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Aljabar Linier & Matriks

Dr. Joko Soebagyo, M.pd. - Personal Name;

KATA PENGANTAR.............................................................................................................. iii\\r\\nDAFTAR ISI.......................................................................................................................... iv\\r\\nDAFTAR GAMBAR............................................................................................................... xi\\r\\nDAFTAR TABEL.................................................................................................................. xiii\\r\\nKEGIATAN PEMBELAJARAN 1 ..............................................................................................1\\r\\nKegiatan Belajar 1: Sistem Linier.........................................................................................1\\r\\nA. Tujuan Pembelajaran: .............................................................................................1\\r\\nB. Indikator Pencapaian Kompetensi ..........................................................................1\\r\\nC. Uraian Materi ..........................................................................................................2\\r\\nPendahuluan ...................................................................................................................2\\r\\n1.1. Pengantar Sistem Persamaan Linier....................................................................2\\r\\n1.1.1. Persamaan Linear........................................................................................2\\r\\n1.1.2. Sistem Persamaan Linear Dengan 2 dan 3 Variabel Tidak Diketahui..........4\\r\\n1.1.3. Perluasan Matriks dan Operasi Baris Elementer.........................................9\\r\\nLatihan 1.1.................................................................................................................12\\r\\nKEGIATAN PEMBELAJARAN 2 ............................................................................................16\\r\\nKegiatan Belajar 2: Eliminasi Gauss...................................................................................16\\r\\nA. Tujuan Pembelajaran: ...........................................................................................16\\r\\nB. Indikator Pencapaian Kompetensi ........................................................................16\\r\\nC. Uraian Materi ........................................................................................................17\\r\\n1.2. Eliminasi Gauss..................................................................................................17\\r\\n1.2.1. Pertimbangan dalam Menyelesaikan Sistem Linier..................................17\\r\\n1.2.2. Bentuk Eselon............................................................................................17\\r\\n1.2.3. Metode Eliminasi.......................................................................................21\\r\\n1.2.4. Sistem Linier Homogen .............................................................................25\\r\\n1.2.5. Variabel Bebas dalam Sistem Linier Homogen..........................................27\\r\\n1.2.6. Eliminasi Gauss dan Back-Substitustion....................................................28\\r\\n\\r\\nAljabar Linier dan Matriks\\r\\nMATEMATIKA – TEKNIK\\r\\nv\\r\\n1.2.7. Beberapa Fakta tentang Bentuk Eselon.................................................... 31\\r\\n1.2.8. Kesalahan Pembulatan dan Ketidakstabilan............................................. 32\\r\\nLatihan 1.2................................................................................................................. 32\\r\\nKEGIATAN PEMBELAJARAN 3............................................................................................ 39\\r\\nKegiatan Belajar 3: Matriks dan Operasi Matriks ............................................................. 39\\r\\nA. Tujuan Pembelajaran:........................................................................................... 39\\r\\nB. Indikator Pencapaian Kompetensi........................................................................ 39\\r\\nC. Uraian Materi........................................................................................................ 40\\r\\n1.3. Matriks dan Operasi Matriks............................................................................. 40\\r\\n1.3.1. Terminologi dan Notasi Matriks................................................................ 40\\r\\n1.3.2. Operasi Matrik .......................................................................................... 42\\r\\n1.3.3. Partisi Matrik............................................................................................. 46\\r\\n1.3.4. Perkalian Matrik dengan Kolom dan Baris................................................ 47\\r\\n1.3.5. Produk Matrik sebagai Kombinasi Linier................................................... 48\\r\\n1.3.6. Bentuk Matrik dari Sistem Linier............................................................... 49\\r\\n1.3.7. Transpose Matriks..................................................................................... 50\\r\\nLatihan 1.3................................................................................................................. 51\\r\\nKEGIATAN PEMBELAJARAN 4............................................................................................ 59\\r\\nKegiatan Belajar 4: Invers: Sifat-sifat Aljabar dari Matriks ............................................... 59\\r\\nA. Tujuan Pembelajaran:........................................................................................... 59\\r\\nB. Indikator Pencapaian Kompetensi........................................................................ 59\\r\\nC. Uraian Materi........................................................................................................ 60\\r\\n1.4. Invers: Sifat-sifat Aljabar dari Matriks............................................................... 60\\r\\n1.4.1. Sifat-Sifat Penjumlahan Matriks dan Perkalian Skalar.............................. 60\\r\\n1.4.2. Sifat-Sifat Perkalian Matriks...................................................................... 62\\r\\n1.4.3. Matriks Nol................................................................................................ 63\\r\\n1.4.4. Matriks Identitas....................................................................................... 64\\r\\n1.4.5. Invers Matriks ........................................................................................... 66\\r\\n1.4.6. Sifat-Sifat Invers........................................................................................ 67\\r\\n1.4.7. Perpangkatan Matriks............................................................................... 71\\r\\n1.4.8. Matriks Polinomial .................................................................................... 73\\r\\n\\r\\nvi Aljabar Linier dan Matriks\\r\\nMATEMATIKA – TEKNIK\\r\\n1.4.9. Sifat-Sifat Transpose..................................................................................73\\r\\nLatihan 1.4.................................................................................................................75\\r\\nKEGIATAN PEMBELAJARAN 5 ............................................................................................80\\r\\nKegiatan Belajar 5: Matriks Elementer dan Metode Penentuan A-1\\r\\n\\r\\n.................................80\\r\\nA. Tujuan Pembelajaran: ...........................................................................................80\\r\\nB. Indikator Pencapaian Kompetensi ........................................................................80\\r\\nC. Uraian Materi ........................................................................................................81\\r\\n1.5. Matriks Elementer dan Metode Penentuan A\\r\\n—1\\r\\n...............................................81\\r\\n1.5.1. Teorema Ekuivalen....................................................................................84\\r\\n1.5.2. Metode untuk Membalik Matriks.............................................................86\\r\\nLatihan 1.5.................................................................................................................89\\r\\nKEGIATAN PEMBELAJARAN 6 ............................................................................................95\\r\\nKegiatan Belajar 6: Sistem Linier Lanjut dan Matriks Invers.............................................95\\r\\nA. Tujuan Pembelajaran: ...........................................................................................95\\r\\nB. Indikator Pencapaian Kompetensi ........................................................................95\\r\\nC. Uraian Materi ........................................................................................................95\\r\\n1.6. Sistem Linier Lanjut dan Matriks Invers............................................................95\\r\\n1.6.1. Banyak Solusi dari Sistem Linier................................................................96\\r\\n1.6.2. Penyelesaian Sistem Linier Dengan Invers Matrik ....................................96\\r\\n1.6.3. Sistem Linier Dengan Koefisien Matrik Secara Umum..............................97\\r\\n1.6.4. Sifat-sifat Matrik Balikan ...........................................................................98\\r\\n1.6.5. Teorema Ekuivalen....................................................................................99\\r\\nLatihan 1.6...............................................................................................................103\\r\\nKEGIATAN PEMBELAJARAN 7 ..........................................................................................106\\r\\nKegiatan Belajar 7: Matriks Diagonal, Triangular dan Simetris.......................................106\\r\\nA. Tujuan Pembelajaran: .........................................................................................106\\r\\nB. Indikator Pencapaian Kompetensi ......................................................................106\\r\\nC. Uraian Materi ......................................................................................................106\\r\\n1.7. Matriks Diagonal, Segitiga dan Simetris..........................................................106\\r\\n1.7.1. Matrik Diagonal.......................................................................................107\\r\\n1.7.2. Matrik Segitiga ........................................................................................108\\r\\n\\r\\nAljabar Linier dan Matriks\\r\\nMATEMATIKA – TEKNIK\\r\\nvii\\r\\n1.7.3. Sifat-Sifat Matrik Segitiga........................................................................ 109\\r\\n1.7.4. Matrik Simetris........................................................................................ 110\\r\\n1.7.5. Keterbalikan dari Matrik Simetris........................................................... 112\\r\\n1.7.6. Produk AAT dan A\\r\\n\\r\\nTA ................................................................................ 112\\r\\nLatihan 1.7............................................................................................................... 113\\r\\nKEGIATAN PEMBELAJARAN 8.......................................................................................... 118\\r\\nKegiatan Belajar 8: Aplikasi Sistem Linier ....................................................................... 118\\r\\nA. Tujuan Pembelajaran:......................................................................................... 118\\r\\nB. Indikator Pencapaian Kompetensi...................................................................... 118\\r\\nC. Uraian Materi...................................................................................................... 118\\r\\n1.8. Aplikasi Sistem Linier ...................................................................................... 118\\r\\n1.8.1. Analisis Jaringan...................................................................................... 118\\r\\n1.8.2. Rangkaian listrik ...................................................................................... 122\\r\\n1.8.3. Menyeimbangkan Persamaan Kimia....................................................... 127\\r\\n1.8.4. Interpolasi Polinomial ............................................................................. 130\\r\\n1.8.5. Kalkulus dan Kegunaan Perhitungan yang Diperlukan ........................... 134\\r\\nLatihan 1.8............................................................................................................... 135\\r\\nKEGIATAN PEMBELAJARAN 9.......................................................................................... 139\\r\\nKegiatan Belajar 9: Model Input-Output Leontief .......................................................... 139\\r\\nA. Tujuan Pembelajaran:......................................................................................... 139\\r\\nB. Indikator Pencapaian Kompetensi...................................................................... 139\\r\\nC. Uraian Materi...................................................................................................... 139\\r\\n1.9. Model Input-Output Leontief ......................................................................... 139\\r\\n1.9.1. Input dan Output dalam Ekonomi .......................................................... 139\\r\\n1.9.2. Model Leontief dari Ekonomi Terbuka ................................................... 141\\r\\n1.9.3. Ekonomi Terbuka Produktif .................................................................... 144\\r\\nLatihan 1.9............................................................................................................... 146\\r\\nSuplemen Latihan 1..................................................................................................... 149\\r\\nKEGIATAN PEMBELAJARAN 10........................................................................................ 153\\r\\nKegiatan Belajar 10: Determinan dengan Ekspansi Kofaktor ......................................... 153\\r\\nA. Tujuan Pembelajaran:......................................................................................... 153\\r\\n\\r\\nviii Aljabar Linier dan Matriks\\r\\nMATEMATIKA – TEKNIK\\r\\nB. Indikator Pencapaian Kompetensi ......................................................................153\\r\\nC. Uraian Materi ......................................................................................................153\\r\\n2.1. Determinan dengan Ekspansi Kofaktor...........................................................154\\r\\n2.1.1. Minor dan Kofaktor.................................................................................154\\r\\n2.1.2. Definisi Determinan Secara Umum.........................................................157\\r\\n2.1.3. Teknik yang Berguna untuk Menghitung Determinan 2 × 2 dan 3 × 3160\\r\\nLatihan 2.1...................................................................................................................161\\r\\nKEGIATAN PEMBELAJARAN 11........................................................................................166\\r\\nKegiatan Belajar 11: Menghitung Determinan dengan Reduksi Baris............................166\\r\\nA. Tujuan Pembelajaran: .........................................................................................166\\r\\nB. Indikator Pencapaian Kompetensi ......................................................................166\\r\\nC. Uraian Materi ......................................................................................................167\\r\\n2.2. Menghitung Determinan dengan Reduksi Baris .............................................167\\r\\n2.2.1. Teorema Dasar........................................................................................167\\r\\n2.2.2. Operasi Baris Elementer..........................................................................167\\r\\n2.2.3. Matriks Elementer...................................................................................169\\r\\n2.2.4. Matriks dengan Baris atau Kolom Proporsional......................................169\\r\\n2.2.5. Menghitung Determinan dengan Reduksi Baris .....................................170\\r\\nLatihan 2.2...................................................................................................................172\\r\\nKEGIATAN PEMBELAJARAN 12 ........................................................................................176\\r\\nKegiatan Belajar 12: Sifat-sifat Determinan: Aturan Cramer..........................................176\\r\\nA. Tujuan Pembelajaran: .........................................................................................176\\r\\nB. Indikator Pencapaian Kompetensi ......................................................................176\\r\\nC. Uraian Materi ......................................................................................................177\\r\\n2.3. Sifat-sifat Determinan: Aturan Cramer...........................................................177\\r\\n2.3.1. Sifat-sifat Dasar Determinan ...................................................................177\\r\\n2.3.2. Determinan dari Produk Matrik ..............................................................178\\r\\n2.3.3. Uji Determinan untuk Keterbalikan ........................................................179\\r\\n2.3.4. Adjoint Suatu Matrik ...............................................................................182\\r\\n2.3.5. Aturan Cramer.........................................................................................186\\r\\n2.3.6. Teorema Ekuivalen..................................................................................189\\r\\n\\r\\nAljabar Linier dan Matriks\\r\\nMATEMATIKA – TEKNIK\\r\\nix\\r\\nLatihan 2.3................................................................................................................... 191\\r\\nSuplemen Latihan 2..................................................................................................... 195\\r\\nKEGIATAN PEMBELAJARAN 13........................................................................................ 199\\r\\nKegiatan Belajar 13: Ruang Vektor Euclid....................................................................... 199\\r\\nA. Tujuan Pembelajaran:......................................................................................... 199\\r\\nB. Indikator Pencapaian Kompetensi...................................................................... 199\\r\\nC. Uraian Materi...................................................................................................... 200\\r\\n3.1. Vektor Ruang-2, Ruang-3, Ruang-n ................................................................ 200\\r\\n3.1.1. Vektor Geometris.................................................................................... 200\\r\\n3.1.2. Penjumlahan Vektor ............................................................................... 201\\r\\n3.1.3. Pengurangan Vektor ............................................................................... 202\\r\\n3.1.4. Perkalian Skalar....................................................................................... 203\\r\\n3.1.5. Vektor Paralel dan Kolinier ..................................................................... 204\\r\\n3.1.6. Penjumlahan Tiga Vektor atau Lebih ...................................................... 204\\r\\n3.1.7. Vektor dalam Sistem Koordinat.............................................................. 205\\r\\n3.1.8. Vektor dengan Titik Awal Tidak di Pusat................................................. 206\\r\\n3.1.9. Ruang-n................................................................................................... 207\\r\\n3.1.10. Operasi Vektor di Rn.............................................................................. 209\\r\\n3.1.11. Menghitung Tanpa Komponen Vektor ................................................... 212\\r\\n3.1.12. Kombinasi Linier...................................................................................... 213\\r\\n3.1.13. Notasi Alternatif untuk Vektor................................................................ 214\\r\\nLatihan 3.1................................................................................................................... 215\\r\\nKEGIATAN PEMBELAJARAN 14........................................................................................ 220\\r\\nKegiatan Belajar 14: Norm, Produk Dot, and Jarak dalam Rn ....................................... 220\\r\\nA. Tujuan Pembelajaran:......................................................................................... 220\\r\\nB. Indikator Pencapaian Kompetensi...................................................................... 220\\r\\nC. Uraian Materi...................................................................................................... 220\\r\\n3.2. Norm, Produk Dot, and Jarak dalam Rn......................................................... 220\\r\\n3.2.1. Norm Vektor ........................................................................................... 221\\r\\n3.2.2. Vektor Satuan.......................................................................................... 223\\r\\n3.2.3. Vektor Satuan Standar............................................................................ 224\\r\\n\\r\\nx Aljabar Linier dan Matriks\\r\\nMATEMATIKA – TEKNIK\\r\\n3.2.4. Jarak dalam Rn .......................................................................................225\\r\\n3.2.5. Produk Titik .............................................................................................226\\r\\n3.2.6. Bentuk Komponen dari Produk Titik .......................................................228\\r\\n3.2.7. Sifat-sifat Aljabar dari Produk Titik..........................................................230\\r\\n3.2.8. Pertidaksamaan Cauchy-Schwarz dan Sudut di Rn................................232\\r\\n3.2.9. Geometri di Rn .......................................................................................233\\r\\n3.2.10. Produk Titik Sebagai Perkalian Matrik ....................................................236\\r\\n3.2.11. Produk Titik ditinjau dari Perkalian Matrik .............................................238\\r\\n3.2.12. Aplikasi Produk Titik pada Nomor ISBN ..................................................238\\r\\nLatihan 3.2...................................................................................................................239\\r\\nKEGIATAN PEMBELAJARAN 15........................................................................................244\\r\\nKegiatan Belajar 15: Ortogonalitas .................................................................................244\\r\\nA. Tujuan Pembelajaran: .........................................................................................244\\r\\nB. Indikator Pencapaian Kompetensi ......................................................................244\\r\\nC. Uraian Materi ......................................................................................................245\\r\\n3.3. Ortogonalitas...................................................................................................245\\r\\n3.3.1. Vektor Ortogonal.....................................................................................245\\r\\n3.3.2. Menentukan Garis dan Bidang dengan Titik dan Normal .......................246\\r\\n3.3.3. Proyeksi Ortogonal..................................................................................248\\r\\n3.3.4. Teorema Pythagoras ...............................................................................252\\r\\n3.3.5. Opsional: Masalah Jarak..........................................................................253\\r\\nLatihan 3.3...................................................................................................................256\\r\\nDAFTAR PUSTAKA............................................................................................................260

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My Library 512. 5 Soe m

BPU02601439

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My Library 512. 5 Soe m

BPU02601439C2

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Detail Information

Series Title: -
Call Number: 512. 5 Soe m
Publisher: Bandung : MANGGU MAKMUR TANJUNG LESTARI., 2020
Collation: x, 318hlm.; 17.5 × 25cm
Language: Indonesia
ISBN/ISSN: 978-602-7715-09-2
Classification: 512. 5
Content Type: -
Media Type: -
Carrier Type: -
Edition: -
Subject(s): Matematika terapan
Matematika teknik
Matriks
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