Wibisono Sukmo Wardhono, ST, MT all numbers have a pattern.

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1 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id all numbers have a pattern

2 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id all patterns contain a message

3 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id all messages reveal a destiny (number 23 movies)

4 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id TIF 4001 aljabar linier

5 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Any question?

6 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id BUDI DARMA SETIAWAN, S.Kom., M.CS s.budidarma @ub.ac.id WIBISONO SUKMO WARDHONO, ST, MT wibiwardhono @ub.ac.id Lecturer BISONWIBI

7 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id wibi wardhono.lecture..ac.id Visit...

8 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id refference’s keyword (s) Linear Algebra Aljabar Linier Aljabar Linier Elementer Matematika Teknik Aljabar Linier & Matriks Aljabar Linear

9 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id refference’s keyword (s) Matriks Determinan Sistem Persamaan Linier Transformasi Linier Aljabar Linier & Matriks Vektor by subject Ruang 2 & Ruang 3 Ruang-ruang vektor Nilai & faktor Eigen

10 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 1 First sight... Pendahuluan Aljabar Linier

11 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 2 Matriks Invers

12 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 3 Pangkat Matriks, Matriks Elementer & Metode mencari A -1

13 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 4 kuis1 MATRIKS

14 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 5 Sistem Persamaan Linier Operasi Baris Elementer Eliminasi Gauss & Gauss-Jordan

15 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 6 - SPL (Lanjutan) - Determinan

16 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 7 Determinan (Lanjutan)

17 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 8 Ujian Tengah Semester

18 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 9 Vektor (Refreshing) Operasi Vektor di R2 & R3

19 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 10 Ruang-ruang Vektor

20 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 11 Ruang-ruang Vektor (lanjutan)

21 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 12 kuis2 VEKTOR

22 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 13 Transformasi Linier

23 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 14 Nilai & Vektor Eigen

24 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 15 kuis3 TransLin & Eigen

25 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id 16 Ujian Akhir Semester

26 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id N 1 = Kehadiran, Tugas & Keaktifan N 2 = Nilai Q1 N 3 = Nilai UTS N 4 = Nilai Q2 N 5 = Nilai Q3 N A = average ( N 1 : N 5 ) PENILAIAN

27 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id START Read: N A N A > 80 ? END Nilai = “A” True False Write: Nilai Read: UAS N A > UAS ? NA = 0,8 N A + 0,2 UAS True False NA = 0,5 N A + 0,5 UAS Nilai  NA

28 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Syarat Mutlak

29 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Komputasi Array

30 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Sekumpulan elemen berupa angka/ simbol yang tersusun dalam baris dan kolom Matriks pqrstuvwxpqrstuvwx

31 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id pqrstuvwxpqrstuvwx Matriks A i jA i j jumlah baris jumlah kolom

32 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id A Matriks A33A33 pqrstuvwxpqrstuvwx a11a12 a13a21a22 a23a31a32 a33a11a12 a13a21a22 a23a31a32 a33 Ordo Matriks: 3 x 3

33 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Berdasarkan ordonya

34 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Persegi Ordo Matriks: n x n 13471347 132695847132695847 15 4 8 3 12 7 910 11 116 6 14 5 213

35 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Kolom Ordo Matriks: n x 1 168168

36 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Baris Ordo Matriks: 1 x n 168168

37 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Tegak Ordo Matriks: m x n Untuk m > n 816527816527

38 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Datar Ordo Matriks: m x n Untuk m < n 281657281657

39 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Berdasarkan elemennya

40 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Diagonal Matriks Persegi dengan semua elemen bernilai 0 Kecuali unsur-unsur pada diagonal utama -100 040 007

41 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Segitiga Matriks Persegi dengan semua elemen bernilai 0 pada unsur-unsur di bawah/ di atas diagonal utama -1549 023-6 00-71 0008 7000 -2300 -4-160 9-518

42 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Skalar Matriks Persegi Dengan semua elemen bernilai sama pada diagonal utama 600060006600060006

43 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Simetri Matriks Persegi dengan elemen a mn = a nm 35-2 514 -24-6 a 11 = a 11 a 12 = a 21 a 22 = a 22 a 13 = a 31 a 32 = a 23 a 33 = a 33

44 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id TRANSPOSE Matriks

45 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks AijAij Transpose matriks A T = A ji 281657281657 268517268517

46 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Matriks Setangkup 35-2 514 -24-6 A = ATA = AT

47 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id OPERASI Matriks

48 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Penjumlahan & Pengurangan Matriks A=A= a11a12 a13a21a22 a23a31a32 a33a11a12 a13a21a22 a23a31a32 a33 B=B= b11b12 b13b21b22 b23b31b32 b33b11b12 b13b21b22 b23b31b32 b33 Ordo matriks harus sama A+B : a ij +b ij A-B : a ij -b ij

49 Wibisono Sukmo Wardhono, ST, MT http://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]; } }

50 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Perkalian skalar dengan matriks A’=kA=A’=kA= ka11ka12 ka13ka21ka22 ka23ka31ka32 ka33ka11ka12 ka13ka21ka22 ka23ka31ka32 ka33

51 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id Perkalian Matriks A32=A32= a11a12a21a22a31a32a11a12a21a22a31a32 B21=B21= b11b21b11b21 A ij dengan B jk menghasilkan matriks C ik C 31 = a 11 *b 11 + a 12 *b 21 a 21 *b 11 + a 22 *b 21 a 31 *b 11 + a 32 *b 21

52 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id LATIHAN -2 8 10 3-1 4 6-5 7 A = 8 1 9 7-3 5 11 4 -2 B = Tentukan: 1. A+B T 2. 2A*B 3. Algoritma 2A T