjutan)
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
12
kuis2VEKTOR
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
13
Transformasi Linier
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
14
Nilai & Vektor Eigen
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
15
kuis3TransLin & Eigen
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
16
Ujian Akhir Semester
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
N1 = Kehadiran, Tugas & Keaktifan
N2 = Nilai Q1 N3 = Nilai UTS N4 = Nilai Q2 N5 = Nilai Q3
NA = average(N1:N5)
PENILAIAN
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
START
Read:NA
NA > 80 ?
END
Nilai = “A”
True
False
Write:Nilai
Read:UAS
NA > UAS ?
NA = 0,8 NA + 0,2 UAS
True
False
NA = 0,5 NA + 0,5 UAS
Nilai NA
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Syarat Mutlak
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
MatriksKomputasi
Array
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Sekumpulan elemen berupa
angka/ simbol yang tersusun dalam
baris dan kolom
Matriks
p q rs t uv w x
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
p q rs t uv w x
Matriks
A i jjumlah barisjumlah kolom
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
A
Matriks
A33
p q rs t uv w x
a11 a12 a13
a21 a22 a23
a31 a32 a33
Ordo Matriks: 3 x 3
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
MatriksBerdasarkan ordonya
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks Persegi
Ordo Matriks: n x n
1 3
4 7
1 3 2
6 9 5
8 4 7
15 4 8 3
12 7 9 10
11 1 16 6
14 5 2 13
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks Kolom
Ordo Matriks: n x 11
6
8
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks Baris
Ordo Matriks: 1 x n
1 6 8
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks Tegak
Ordo Matriks: m x nUntuk m > n8 1
6 5
2 7
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks Datar
Ordo Matriks: m x nUntuk m < n
2 8 1
6 5 7
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
MatriksBerdasarkan elemennya
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks DiagonalMatriks Persegi dengansemua elemen bernilai 0
Kecuali unsur-unsur pada diagonal utama
-1 0 0
0 4 0
0 0 7
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
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
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks SkalarMatriks Persegi
Dengan semua elemenbernilai sama pada diagonal utama
6 0 0
0 6 0
0 0 6
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks SimetriMatriks Persegi dengan
elemen
amn = anm3 5 -2
5 1 4
-2 4 -6
a11 = a11a12 = a21a22 = a22a13 = a31a32 = a23a33 = a33
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
TRANSPOSE
Matriks
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks
Aij
Transpose matriks
AT = Aji
2 8 1
6 5 7
2 6
8 5
1 7
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Matriks Setangkup
3 5 -2
5 1 4
-2 4 -6
A = AT
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
OPERASI
Matriks
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
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
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
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];
}}
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Perkalian skalar dengan matriks
A’=kA=ka11 ka12 ka13
ka21 ka22 ka23
ka31 ka32 ka33
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Perkalian Matriks
A32=a11 a12
a21 a22
a31 a32
B21=b11
b21
Aij dengan Bjk menghasilkan matriks Cik
C31=a11*b11 + a12*b21
a21*b11 + a22*b21
a31*b11 + a32*b21
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
LATIHAN
-2 8 103 -1 46 -5 7
A =8 1 97 -3 511 4 -2
B =
Tentukan: 1. A+BT
2. 2A*B3. Algoritma 2AT