Modul 8 MTK Paket C Irisan dan Matriks

MODUL TEMA 8

Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks i MODUL TEMA 8

ii MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Modul Dinamis: Modul ini merupakan salah satu contoh bahan ajar pendidikan kesetaraan yang berbasis pada kompetensi inti dan kompetensi dasar dan didesain sesuai kurikulum 2013. Sehingga modul ini merupakan dokumen yang bersifat dinamis dan terbuka lebar sesuai dengan kebutuhan dan kondisi daerah masing-masing, namun merujuk pada tercapainya standar kompetensi dasar. Matematika Paket C - Setara SMA/MA kelas XI Modul Tema 8 : Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks Penulis: Nursanto Diterbitkan oleh: Direktorat Pembinaan Pendidikan Keaksaraan dan Kesetaraan- Ditjen Pendidikan Anak Usia Dini dan Pendidikan Masyarakat-Kementerian Pendidikan dan Kebudayaan, 2018 iv+ 36 hlm + illustrasi + foto; 21 x 28,5 cm Hak Cipta © 2018 pada Kementerian Pendidikan dan Kebudayaan Dilindungi Undang-Undang

iii Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks Kata Pengantar Pendidikan kesetaraan sebagai pendidikan alternatif memberikan layanan kepada mayarakat yang karena kondisi geografi s, sosial budaya, ekonomi dan psikologis tidak berkesempatan mengikuti pendidikan dasar dan menengah di jalur pendidikan formal. Kurikulum pendidikan kesetaraan dikembangkan mengacu pada kurikulum 2013 pendidikan dasar dan menengah hasil revisi berdasarkan peraturan Mendikbud No.24 tahun 2016. Proses adaptasi kurikulum 2013 ke dalam kurikulum pendidikan kesetaraan adalah melalui proses kontekstualisasi dan fungsionalisasi dari masing-masing kompetensi dasar, sehingga peserta didik memahami makna dari setiap kompetensi yang dipelajari. Pembelajaran pendidikan kesetaraan menggunakan prinsip fl exible learning sesuai dengan karakteristik peserta didik kesetaraan. Penerapan prinsip pembelajaran tersebut menggunakan sistem pembelajaran modular dimana peserta didik memiliki kebebasan dalam penyelesaian tiap modul yang di sajikan. Konsekuensi dari sistem tersebut adalah perlunya disusun modul pembelajaran pendidikan kesetaraan yang memungkinkan peserta didik untuk belajar dan melakukan evaluasi ketuntasan secara mandiri. Tahun 2017 Direktorat Pembinaan Pendidikan Keaksaraan dan Kesetaraan, Direktorat Jendral Pendidikan Anak Usia Dini dan Pendidikan Masyarakat mengembangkan modul pembelajaran pendidikan kesetaraan dengan melibatkan Pusat Kurikulum dan Perbukuan Kemdikbud, para akademisi, pamong belajar, guru dan tutor pendidikan kesetaraan. Modul pendidikan kesetaraan disediakan mulai paket A tingkat kompetensi 2 (kelas 4 Paket A). Sedangkan untuk peserta didik Paket A usia sekolah, modul tingkat kompetensi 1 (Paket A setara SD kelas 1-3) menggunakan buku pelajaran Sekolah Dasar kelas 1-3, karena mereka masih memerlukan banyak bimbingan guru/tutor dan belum bisa belajar secara mandiri. Kami mengucapkan terimakasih atas partisipasi dari Pusat Kurikulum dan Perbukuan Kemdikbud, para akademisi, pamong belajar, guru, tutor pendidikan kesetaraan dan semua pihak yang telah berpartisipasi dalam penyusunan modul ini. Jakarta, Desember 2018 Direktur Jenderal Harris Iskandar

v MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 1 Daftar Isi 0RGXOfl.HWHUDWXUDQ%DULVDQGDQ3HQ\DMLDQ'DWDGDODP%HQWXN0DWULNV 3HWXQMXN3HQJJXQDDQ0RGXO 3HQJDQWDU0RGXO 8QLW%DULVDQ.HQGDUDDQGL6HEXDK3DUNLUDQ 8UDLDQ0DWHULffl fl 3HQJHUWLDQ0DWULNV fl -HQLVMHQLV0DWULNV fl 2SHUDVL'DVDU0DWULNV fl3HQMXPODKDQGDQSHQJXUDQJDQ0DWULNV fl3HUNDOLDQ0DWULNV 6RDO/DWLKDQ fl'HWHUPLQDQGDQ,QYHUV0DWULNV fl'HWHUPLQDQ0DWULNV  D'HWHUPLQDQ0DWULNV2UGR[ E'HWHUPLQDQ0DWULNV2UGR[ fl,QYHUV0DWULNV D ,QYHUVPDWULNVRUGR× E ,QYHUVPDWULNVRUGR× 6RDO/DWLKDQ fl7UDQVSRVH0DWULNV 6RDO/DWLKDQ Unit 2 Jadwal Perjalanan dan Tabel Komoditas Barang Uraian Materiǣ fl.HVDPDDQ0DWULNV fl$SOLNDVL0DWULNV fl$SOLNDVL'HWHUPLQDQ0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU fl$SOLNDVL,QYHUV0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU 6RDO/DWLKDQ 5DQJNXPDQ 6DUDQ5HIHUHQVL .ULWHULD3LQGDK/XOXV0RGXO 3HQLODLDQ .XQFL-DZDEDQ 'DIWDU3XVWDND 3URILO3HQXOLV««««««««««««««««««««««««««««« 02'8/ .(7(5$785$1%$5,6$1'$1 3(1<$-,$1'$7$'$/$0%(178.0$75,.6 Petunjuk Penggunaan Modul ‘†—Ž‹‹‡‰—Žƒ• –‡–ƒ‰’‡‡”ƒ’ƒ‘•‡’matriks•‡„ƒ‰ƒ‹—’—Žƒ„‹Žƒ‰ƒƒ—’— •‹„‘Ž ›ƒ‰ ›ƒ‰†‹„‡–—„‡”†ƒ•ƒ”ƒ„ƒ”‹•†ƒ ‘Ž‘•‡”–ƒ‡›‡Ž‡•ƒ‹ƒ’‡”ƒ•ƒŽƒŠƒ •‡Šƒ”‹ǦŠƒ”‹Žƒ‹›ƒ›ƒ‰„‡”ƒ‹–ƒ†‡‰ƒƒ–”‹•Ǥ‡„ƒŠƒ•ƒ‹‹†‹ƒ™ƒŽ‹†‡‰ƒ‡ƒŠƒ‹ Ž‡„‹Š †ƒŽƒ –‡–ƒ‰ ƒ–”‹•ǡ ‡‡—ƒ Œ‡‹•ǦŒ‡‹• ƒ–”‹•ǡ ‘’‡”ƒ•‹ ƒ–”‹• „ƒ‹ ’‡Œ—ŽƒŠƒǡ’‡‰—”ƒ‰ƒǡ’‡”ƒŽ‹ƒǡ†‡–‡”‹ƒ†ƒ‹˜‡”•ƒ–”‹•ǡ–”ƒ•’‘•ƒ–”‹•ǡ•‡”–ƒ ‡‰ƒ’Ž‹ƒ•‹ƒ†‡–‡”‹ƒƒ—’—‹˜‡”•ƒ–”‹•‡†ƒŽƒ•‹•–‡’‡”•ƒƒƒŽ‹‡ƒ”Ǥ‡Žƒ‹ ’‡Œ‡Žƒ•ƒ‡‰‡ƒ‹ƒ–‡”‹›ƒ‰†‹–ƒ’‹Žƒǡ‘†—Ž‹‹Œ—‰ƒ†‹Ž‡‰ƒ’‹†‡‰ƒŽƒ–‹Šƒ—–— ‡‰—Œ‹ ’‡ƒŠƒƒ †ƒ ’‡‰—ƒ•ƒƒ †ƒ”‹ ’‡•‡”–ƒ †‹†‹ –‡”Šƒ†ƒ’ ƒ–‡”‹ ›ƒ‰ –‡ŽƒŠ †‹ ’‡ŽƒŒƒ”‹›ƒǤ‘†—Ž‹‹†‹•—•—†‡‰ƒ„ƒŠƒ•ƒ›ƒ‰•‡†‡”Šƒƒǡ†ƒ†‹„—ƒ–„‡”—”—–ƒ•‡•—ƒ‹†‡ ‰ƒ —”—–ƒ ƒ–‡”‹ ›ƒ‰ –‡”Ž‡„‹Š †ƒŠ—Ž— ’‡”Ž— †‹—ƒ•ƒ‹Ǥ –— ‹–—ǡ •‡„‡Ž— ‡’‡ŽƒŒƒ”‹ ‘†—Ž‹‹•‡„ƒ‹›ƒǤ ͳǤƒ…ƒ’‡‰ƒ–ƒ”‘†—Ž—–—‡‰‡–ƒŠ—‹ƒ”ƒŠ’‡‰‡„ƒ‰ƒ‘†—Ž ʹǤ‡„ƒ…ƒ‘’‡–‡•‹†ƒ•ƒ”†ƒ–—Œ—ƒ›ƒ‰‹‰‹†‹…ƒ’ƒ‹‡ŽƒŽ—‹‘†—ŽǤ ͵Ǥ ‰ƒ”‡’‡”‘Ž‡Š ‰ƒ„ƒ”ƒ ›ƒ‰ —–—Š‡‰‡ƒ‹‘†—Žǡƒƒ ’‡‰‰—ƒ ’‡”Ž—‡„ƒ…ƒ †ƒ‡ƒŠƒ‹’‡–ƒ‘•‡’Ǥ ͶǤ‡’‡ŽƒŒƒ”‹‘†—Ž•‡…ƒ”ƒ„‡”—”—–ƒƒ‰ƒ”‡’‡”‘Ž‡Š’‡ƒŠƒƒ›ƒ‰—–—ŠǤ ͷǤ—–‹•‡—ƒ–ƒŠƒ’ƒ†ƒ’‡–—Œ—›ƒ‰ƒ†ƒ’ƒ†ƒ‘†—Ž‹‹ Tujuan yang Diharapkan Setelah Mempelajari Modul —Œ—ƒ’‡„‡ŽƒŒƒ”ƒ‘†—Ž‹‹ǡƒ‰ƒ”†ƒǣ ͳǤ‡ƒŠƒ‹‘•‡’†ƒŒ‡‹•ǦŒ‡‹•ƒ–”‹•†ƒ’‡‡”ƒ’ƒ›ƒ†ƒŽƒ‡›‡Ž‡•ƒ‹ƒƒ•ƒŽƒŠ ‡Š‹†—’ƒ•‡Šƒ”‹ǦŠƒ”‹Ǥ ʹǤ‡”ƒ’‹Ž‡Žƒ—ƒ‘’‡”ƒ•‹ƒ–”‹•†ƒ‡›‡Ž‡•‹ƒƒ•ƒŽƒŠ•‡Šƒ”‹ǦŠƒ”‹Ǥ ͵Ǥ ‡”„‡–— †ƒ ‡‹Ž‹‹ •‹ƒ’ ‡ƒ†‹”‹ƒǡ „‡”–‹†ƒ Ž‘‰‹•ǡ –‹†ƒ —†ƒŠ ‡›‡”ƒŠ †ƒ ’‡”…ƒ›ƒ†‹”‹‡‰‰—ƒƒƒ–‡ƒ–‹ƒ†ƒŽƒ’‡‰‡„ƒ‰ƒ‡Š‹†—’ƒ•‡Šƒ”‹ǦŠƒ”‹Ǥ‡…ƒ”ƒ Š—•—•ǡ •‡–‡ŽƒŠ ‡’‡ŽƒŒƒ”‹ ‘†—Ž ‹‹ǡ †ƒ †‹Šƒ”ƒ’ƒ ‡‹Ž‹‹ ‡ƒ’—ƒ ’‡‰‡–ƒŠ—ƒ †ƒ ‡–‡”ƒ’‹Žƒ †ƒŽƒ ‡‡—ƒ ‘•‡’ ƒ–”‹• †ƒ ‡›‡Ž‡•ƒ‹ƒ ƒ•ƒŽƒŠ‘–‡•–—ƒŽǢ‡‡–—ƒǡ‡‰‰—ƒƒǡ†ƒ‡›‡Ž‡•ƒ‹ƒƒ•ƒŽƒŠƒ–”‹•Ǥ

v MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 1 Daftar Isi 0RGXO.HWHUDWXUDQ%DULVDQGDQ3HQ\DMLDQ'DWDGDODP%HQWXN0DWULNV 3HWXQMXN3HQJJXQDDQ0RGXO 3HQJDQWDU0RGXO 8QLW%DULVDQ.HQGDUDDQGL6HEXDK3DUNLUDQ 8UDLDQ0DWHUL  3HQJHUWLDQ0DWULNV  -HQLVMHQLV0DWULNV  2SHUDVL'DVDU0DWULNV 3HQMXPODKDQGDQSHQJXUDQJDQ0DWULNV 3HUNDOLDQ0DWULNV 6RDO/DWLKDQ 'HWHUPLQDQGDQ,QYHUV0DWULNV 'HWHUPLQDQ0DWULNV  D'HWHUPLQDQ0DWULNV2UGR[ E'HWHUPLQDQ0DWULNV2UGR[ ,QYHUV0DWULNV D ,QYHUVPDWULNVRUGR× E ,QYHUVPDWULNVRUGR× 6RDO/DWLKDQ 7UDQVSRVH0DWULNV 6RDO/DWLKDQ Unit 2 Jadwal Perjalanan dan Tabel Komoditas Barang Uraian Materiǣ .HVDPDDQ0DWULNV $SOLNDVL0DWULNV $SOLNDVL'HWHUPLQDQ0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU $SOLNDVL,QYHUV0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU 6RDO/DWLKDQ 5DQJNXPDQ 6DUDQ5HIHUHQVL .ULWHULD3LQGDK/XOXV0RGXO 3HQLODLDQ .XQFL-DZDEDQ 'DIWDU3XVWDND 3URILO3HQXOLV««««««««««««««««««««««««««««« 02'8/fl .(7(5$785$1%$5,6$1'$1 3(1<$-,$1'$7$'$/$0%(178.0$75,.6 Petunjuk Penggunaan Modul ‘†—Ž‹‹‡‰—Žƒ• –‡–ƒ‰’‡‡”ƒ’ƒ‘•‡’matriks•‡„ƒ‰ƒ‹—’—Žƒ„‹Žƒ‰ƒƒ—’— •‹„‘Ž ›ƒ‰ ›ƒ‰†‹„‡–—„‡”†ƒ•ƒ”ƒ„ƒ”‹•†ƒ ‘Ž‘•‡”–ƒ‡›‡Ž‡•ƒ‹ƒ’‡”ƒ•ƒŽƒŠƒ •‡Šƒ”‹ǦŠƒ”‹Žƒ‹›ƒ›ƒ‰„‡”ƒ‹–ƒ†‡‰ƒƒ–”‹•Ǥ‡„ƒŠƒ•ƒ‹‹†‹ƒ™ƒŽ‹†‡‰ƒ‡ƒŠƒ‹ Ž‡„‹Š †ƒŽƒ –‡–ƒ‰ ƒ–”‹•ǡ ‡‡—ƒ Œ‡‹•ǦŒ‡‹• ƒ–”‹•ǡ ‘’‡”ƒ•‹ ƒ–”‹• „ƒ‹ ’‡Œ—ŽƒŠƒǡ’‡‰—”ƒ‰ƒǡ’‡”ƒŽ‹ƒǡ†‡–‡”‹ƒ†ƒ‹˜‡”•ƒ–”‹•ǡ–”ƒ•’‘•ƒ–”‹•ǡ•‡”–ƒ ‡‰ƒ’Ž‹ƒ•‹ƒ†‡–‡”‹ƒƒ—’—‹˜‡”•ƒ–”‹•‡†ƒŽƒ•‹•–‡’‡”•ƒƒƒŽ‹‡ƒ”Ǥ‡Žƒ‹ ’‡Œ‡Žƒ•ƒ‡‰‡ƒ‹ƒ–‡”‹›ƒ‰†‹–ƒ’‹Žƒǡ‘†—Ž‹‹Œ—‰ƒ†‹Ž‡‰ƒ’‹†‡‰ƒŽƒ–‹Šƒ—–— ‡‰—Œ‹ ’‡ƒŠƒƒ †ƒ ’‡‰—ƒ•ƒƒ †ƒ”‹ ’‡•‡”–ƒ †‹†‹ –‡”Šƒ†ƒ’ ƒ–‡”‹ ›ƒ‰ –‡ŽƒŠ †‹ ’‡ŽƒŒƒ”‹›ƒǤ‘†—Ž‹‹†‹•—•—†‡‰ƒ„ƒŠƒ•ƒ›ƒ‰•‡†‡”Šƒƒǡ†ƒ†‹„—ƒ–„‡”—”—–ƒ•‡•—ƒ‹†‡ ‰ƒ —”—–ƒ ƒ–‡”‹ ›ƒ‰ –‡”Ž‡„‹Š †ƒŠ—Ž— ’‡”Ž— †‹—ƒ•ƒ‹Ǥ –— ‹–—ǡ •‡„‡Ž— ‡’‡ŽƒŒƒ”‹ ‘†—Ž‹‹•‡„ƒ‹›ƒǤ ͳǤƒ…ƒ’‡‰ƒ–ƒ”‘†—Ž—–—‡‰‡–ƒŠ—‹ƒ”ƒŠ’‡‰‡„ƒ‰ƒ‘†—Ž ʹǤ‡„ƒ…ƒ‘’‡–‡•‹†ƒ•ƒ”†ƒ–—Œ—ƒ›ƒ‰‹‰‹†‹…ƒ’ƒ‹‡ŽƒŽ—‹‘†—ŽǤ ͵Ǥ ‰ƒ”‡’‡”‘Ž‡Š ‰ƒ„ƒ”ƒ ›ƒ‰ —–—Š‡‰‡ƒ‹‘†—Žǡƒƒ ’‡‰‰—ƒ ’‡”Ž—‡„ƒ…ƒ †ƒ‡ƒŠƒ‹’‡–ƒ‘•‡’Ǥ ͶǤ‡’‡ŽƒŒƒ”‹‘†—Ž•‡…ƒ”ƒ„‡”—”—–ƒƒ‰ƒ”‡’‡”‘Ž‡Š’‡ƒŠƒƒ›ƒ‰—–—ŠǤ ͷǤ—–‹•‡—ƒ–ƒŠƒ’ƒ†ƒ’‡–—Œ—›ƒ‰ƒ†ƒ’ƒ†ƒ‘†—Ž‹‹ Tujuan yang Diharapkan Setelah Mempelajari Modul —Œ—ƒ’‡„‡ŽƒŒƒ”ƒ‘†—Ž‹‹ǡƒ‰ƒ”†ƒǣ ͳǤ‡ƒŠƒ‹‘•‡’†ƒŒ‡‹•ǦŒ‡‹•ƒ–”‹•†ƒ’‡‡”ƒ’ƒ›ƒ†ƒŽƒ‡›‡Ž‡•ƒ‹ƒƒ•ƒŽƒŠ ‡Š‹†—’ƒ•‡Šƒ”‹ǦŠƒ”‹Ǥ ʹǤ‡”ƒ’‹Ž‡Žƒ—ƒ‘’‡”ƒ•‹ƒ–”‹•†ƒ‡›‡Ž‡•‹ƒƒ•ƒŽƒŠ•‡Šƒ”‹ǦŠƒ”‹Ǥ ͵Ǥ ‡”„‡–— †ƒ ‡‹Ž‹‹ •‹ƒ’ ‡ƒ†‹”‹ƒǡ „‡”–‹†ƒ Ž‘‰‹•ǡ –‹†ƒ —†ƒŠ ‡›‡”ƒŠ †ƒ ’‡”…ƒ›ƒ†‹”‹‡‰‰—ƒƒƒ–‡ƒ–‹ƒ†ƒŽƒ’‡‰‡„ƒ‰ƒ‡Š‹†—’ƒ•‡Šƒ”‹ǦŠƒ”‹Ǥ‡…ƒ”ƒ Š—•—•ǡ •‡–‡ŽƒŠ ‡’‡ŽƒŒƒ”‹ ‘†—Ž ‹‹ǡ †ƒ †‹Šƒ”ƒ’ƒ ‡‹Ž‹‹ ‡ƒ’—ƒ ’‡‰‡–ƒŠ—ƒ †ƒ ‡–‡”ƒ’‹Žƒ †ƒŽƒ ‡‡—ƒ ‘•‡’ ƒ–”‹• †ƒ ‡›‡Ž‡•ƒ‹ƒ ƒ•ƒŽƒŠ‘–‡•–—ƒŽǢ‡‡–—ƒǡ‡‰‰—ƒƒǡ†ƒ‡›‡Ž‡•ƒ‹ƒƒ•ƒŽƒŠƒ–”‹•Ǥ

MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 3 Pengantar Modul ƒ›ƒ’‡”‹•–‹™ƒƒ–ƒ—•‹–—ƒ•‹•‡Šƒ”‹ǦŠƒ”‹›ƒ‰†ƒ’ƒ–†‹›ƒ–ƒƒ†ƒŽƒ•‹„‘Žƒ–ƒ—–ƒ„‡Ž›ƒ‰ •‡†‡”Šƒƒǡ”‹‰ƒ•†ƒƒ—”ƒ–ƒ‰ƒ”Ž‡„‹Š—†ƒŠ†‹’ƒŠƒ‹•‡Š‹‰‰ƒ’‡”Ž—†‹‡ƒŽƒ‘•‡’ ƒ–”‹•ǡ „ƒ‹ ’‡”•ƒƒƒ ƒ—’— ‘’‡”ƒ•‹ ›ƒ‰ †‹‰—ƒƒ›ƒǤ ƒ†ƒ ‘†—Ž ‹‹ ƒƒ †‹„ƒŠƒ• –‡–ƒ‰ƒ–”‹•–‡”—–ƒƒ›ƒ‰–‡”ƒ‹–†‡‰ƒŒ‡‹•ǦŒ‡‹•ƒ–”‹•ǡ‘’‡”ƒ•‹†ƒ•ƒ”ƒ–”‹•„ƒ‹ ’‡Œ—ŽƒŠƒǡ ’‡‰—”ƒ‰ƒ ƒ—’— ’‡”ƒŽ‹ƒ ƒ–”‹•ǡ †ƒ ’‡‰‰—ƒƒ †ƒ”‹ †‡–‡”‹ƒ ƒ—’—‹˜‡”•ƒ–”‹••‡”–ƒ–”ƒ•’‘•‡ƒ–”‹•ǡƒ’Ž‹ƒ•‹ƒ–”‹•—–—‡›‡Ž‡•ƒ‹ƒ•‹•–‡ ’‡”•ƒƒƒ Ž‹‡ƒ”Ǥ ‡–ƒ ‘•‡’ †ƒ”‹ ƒ–‡”‹ ’‡ŽƒŒƒ”ƒ –‡”•‡„—– †ƒ’ƒ– †‹‰ƒ„ƒ”ƒ •‡„ƒ‰ƒ‹ „‡”‹—–Ǥ Wffid<KE^ffiW DĂƚƌŝŬƐ WĞŶŐĞƌƚŝĂŶĚĂŶũĞŶŝƐ ŵĂƚƌŝŬƐ ffiůĞŵĞŶŵĂƚƌŝŬƐ DĂƚƌŝŬƐďĂƌŝƐ DĂƚƌŝŬƐŬŽůŽŵ DĂƚƌŝŬƐƉĞƌƐĞŐŝ DĂƚƌŝŬƐƉĞƌƐĞŐŝƉĂŶũĂŶŐ DĂƚƌŝŬƐĚŝĂŐŽŶĂů DĂƚƌŝŬƐƐĞŐŝƚŝŐĂ DĂƚƌŝŬƐ/ĚĞŶƚŝƚĂƐ ^ŝĨĂƚĚĂŶŽƉĞƌĂƐŝŵĂƚƌŝŬƐ WĞŶũƵŵůĂŚĂŶŵĂƚƌŝŬƐ WĞŶŐƵƌĂŶŐĂŶŵĂƌŝŬƐ WĞƌŬĂůŝĂŶŵĂƚƌŝŬƐ <ĞƐĂŵĂĂŶŵĂƚƌŝŬƐ DĂƚƌŝŬƐƚƌĂŶƐƉŽƐĞ ĞƚĞƌŵŝŶĂŶDĂƚƌŝŬƐ /ŶǀĞƌƐŵĂƚƌŝŬƐ  81,7%$5,6$1.(1'$5$$1',6(%8$+3$5.,5$1  Harian Terbit, Parkir di Jakarta (Senin, 29 Agustus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

MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 3 Pengantar Modul ƒ›ƒ’‡”‹•–‹™ƒƒ–ƒ—•‹–—ƒ•‹•‡Šƒ”‹ǦŠƒ”‹›ƒ‰†ƒ’ƒ–†‹›ƒ–ƒƒ†ƒŽƒ•‹„‘Žƒ–ƒ—–ƒ„‡Ž›ƒ‰ •‡†‡”Šƒƒǡ”‹‰ƒ•†ƒƒ—”ƒ–ƒ‰ƒ”Ž‡„‹Š—†ƒŠ†‹’ƒŠƒ‹•‡Š‹‰‰ƒ’‡”Ž—†‹‡ƒŽƒ‘•‡’ ƒ–”‹•ǡ „ƒ‹ ’‡”•ƒƒƒ ƒ—’— ‘’‡”ƒ•‹ ›ƒ‰ †‹‰—ƒƒ›ƒǤ ƒ†ƒ ‘†—Ž ‹‹ ƒƒ †‹„ƒŠƒ• –‡–ƒ‰ƒ–”‹•–‡”—–ƒƒ›ƒ‰–‡”ƒ‹–†‡‰ƒŒ‡‹•ǦŒ‡‹•ƒ–”‹•ǡ‘’‡”ƒ•‹†ƒ•ƒ”ƒ–”‹•„ƒ‹ ’‡Œ—ŽƒŠƒǡ ’‡‰—”ƒ‰ƒ ƒ—’— ’‡”ƒŽ‹ƒ ƒ–”‹•ǡ †ƒ ’‡‰‰—ƒƒ †ƒ”‹ †‡–‡”‹ƒ ƒ—’—‹˜‡”•ƒ–”‹••‡”–ƒ–”ƒ•’‘•‡ƒ–”‹•ǡƒ’Ž‹ƒ•‹ƒ–”‹•—–—‡›‡Ž‡•ƒ‹ƒ•‹•–‡ ’‡”•ƒƒƒ Ž‹‡ƒ”Ǥ ‡–ƒ ‘•‡’ †ƒ”‹ ƒ–‡”‹ ’‡ŽƒŒƒ”ƒ –‡”•‡„—– †ƒ’ƒ– †‹‰ƒ„ƒ”ƒ •‡„ƒ‰ƒ‹ „‡”‹—–Ǥ Wd<KE^W DĂƚƌŝŬƐ WĞŶŐĞƌƚŝĂŶĚĂŶũĞŶŝƐ ŵĂƚƌŝŬƐ ůĞŵĞŶŵĂƚƌŝŬƐ DĂƚƌŝŬƐďĂƌŝƐ DĂƚƌŝŬƐŬŽůŽŵ DĂƚƌŝŬƐƉĞƌƐĞŐŝ DĂƚƌŝŬƐƉĞƌƐĞŐŝƉĂŶũĂŶŐ DĂƚƌŝŬƐĚŝĂŐŽŶĂů DĂƚƌŝŬƐƐĞŐŝƚŝŐĂ DĂƚƌŝŬƐ/ĚĞŶƚŝƚĂƐ ^ŝĨĂƚĚĂŶŽƉĞƌĂƐŝŵĂƚƌŝŬƐ WĞŶũƵŵůĂŚĂŶŵĂƚƌŝŬƐ WĞŶŐƵƌĂŶŐĂŶŵĂƌŝŬƐ WĞƌŬĂůŝĂŶŵĂƚƌŝŬƐ <ĞƐĂŵĂĂŶŵĂƚƌŝŬƐ DĂƚƌŝŬƐƚƌĂŶƐƉŽƐĞ ĞƚĞƌŵŝŶĂŶDĂƚƌŝŬƐ /ŶǀĞƌƐŵĂƚƌŝŬƐ  81,7%$5,6$1.(1'$5$$1',6(%8$+3$5.,5$1  Harian Terbit, Parkir di Jakarta (Senin, 29 Agustus 2016 00:26 WIB)   ,OXVWUDVL GLDWDV PHQJJDPEDUNDQ VHEXDK SDUNLUDQ \DQJ DGD GL NRWD -DNDUWD 1DK GDUL LOXVWUDVL NLWD DNDQPHPSHODMDULWHQWDQJPDWULNV6HEHOXPNLWDSHODMDULPDWULNVOHELKPHQGDODPPDND NLWD KDUXV WDKXDSDLWXPDWULNV fl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fflDGLEDFDEDULVNHGDQNRORPNHffDGLEDFDEDULV NHGDQNRORPNHffDWDXDPQ\DQJEHUDUWLEDULVNHPGDQNRORPNHQ%DQ\DNQ\DEDULVGDQNRORP

MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 5 GDODP PDWULNV GLVHEXW GHQJDQRUGR8UXWDQ \DQJ SHUOX GLLQJDW DGDODKEDULV NHPXGLDQ NRORP 0LVDONDQ 0DWULNV$GHQJDQRUGR[ ELDVDQ\D GLQ\DWDNDQGHQJDQ$[ fl -HQLVMHQLV0DWULNV L0DWULNV1RO2 'LQDPDNDQPDWULNVQRONDUHQDVHPXDHOHPHQQ\DEHUQLODL12/ &RQWRKffl $ ቂ ૙ ૙ ૙ ૙ቃ% ቂ ૙૙૙ ૙૙૙ቃ LL0DWULNVSHUVHJL $GDODKPDWULNV\DQJEDQ\DNEDULVQ\DVDPDGHQJDQEDQ\DNNRORPQ\D0DWULNVSHUVHJLGLVHEXWSXOD GHQJDQPDWULNVEXMXUVDQJNDU &RQWRKffl $ ቂ ͳ ʹ ͵ Ͷቃ LLL0DWULNV6NDODU 0DWULNVVNDODUDGDODKPDWULNVSHUVHJL\DQJHOHPHQHOHPHQSDGDODMXUGLDJRQDOQ\DEHUQLODLVDPD FRQWRKffl & ቂ ૛ ૙ ૙ ૛ቃ' ൥ ૞૙૙ ૙૞૙ ૙૙૞ ൩ LY0DWULNV,GHQWLWDV $GDODKPDWULNVVNDODU\DQJHOHPHQHOHPHQGLDJRQDOXWDPDQ\DEHUQLODL &RQWRKffl $ ቂ ૚ ૙ ૙ ૚ቃ% ൥ ૚૙૙ ૙૚૙ ૙૙૚ ൩ Y0DWULNV6HJLWLJD$WDV $GDODKPDWULNVSHUVHJL\DQJHOHPHQHOHPHQGLEDZDKGLDJRQDOXWDPDQ\DNLULDWDVNHNDQDQEDZDK EHUQLODLQRO &RQWRKffl & ቂ ૛ ૞ ૙ ૚ቃ' ൥ ૚ૠ૟ ૙૜ૡ ૙૙૝ ൩ YL0DWULNV6HJLWLJD%DZDK .HEDOLNDQGDULVHJLWLJDDWDVPDWULNVVHJLWLJDEDZDKDGDODKPDWULNVSHUVHJL\DQJHOHPHQHOHPHQGL DWDVGLDJRQDOXWDPDQ\DEHUQLODLQRO &RQWRKffl $ ቂ ૝ ૙ ૟ ૚ቃ% ൥ ૛૙૙ ૝૞૙ ૠ૜૚ ൩ YL0DWULNV'LDJRQDO DGDODKPDWULNVEXMXUVDQJNDU\DQJVHPXDHOHPHQGLOXDUGLDJRQDOXWDPDDGDODKQRO &RQWRK ( ቂ ૚ ૙ ૙ቃ) ൥ ૚૙૙ ૙૛૙ ૙૙૜ ൩  2SHUDVL'DVDU0DWULNV 3HQMXPODKDQGDQSHQJXUDQJDQPDWULNV 3HQMXPODKDQVHUWDSHQJXUDQJDQGDODPPDWULNVKDQ\DGDSDWGLODNXNDQDSDELODNHGXDPDWULNV PHPSXQ\DLXNXUDQDWDXRUGR\DQJVDPD(OHPHQHOHPHQGDODPVXDWXPDWULNV\DQJGLMXPODKNDQ DWDXGLNXUDQJNDQ\DLWXHOHPHQ\DQJPHPLONLSRVLVLOHWDN\DQJVDPD &RQWRK 'LNHWDKXL$ ቀ ʹ െ͵ ͵ ͷ ቁ% ቀ െͶ ͸ ͷ Ͳቁ 7HQWXNDQ$% -DZDE ቀ ʹ െ͵ ͵ ͷ ቁቀ െͶ ͸ ͷ Ͳቁ ቀ ʹ ൅ ሺെͶሻ െ͵ ൅ ͸ ͵൅ͷ ͷ൅Ͳ ቁ ቀ െʹ ͵ ͺ ͷቁ 'LNHWDKXL& ቀ Ͷʹͳ െ͵ ͸ െͳቁ' ቀ ͹ െͶ ͸ ͵ ͷ െͺቁ 7HQWXNDQ&±' -DZDE ቀ Ͷʹͳ െ͵ ͸ െͳቁቀ ͹ െͶ ͸ ͵ ͷ െͺቁ ቀ Ͷ െ ͹ ʹ െ ሺെͶሻ ͳ െ ͸ െ͵ െ ͵ ͸ െ ͷ െͳ െ ͺቁ ቀ െ͵ ͸ െͷ െ͸ ͳ െͻቁ 3HUNDOLDQ0DWULNV $ 3HUNDOLDQPDWULNVGHQJDQVNDODU 3HUNDOLDQPDWULNVGHQJDQVNDODUDGDODHQJDOLNDQVHPXDHOHPHQHOHPHQPDWULNVHQJDQVNDODUQ\D

MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 5 GDODP PDWULNV GLVHEXW GHQJDQRUGR8UXWDQ \DQJ SHUOX GLLQJDW DGDODKEDULV NHPXGLDQ NRORP 0LVDONDQ 0DWULNV$GHQJDQRUGR[ ELDVDQ\D GLQ\DWDNDQGHQJDQ$[  -HQLVMHQLV0DWULNV L0DWULNV1RO2 'LQDPDNDQPDWULNVQRONDUHQDVHPXDHOHPHQQ\DEHUQLODL12/ &RQWRK $ ቂ ૙ ૙ ૙ ૙ቃ% ቂ ૙૙૙ ૙૙૙ቃ LL0DWULNVSHUVHJL $GDODKPDWULNV\DQJEDQ\DNEDULVQ\DVDPDGHQJDQEDQ\DNNRORPQ\D0DWULNVSHUVHJLGLVHEXWSXOD GHQJDQPDWULNVEXMXUVDQJNDU &RQWRK $ ቂ ͳ ʹ ͵ Ͷቃ LLL0DWULNV6NDODU 0DWULNVVNDODUDGDODKPDWULNVSHUVHJL\DQJHOHPHQHOHPHQSDGDODMXUGLDJRQDOQ\DEHUQLODLVDPD FRQWRK & ቂ ૛ ૙ ૙ ૛ቃ' ൥ ૞૙૙ ૙૞૙ ૙૙૞ ൩ LY0DWULNV,GHQWLWDV $GDODKPDWULNVVNDODU\DQJHOHPHQHOHPHQGLDJRQDOXWDPDQ\DEHUQLODL &RQWRK $ ቂ ૚ ૙ ૙ ૚ቃ% ൥ ૚૙૙ ૙૚૙ ૙૙૚ ൩ Y0DWULNV6HJLWLJD$WDV $GDODKPDWULNVSHUVHJL\DQJHOHPHQHOHPHQGLEDZDKGLDJRQDOXWDPDQ\DNLULDWDVNHNDQDQEDZDK EHUQLODLQRO &RQWRK & ቂ ૛ ૞ ૙ ૚ቃ' ൥ ૚ૠ૟ ૙૜ૡ ૙૙૝ ൩ YL0DWULNV6HJLWLJD%DZDK .HEDOLNDQGDULVHJLWLJDDWDVPDWULNVVHJLWLJDEDZDKDGDODKPDWULNVSHUVHJL\DQJHOHPHQHOHPHQGL DWDVGLDJRQDOXWDPDQ\DEHUQLODLQRO &RQWRK $ ቂ ૝ ૙ ૟ ૚ቃ% ൥ ૛૙૙ ૝૞૙ ૠ૜૚ ൩ YL0DWULNV'LDJRQDO DGDODKPDWULNVEXMXUVDQJNDU\DQJVHPXDHOHPHQGLOXDUGLDJRQDOXWDPDDGDODKQRO &RQWRKffl ( ቂ ૚ ૙ ૙ ૛ቃ) ൥ ૚૙૙ ૙૛૙ ૙૙૜ ൩ fl 2SHUDVL'DVDU0DWULNV fl3HQMXPODKDQGDQSHQJXUDQJDQPDWULNV 3HQMXPODKDQVHUWDSHQJXUDQJDQGDODPPDWULNVKDQ\DGDSDWGLODNXNDQDSDELODNHGXDPDWULNV PHPSXQ\DLXNXUDQDWDXRUGR\DQJVDPD(OHPHQHOHPHQGDODPVXDWXPDWULNV\DQJGLMXPODKNDQ DWDXGLNXUDQJNDQ\DLWXHOHPHQ\DQJPHPLONLSRVLVLOHWDN\DQJVDPD &RQWRKffl 'LNHWDKXLffl$ ቀ ʹ െ͵ ͵ ͷ ቁ% ቀ െͶ ͸ ͷ Ͳቁ 7HQWXNDQffl$% -DZDEffl ቀ ʹ െ͵ ͵ ͷ ቁቀ െͶ ͸ ͷ Ͳቁ ቀ ʹ ൅ ሺെͶሻ െ͵ ൅ ͸ ͵൅ͷ ͷ൅Ͳ ቁ ቀ െʹ ͵ ͺ ͷቁ 'LNHWDKXLffl& ቀ Ͷʹͳ െ͵ ͸ െͳቁ' ቀ ͹ െͶ ͸ ͵ ͷ െͺቁ 7HQWXNDQffl&±' -DZDEffl ቀ Ͷʹͳ െ͵ ͸ െͳቁቀ ͹ െͶ ͸ ͵ ͷ െͺቁ ቀ Ͷ െ ͹ ʹ െ ሺെͶሻ ͳ െ ͸ െ͵ െ ͵ ͸ െ ͷ െͳ െ ͺቁ ቀ െ͵ ͸ െͷ െ͸ ͳ െͻቁ fl3HUNDOLDQ0DWULNV $ 3HUNDOLDQPDWULNVGHQJDQVNDODU 3HUNDOLDQPDWULNVGHQJDQVNDODUDGDODKPHQJDOLNDQVHPXDHOHPHQHOHPHQPDWULNVGHQJDQVNDODUQ\D

MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 7 &RQWRKffl ൭ ݏ ܾܽܿ ݂݀݁ ݄݃ ݅൱ ൭ ܿݏ ܾݏ ܽݏ ݂ݏ ݁ݏ ݀ݏ ൱݅ݏ ݄ݏ ݃ݏ &REDSHUKDWLNDQFDUDPHODNXNDQSHUNDOLDQPDWULNVGHQJDQVNDODUEHULNXWffl 'LNHWDKXLVNDODUV GHQJDQPDWULNV$ ൭ ʹ ͷ ͵ ʹ ͸ Ͷ ൱ V$ ൭ ʹ ͷ ͵ ʹ ͸ Ͷ ൱ ൭ ͸ ͳͷ ͻ ͸ ͳͺ ͳʹ ൱  % 3HUNDOLDQGXDPDWULNV 0LVDONDQ$PDWULNVGHQJDQRUGRP[QGDQ%PDWULNVGHQJDQRUGRQ[S3HUNDOLDQGXDPDWULNV GDSDWGLODNXNDQDSDELODMXPODKNRORPPDWULNVSHUWDPDVDPDGHQJDQMXPODKEDULVPDWULNVNHGXD -DGLPDWULNV$P[QGDSDWGLNDOLNDQGHQJDQPDWULNV%Q[SGHQJDQKDVLOPDWULNV&GHQJDQRUGRP[S 6HOSDGDEDULVSHUWDPDGDQNRORPSHUWDPDGDULPDWULNV&PHUXSDNDQMXPODKGDULKDVLONDOLWLDSVHO PDWULNV$SDGDEDULVSHUWDPDGHQJDQVHOSDGDNRORPSHUWDPDGDULPDWULNV%0LVDONDQ$  ቂ ܽଵଵ ܽଵଶ ܽଵଷ ܽଶଵ ܽଶଶ ܽଶଷቃGDQ% ൥ ܾଵଵ ܾଵଶ ܾଶଵ ܾଶଶ ܾଷଵ ܾଷଶ ൩-XPODKNRODPPDWULNV$VDPDGHQJDQMXPODKEDULVPDWULNV %MDGL$GDSDWGLNDOLNDQGDULNLULGHQJDQ%\DLWXffl $î% $%  ቂ ܽଵଵ ܽଵଶ ܽଵଷ ܽଶଵ ܽଶଶ ܽଶଷቃ ൥ ܾଵଵ ܾଵଶ ܾଶଵ ܾଶଶ ܾଷଵ ܾଷଶ ൩  ൤ ܽଵଵܾଵଵ ൅ ܽଵଶܾଶଵ ൅ ܽଵଷܾଷଵ ܽଵଵܾଵଶ ൅ ܽଵଶܾଶଶ ൅ ܽଵଷܾଷଶ ܽଶଵܾଵଵ ൅ ܽଶଶܾଶଵ ൅ ܽଶଷܾଷଵ ܽଶଵܾଵଶ ൅ ܽଶଶܾଶଶ ൅ ܽଶଷܾଷଶ ൨ &RQWRK 0LVDONDQ$ ቂ ͳ െͳ ʹ ͵ Ͳ െͳቃGDQ% ൥ ͳ ʹ Ͳ െͳ െ͵ ͳ ൩0DNDD7HQWXNDQ$%ffEDSDNDK$% %$" D $% ቂ ͳ െͳ ʹ ͵ Ͳ െͳቃ ൥ ͳ ʹ Ͳ െͳ െ͵ ͳ ൩  ൤ ሺͳሻሺͳሻ ൅ ሺെͳሻሺͲሻ ൅ ሺʹሻሺെ͵ሻ ሺͳሻሺʹሻ ൅ ሺെͳሻሺെͳሻ ൅ ሺʹሻሺͳሻ ሺ͵ሻሺͳሻ ൅ ሺͲሻሺͲሻ ൅ ሺെͳሻሺെ͵ሻ ሺ͵ሻሺʹሻ ൅ ሺͲሻሺെͳሻ ൅ ሺെͳሻሺͳሻ ൨  ቂ ͳ൅Ͳെ͸ ʹ൅ͳ൅ʹ ͵൅Ͳ൅͵ ͸൅Ͳെͳቃ ቂ െͷ ͷ ͸ ͷቃ E 0DWULNV$PHPLOLNLRUGR[GDQPDWULNV%PHPLOLNLRUGR[-DGL%GDSDWGLNDOLNDQ GDULNLULGHQJDQ$\DLWX %$ ൥ ͳ ʹ Ͳ െͳ െ͵ ͳ ൩ቂ ͳ െͳ ʹ ͵ Ͳ െͳቃ  ቎ ሺͳሻሺͳሻ ൅ ሺʹሻሺ͵ሻ ሺͳሻሺെͳሻ ൅ ሺʹሻሺͲሻ ሺͳሻሺʹሻ ൅ ሺʹሻሺെͳሻ ሺͲሻሺͳሻ ൅ ሺെͳሻሺ͵ሻ ሺͲሻሺെͳሻ ൅ ሺെͳሻሺͲሻ ሺͲሻሺʹሻ ൅ ሺെͳሻሺെͳሻ ሺെ͵ሻሺͳሻ ൅ ሺͳሻሺ͵ሻ ሺെ͵ሻሺെͳሻ ൅ ሺͳሻሺͲሻ ሺെ͵ሻሺʹሻ ൅ ሺͳሻሺെͳሻ ቏  ൥ ͹ െͳ Ͳ െ͵ Ͳ ͳ Ͳ ͵ െ͹ ൩ 'DSDWGLVLPSXONDQEDKZDMLND$GDQ%PDWULNV\DQJGDSDWGLNDOLNDQPDND$%%$ 8QWXNSHPEDKDVDQSHUNDOLDQPDWULNVXNXUDQ[GHQJDQXNXUDQ[ 3HUKDWLNDQFRQWRKEHULNXW 'LNHWDKXL $ ൭ ͳ ͵ ʹ ʹ Ͷ ͵ ൱GDQ% ቀ Ͷ ͳ ቁ -DZDE $[% ൭ ͳ ͵ ʹ ʹ Ͷ ͵ ൱[ቀ Ͷ ͳ ቁ ൌ ൭ ͳݔͶ ൅ ͵ݔͳ ͳݔʹ ൅ Ͷݔʹ ͶݔͶ ൅ ͵ݔͳ ൱ ൌ ൭ Ͷ൅͵ ͺ൅ʹ ͳ͸ ൅ ͵ ൱ ൌ ൭ ͹ ͳͲ ͳͻ ൱ 6LIDWVLIDWRSHUDVLSHUNDOLDQPDWULNVPHOLSXWLVLIDWDVRVLDWLIGDQGLVWULEXWLI /DWLKDQ 6HOHVDLNDQVRDOGLEDZDKLQLGHQJDQEHQDU  'LNHWDKXLPDWULNV; ൭ Ͷ ʹ ͵ ͷ ͻ ͹ ൱GDQPDWULNV< ൭ ͹ ͷ ͺ ͸ ͵ Ͷ ൱ 7HQWXNDQ ;<GDQ;< 6LIDW$VRVLDWLI࡭ሺ࡯࡮ሻ ൌ ሺ࡮࡭ሻ࡯ ࡯࡮ ൅ ࡯࡭ ൌ ࡯ሻ࡮൅࡭ሺGDQ࡯࡭ ൅ ࡮࡭ ൌ ሻ࡯൅࡮ሺ࡭LVWULEXWLI'6LIDW 3HUNDOLDQPDWULNVWLGDNNRPXWDWLI$%%$ 6LIDWVLIDW2SHUDVL3HUNDOLDQ0DWULNV

MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 7 &RQWRK ൭ ݏ ܾܽܿ ݂݀݁ ݄݃ ݅൱ ൭ ܿݏ ܾݏ ܽݏ ݂ݏ ݁ݏ ݀ݏ ൱݅ݏ ݄ݏ ݃ݏ &REDSHUKDWLNDQFDUDPHODNXNDQSHUNDOLDQPDWULNVGHQJDQVNDODUEHULNXW 'LNHWDKXLVNDODUV GHQJDQPDWULNV$ ൭ ʹ ͷ ͵ ʹ ͸ Ͷ ൱ V$ ൭ ʹ ͷ ͵ ʹ ͸ Ͷ ൱ ൭ ͸ ͳͷ ͻ ͸ ͳͺ ͳʹ ൱  % 3HUNDOLDQGXDPDWULNV 0LVDONDQ$PDWULNVGHQJDQRUGRP[QGDQ%PDWULNVGHQJDQRUGRQ[S3HUNDOLDQGXDPDWULNV GDSDWGLODNXNDQDSDELODMXPODKNRORPPDWULNVSHUWDPDVDPDGHQJDQMXPODKEDULVPDWULNVNHGXD -DGLPDWULNV$P[QGDSDWGLNDOLNDQGHQJDQPDWULNV%Q[SGHQJDQKDVLOPDWULNV&GHQJDQRUGRP[S 6HOSDGDEDULVSHUWDPDGDQNRORPSHUWDPDGDULPDWULNV&PHUXSDNDQMXPODKGDULKDVLONDOLWLDSVHO PDWULNV$SDGDEDULVSHUWDPDGHQJDQVHOSDGDNRORPSHUWDPDGDULPDWULNV%0LVDONDQ$  ቂ ܽଵଵ ܽଵଶ ܽଵଷ ܽଶଵ ܽଶଶ ܽଶଷቃGDQ% ൥ ܾଵଵ ܾଵଶ ܾଶଵ ܾଶଶ ܾଷଵ ܾଷଶ ൩-XPODKNRODPPDWULNV$VDPDGHQJDQMXPODKEDULVPDWULNV %MDGL$GDSDWGLNDOLNDQGDULNLULGHQJDQ%\DLWX $î% $%  ቂ ܽଵଵ ܽଵଶ ܽଵଷ ܽଶଵ ܽଶଶ ܽଶଷቃ ൥ ܾଵଵ ܾଵଶ ܾଶଵ ܾଶଶ ܾଷଵ ܾଷଶ ൩  ൤ ܽଵଵܾଵଵ ൅ ܽଵଶܾଶଵ ൅ ܽଵଷܾଷଵ ܽଵଵܾଵଶ ൅ ܽଵଶܾଶଶ ൅ ܽଵଷܾଷଶ ܽଶଵܾଵଵ ൅ ܽଶଶܾଶଵ ൅ ܽଶଷܾଷଵ ܽଶଵܾଵଶ ൅ ܽଶଶܾଶଶ ൅ ܽଶଷܾଷଶ ൨ &RQWRK 0LVDONDQ$ ቂ ͳ െͳ ʹ ͵ Ͳ െͳቃGDQ% ൥ ͳ ʹ Ͳ െͳ െ͵ ͳ ൩0DNDD7HQWXNDQ$%EDSDNDK$% %$" D $% ቂ ͳ െͳ ʹ ͵ Ͳ െͳቃ ൥ ͳ ʹ Ͳ െͳ െ͵ ͳ ൩  ൤ ሺͳሻሺͳሻ ൅ ሺെͳሻሺͲሻ ൅ ሺʹሻሺെ͵ሻ ሺͳሻሺʹሻ ൅ ሺെͳሻሺെͳሻ ൅ ሺʹሻሺͳሻ ሺ͵ሻሺͳሻ ൅ ሺͲሻሺͲሻ ൅ ሺെͳሻሺെ͵ሻ ሺ͵ሻሺʹሻ ൅ ሺͲሻሺെͳሻ ൅ ሺെͳሻሺͳሻ ൨  ቂ ͳ൅Ͳെ͸ ʹ൅ͳ൅ʹ ͵൅Ͳ൅͵ ͸൅Ͳെͳቃ ቂ െͷ ͷ ͸ ͷቃ E 0DWULNV$PHPLOLNLRUGR[GDQPDWULNV%PHPLOLNLRUGR[-DGL%GDSDWGLNDOLNDQ GDULNLULGHQJDQ$\DLWX %$ ൥ ͳ ʹ Ͳ െͳ െ͵ ͳ ൩ቂ ͳ െͳ ʹ ͵ Ͳ െͳቃ  ቎ ሺͳሻሺͳሻ ൅ ሺʹሻሺ͵ሻ ሺͳሻሺെͳሻ ൅ ሺʹሻሺͲሻ ሺͳሻሺʹሻ ൅ ሺʹሻሺെͳሻ ሺͲሻሺͳሻ ൅ ሺെͳሻሺ͵ሻ ሺͲሻሺെͳሻ ൅ ሺെͳሻሺͲሻ ሺͲሻሺʹሻ ൅ ሺെͳሻሺെͳሻ ሺെ͵ሻሺͳሻ ൅ ሺͳሻሺ͵ሻ ሺെ͵ሻሺെͳሻ ൅ ሺͳሻሺͲሻ ሺെ͵ሻሺʹሻ ൅ ሺͳሻሺെͳሻ ቏  ൥ ͹ െͳ Ͳ െ͵ Ͳ ͳ Ͳ ͵ െ͹ ൩ 'DSDWGLVLPSXONDQEDKZDMLND$GDQ%PDWULNV\DQJGDSDWGLNDOLNDQPDND$%%$ 8QWXNSHPEDKDVDQSHUNDOLDQPDWULNVXNXUDQ[GHQJDQXNXUDQ[ 3HUKDWLNDQFRQWRKEHULNXW 'LNHWDKXLffl $ ൭ ͳ ͵ ʹ ʹ Ͷ ͵ ൱GDQ% ቀ Ͷ ͳ ቁ -DZDEffl $[% ൭ ͳ ͵ ʹ ʹ Ͷ ͵ ൱[ቀ Ͷ ͳ ቁ ൌ ൭ ͳݔͶ ൅ ͵ݔͳ ͳݔʹ ൅ Ͷݔʹ ͶݔͶ ൅ ͵ݔͳ ൱ ൌ ൭ Ͷ൅͵ ͺ൅ʹ ͳ͸ ൅ ͵ ൱ ൌ ൭ ͹ ͳͲ ͳͻ ൱ 6LIDWVLIDWRSHUDVLSHUNDOLDQPDWULNVPHOLSXWLVLIDWDVRVLDWLIGDQGLVWULEXWLI /DWLKDQ 6HOHVDLNDQVRDOGLEDZDKLQLGHQJDQEHQDU  'LNHWDKXLPDWULNV; ൭ Ͷ ʹ ͵ ͷ ͻ ͹ ൱GDQPDWULNV< ൭ ͹ ͷ ͺ ͸ ͵ Ͷ ൱ 7HQWXNDQ ;<GDQ;< 6LIDW$VRVLDWLIffl࡭ሺ࡯࡮ሻ ൌ ሺ࡮࡭ሻ࡯ ࡯࡮ ൅ ࡯࡭ ൌ ࡯ሻ࡮൅࡭ሺGDQ࡯࡭ ൅ ࡮࡭ ൌ ሻ࡯൅࡮ሺ࡭fflLVWULEXWLI'6LIDW 3HUNDOLDQPDWULNVWLGDNNRPXWDWLIffl$%%$ 6LIDWVLIDW2SHUDVL3HUNDOLDQ0DWULNV

MatemaƟ k Paket C - tara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 9  'LNHWDKXLVNDODUD ଵ ଷ GDQPDWULNV/ ቀ ͳʹ ͵ ͻ ͸ ͳͷ ͸ቁ 7HQWXNDQ D<  'LNHWDKXLPDWULNV0 ൭ ʹ Ͷ Ͷ ͵ ʹ ͳ ൱GDQPDWULNV1 ቀ Ͷ͵ͳ ͸ͷʹቁ 7HQWXNDQ 01 -LND$DGODKPDWULNV[WHQWXNDQODKSHQ\HOHVDLDQVHWLDSSHUVDPDDQEHULNXWLQL D$ ቀ ͸ െͳͷ ͻ ͳʹ ቁE$ቀ ͵ ͳ Ͷ ʹቁ ቀ ͻ ͷ ʹ ͺቁF$ቀ ͵ ͳ Ͷ Ͷቁ ቀ ͷ ͵ Ͳ ͳʹቁ  -LND$ ቀ Ͷ ͷ ͳ ʹቁff% ቀ ͳ Ͳ ͵ Ͷቁff& ቀ െʹ ͳ െ͵ ͲቁWHQWXNDQODKfflD%&   E$& F$%&    G%$&$ fl7UDQVSRVH0DWULNV $GDODKPDWULNVEDUX\DQJPHUXSDNDQKDVLOSHUWXNDUDQEDULVGDQNRORP 7UDQSRVHPDWULNVGLQRWDVLNDQ$W GLEDFDffl$WUDQVSRVH 6HKLQJJDWUDQVSRVHPDWULNV$DGDODK$W  -LND » ¼ º « ¬ ª =       b b b a a a A PDND » » » ¼ º « « « ¬ ª =      a b a b a b At -LNDPDWULNV$EHURUGRPîQPDNDWUDQVSRVH$PHPLOLNLRUGRQîP 6HFDUD8PXPELVDGLWXOLVNDQffl &RQWRKffl  » ¼ º « ¬ ª × =    A   PDND » ¼ º « ¬ ª ×       t A  » ¼ º « ¬ ª × =       B  PDND » » » ¼ º « « « ¬ ª × =         t B fl ,QYHUVGDQ'HWHUPLQDQ0DWULNV Am × n ͕ŵĂŬĂ n m t A × ĂůĂŵ ƐŝƐƚĞŵ ďŝůĂŶŐĂŶ ƌĞĂů ŬŝƚĂ ŵĞŶŐĞŶĂů ƐĞŚŝŶŐŐĂ ƉĞƌŬĂůŝĂŶ ƐĞďƵŚ ďŝůĂŶŐĂŶ ĚĞŶŐĂŶ ŬĞďĂůŝŬĂŶŶLJĂŚĂƐŝůŶLJĂϭ͘DŝƐĂůŶLJĂϮŬĞďĂůŝŬĂŶŶLJĂЪĂƚĂƵϮͲϭŬĂƌĞŶĂϮ;ЪͿсϭ͕ŬĞďĂůŝŬĂŶĚĂƌŝ ʹϯĂĚĂůĂŚϭͬϯĂƚĂƵϯͲϭ͕ĚĂŶƐĞďĂŐĂŝŶLJĂ͘ DŝƐĂůŬĂŶ ŵĂƚƌŝŬƐ ƉĞƌƐĞŐŝ  с » ¼ º « ¬ ª −  −     ĚĂŶ  с  » ¼ º « ¬ ª − −     ͘ ^ĞŬĂƌĂŶŐ ƉĞƌŚĂƚŝŬĂŶ ƉĞƌŬĂůŝĂŶŵĂƚƌŝŬƐďĞƌŝŬƵƚ͘ с » ¼ º « ¬ ª −  −    » ¼ º « ¬ ª −−     с » ¼ º « ¬ ª − − + − − − + − − + − +             с » ¼ º « ¬ ª     с/ с » ¼ « ¬ ª − −     » ¼ º « ª −  −    с » ¼ º « ¬ ª + − + − − + − − + − −            с » ¼ º « ¬ ª     с/ <ŝƚĂ ŬĂƚĂŬĂŶŵĂƚƌŝŬƐ ŵĞƌƵƉĂŬĂŶŵĂƚƌŝŬƐ ŝŶǀĞƌƐ ĚĂƌŝ  ;ĚŝƚƵůŝƐ ͲϭͿ ŬĂƌĞŶĂ с Ͳϭс/͘ ƉĂŬĂŚ ƐĞƚŝĂƉ ŵĂƚƌŝŬƐ ƉĞƌƐĞŐŝ ŵĞŵŝůŝŬŝ ŝŶǀĞƌƐ͍ DŝƐĂůŶLJĂ͕ ĂƉĂŬĂŚ ŵĂƚƌŝŬƐ ^ с » ¼ º « ¬ ª     ŵĞŵŝůŝŬŝŝŶǀĞƌƐ͍ŶĚĂŝŬĂŶŵĂƚƌŝŬƐ^ŵĞŵŝůŝŬŝŝŶǀĞƌƐ^Ͳϭс » ¼ º « ¬ ª c d a b ͕ŵĂŬĂĚŝƉĞƌŽůĞŚ͗ ^^Ͳϭс/ » ¼ º « ¬ ª     » ¼ º « ¬ ª c d a b с » ¼ º « ¬ ª       ;ƵƌĂŝŬĂŶƉĞƌŬĂůŝĂŶŵĂƚƌŝŬƐƌƵĂƐŬŝƌŝͿ » ¼ º « ¬ ª + + + + a c b d a c b d         с » ¼ º « ¬ ª      ;ŐƵŶĂŬĂŶƉĞŶŐĞƌƚŝĂŶŬĞƐĂŵĂĂŶŵĂƚƌŝŬƐͿ ĚŝƉĞƌŽůĞŚƐŝƐƚĞŵƉĞƌƐĂŵĂĂŶ ϯĂнϲĐсϭ  ϯďнϲĚсϬ ϮĂнϰĐсϬ  ϮďнϰĚсϭ ĞŶŐĂŶŵĞŶLJĞĚĞƌŚĂŬĂŶĚĂŶŵĞŶŐƵƌĂŶŐŬĂŶƉĞƌƐĂŵĂĂŶͲƉĞƌƐĂŵĂĂŶƚĞƌƐĞďƵƚĚŝƉĞƌŽůĞŚ ĂнϯĐсЪ  ďнϮĚсϬ ĂнϮĐсϬ  ďнϮĚсЪ ͲͲͲͲͲͲͲͲͲͲͲͲʹ  ͲͲͲͲͲͲͲͲͲͲͲͲͲͲʹ

MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 9  'LNHWDKXLVNDODUD ଵ ଷ GDQPDWULNV/ ቀ ͳʹ ͵ ͻ ͸ ͳͷ ͸ቁ 7HQWXNDQ D<  'LNHWDKXLPDWULNV0 ൭ ʹ Ͷ Ͷ ͵ ʹ ͳ ൱GDQPDWULNV1 ቀ Ͷ͵ͳ ͸ͷʹቁ 7HQWXNDQ 01 -LND$DGDODKPDWULNV[WHQWXNDQODKSHQ\HOHVDLDQVHWLDSSHUVDPDDQEHULNXWLQL D$ ቀ ͸ െͳͷ ͻ ͳʹ ቁE$ቀ ͵ ͳ Ͷ ʹቁ ቀ ͻ ͷ ʹ ͺቁF$ቀ ͵ ͳ Ͷ Ͷቁ ቀ ͷ ͵ Ͳ ͳʹቁ  -LND$ ቀ Ͷ ͷ ͳ ʹቁ% ቀ ͳ Ͳ ͵ Ͷቁ& ቀ െʹ ͳ െ͵ ͲቁWHQWXNDQODK D%&   E$& F$%&    G%$&$ 7UDQVSRVH0DWULNV $GDODKPDWULNVEDUX\DQJPHUXSDNDQKDVLOSHUWXNDUDQEDULVGDQNRORP 7UDQSRVHPDWULNVGLQRWDVLNDQ$W GLEDFD$WUDQVSRVH 6HKLQJJDWUDQVSRVHPDWULNV$DGDODK$W  -LND » ¼ º « ¬ ª =       b b b a a a A PDND » » » ¼ º « « « ¬ ª =       a b a b a b At -LNDPDWULNV$EHURUGRPîQPDNDWUDQVSRVH$PHPLOLNLRUGRQîP 6HFDUD8PXPELVDGLWXOLVNDQ &RQWRK  » ¼ º « ¬ ª × =     A   PDND » ¼ º « ¬ ª × =       t A  » ¼ º « ¬ ª × =       B  PDND » » » ¼ º « « « ¬ ª × =         t B  ,QYHUVGDQ'HWHUPLQDQ0DWULNV Am × n ͕ŵĂŬĂ n m t A × ĂůĂŵ ƐŝƐƚĞŵ ďŝůĂŶŐĂŶ ƌĞĂů ŬŝƚĂ ŵĞŶŐĞŶĂů ƐĞŚŝŶŐŐĂ ƉĞƌŬĂůŝĂŶ ƐĞďƵĂŚ ďŝůĂŶŐĂŶ ĚĞŶŐĂŶ ŬĞďĂůŝŬĂŶŶLJĂŚĂƐŝůŶLJĂϭ͘DŝƐĂůŶLJĂϮŬĞďĂůŝŬĂŶŶLJĂЪĂƚĂƵϮͲϭŬĂƌĞŶĂϮ;ЪͿсϭ͕ŬĞďĂůŝŬĂŶĚĂƌŝ ʹϯĂĚĂůĂŚϭͬϯĂƚĂƵϯͲϭ͕ĚĂŶƐĞďĂŐĂŝŶLJĂ͘ DŝƐĂůŬĂŶ ŵĂƚƌŝŬƐ ƉĞƌƐĞŐŝ  с » ¼ º « ¬ ª −  −     ĚĂŶ  с  » ¼ º « ¬ ª − −     ͘ ^ĞŬĂƌĂŶŐ ƉĞƌŚĂƚŝŬĂŶ ƉĞƌŬĂůŝĂŶŵĂƚƌŝŬƐďĞƌŝŬƵƚ͘ с » ¼ º « ¬ ª −  −    » ¼ º « ¬ ª − −     с » ¼ º « ¬ ª − − + − − − + − − + − +             с » ¼ º « ¬ ª     с/ с » ¼ º « ¬ ª − −     » ¼ º « ¬ ª −  −    с » ¼ º « ¬ ª + − + − − + − − + − −            с » ¼ º « ¬ ª     с/ <ŝƚĂ ŬĂƚĂŬĂŶŵĂƚƌŝŬƐ ŵĞƌƵƉĂŬĂŶŵĂƚƌŝŬƐ ŝŶǀĞƌƐ ĚĂƌŝ  ;ĚŝƚƵůŝƐ ͲϭͿ ŬĂƌĞŶĂ с Ͳϭс/͘ ƉĂŬĂŚ ƐĞƚŝĂƉ ŵĂƚƌŝŬƐ ƉĞƌƐĞŐŝ ŵĞŵŝůŝŬŝ ŝŶǀĞƌƐ͍ DŝƐĂůŶLJĂ͕ ĂƉĂŬĂŚ ŵĂƚƌŝŬƐ ^ с » ¼ º « ¬ ª     ŵĞŵŝůŝŬŝŝŶǀĞƌƐ͍ŶĚĂŝŬĂŶŵĂƚƌŝŬƐ^ŵĞŵŝůŝŬŝŝŶǀĞƌƐ^Ͳϭс » ¼ º « ¬ ª c d a b ͕ŵĂŬĂĚŝƉĞƌŽůĞŚ͗ ^^Ͳϭс/ » ¼ º « ¬ ª     » ¼ º « ¬ ª c d a b с » ¼ º « ¬ ª       ;ƵƌĂŝŬĂŶƉĞƌŬĂůŝĂŶŵĂƚƌŝŬƐƌƵĂƐŬŝƌŝͿ » ¼ º « ¬ ª + + + + a c b d a c b d         с » ¼ º « ¬ ª      ;ŐƵŶĂŬĂŶƉĞŶŐĞƌƚŝĂŶŬĞƐĂŵĂĂŶŵĂƚƌŝŬƐͿ ĚŝƉĞƌŽůĞŚƐŝƐƚĞŵƉĞƌƐĂŵĂĂŶ ϯĂнϲĐсϭ  ϯďнϲĚсϬ ϮĂнϰĐсϬ  ϮďнϰĚсϭ ĞŶŐĂŶŵĞŶLJĞĚĞƌŚĂŬĂŶĚĂŶŵĞŶŐƵƌĂŶŐŬĂŶƉĞƌƐĂŵĂĂŶͲƉĞƌƐĂŵĂĂŶƚĞƌƐĞďƵƚĚŝƉĞƌŽůĞŚ ĂнϯĐсЪ  ďнϮĚсϬ ĂнϮĐсϬ  ďнϮĚсЪ ͲͲͲͲͲͲͲͲͲͲͲͲʹ  ͲͲͲͲͲͲͲͲͲͲͲͲͲͲʹ

0 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 11 ĐсЪ  ϬсʹЪ ;ŵĞŶŐŚĂƐŝůŬĂŶƉĞƌŶLJĂƚĂĂŶƚŝĚĂŬďĞŶĂƌͿ <ĂƌĞŶĂ ƐŝƐƚĞŵ ƉĞƌƐĂŵĂĂŶ ƚĞƌƐĞďƵƚ ŵĞŶŐŚĂƐŝůŬĂŶ ƉĞƌŶLJĂƚĂĂŶ ƚŝĚĂŬ ďĞŶĂƌ ĂƚĂƵ ŵĞŶŝŵďƵůŬĂŶ ƉĞƌƚĞŶƚĂŶŐĂŶ͕ŝŶŝ ďĞƌĂƌƚŝ ƐŝƐƚĞŵ ƉĞƌƐĂŵĂĂŶ ƚŝĚĂŬŵĞŵŝůŝŬŝ ƐŽůƵƐŝ͘ :ĂĚŝ͕ ƚŝĚĂŬ ĂĚĂ ŵĂƚƌŝŬƐ ^Ͳϭ LJĂŶŐ ŵĞƌƵƉĂŬĂŶ ŝŶǀĞƌƐ ĚĂƌŝ ŵĂƚƌŝŬƐ ^ с » ¼ º « ¬ ª     ͘ <ĞƐŝŵƉƵůĂŶŶLJĂ͕ ƚŝĚĂŬ ƐĞŵƵĂŵĂƚƌŝŬƐƉĞƌƐĞŐŝŵĞŵŝůŝŬŝŝŶǀĞƌƐ͘^ĞďĞůƵŵďĞƌůĂŶũƵƚŬĞƉĞŶŐĞƌƚŝĂŶŵĂƚƌŝŬƐŝŶǀĞƌƐ͕ŬŝƚĂ ďĂŚĂƐĚĞƚĞƌŵŝŶĂŶƐĞďƵĂŚŵĂƚƌŝŬƐLJĂŶŐŵĞŶƵŶũƵŬŬĂŶŝŶǀĞƌƐŵĂƚƌŝŬƐĂĚĂĂƚĂƵƚŝĚĂŬĂĚĂ͘ fl'HWHUPLQDQ0DWULNV &DUDPHQJKLWXQJGHWHUPLQDQPDWULNVSHUVHJLWHUJDQWXQJXNXUDQPDWULNVWHUVHEXW&DUD PHQJKLWXQJQLODLGHWHUPLQDQPDWULNVEXMXUVDQJNDUGHQJDQRUGR[DNDQEHUEHGDGHQJDQ FDUDPHQJKLWXQJPDWULNVEXMXUVDQJNDUGHQJDQRUGR[ D 'HWHUPLQDQ0DWULNV2UGR[ 'LNHWDKXLPDWULNVRUGR[GLQ\DWDNDQVHSHUWLEHQWXNGLEDZDK $ ቂ ܽ ܾ ܿ ݀ቃ 1LODLGHWHUPLQDQ$GLVLPERONDQGHQJDQȁܣȁFDUDPHQJKLWXQJQLODLGHWHUPLQDQ$GDSDWGLOLKDW VHSHUWLSDGDFDUDGLEDZDKLQLffl det$ ȁܣȁ ൌ ܽ݀ െ ܾܿ &RQWRKffl 7HQWXNDQQLODLGHWHUPLQDQPDWULNV% ቂ ʹ ͳ Ͷ ͷቃ -DZDEffl ȁܣȁ ൌ ܽ݀ െ ܾܿ ൌ ʹǤͷ െ ͳǤͶ ൌ ͳͲ െ Ͷ ൌ ͸ E 'HWHUPLQDQ0DWULNV2UGR[ 0DWULNV2UGRDGDODKPDWULNVEXMXUVDQJNDUGHQJDQEDQ\DNQ\DNRORPGDQEDULVVDPDGHQJDQWLJD %HQWXNXPXPPDWULNVRUGRDGDODKVHEDJDLEHULNXWffl $ ൥ ܾܽܿ ݂݀݁ ݄݃ ݅൩ &DUDPHQJKLWXQJGHWHUPLQDQSDGDPDWULNVGHQJDQRUGRWLJDELDVDGLVHEXWGHQJDQAturan Sarrus 8QWXNOHELKMHODVQ\DOLKDWSHQMHODVDQSDGDJDPEDUGLEDZDKLQLffl &RQWRK 7HQWXNDQQLODLGHWHUPLQDQPDWULNV0 ൥ Ͷʹͷ ͵͸͸ ͳ͵ʹ ൩ -DZDE ȁܯȁ ൌ ͶǤ͸Ǥʹ ൅ ʹǤ͸Ǥͳ ൅ ͷǤ͵Ǥ͵ െ ͷǤ͸Ǥͳ െ ͶǤ͸Ǥ͵ െ ʹǤ͵Ǥ͵ ൌ Ͷͺ ൅ ͳʹ ൅ Ͷͷ െ ͵Ͳ െ ͹ʹ െ ͳͺ ൌ ͳͲͷ െ ͳʹͲ ൌ െͳͷ ,QYHUV0DWULNV D ,QYHUVPDWULNVRUGR×  ܾ ܽቂ ൌ ܣܽ݇݅ܬ ܿ ݀ቃ ǡ ݉ܽ݇ܽ A-1 ଵ ୢୣ୲ ஺ ቂ ݀ െܾ െܿ ܽ ቃ &RQWRK -LND$ ቂ ͵ െʹ െͷ Ͷ ቃPDND$  ଵ ଷǤସିሺିଶሻǤሺିହሻ ቂ Ͷ ʹ ͷ ͵ቃ   ଵ ଵଶିଵ଴ ቂ Ͷ ʹ ͷ ͵ቃ   ଵ ଶ ቂ Ͷ ʹ ͷ ͵ቃ  ቎ ସ ଶ ଶ ଶ ହ ଶ ଷ ଶ ቏ E ,QYHUVPDWULNVRUGR× 6HEHOXPPHQHQWXNDQLQYHUVPDWULNVSHUVHJL$RUGRWLJDDWDXOHELKSHUOXGLSHUNHQDONDQ NRIDNWRUPLQRUPDWULNV$DWDX0LMGDQDGMRLQPDWULNV$DWDXDGM$-LND » » » ¼ º « « « ¬ ª = g h i d e f a b c A  PDND L 0LQRUGDULPDWULNVA   Mij DGDODKGHWHUPLQDQPDWULN\DQJGLSUROHGHQJDQPHQJKDSXV EDULVNH±iGDQNRORPNH±j

0 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 11 ĐсЪ  ϬсʹЪ ;ŵĞŶŐŚĂƐŝůŬĂŶƉLJĂƚĂĂŶƚŝĚĂŬďĞŶĂƌͿ <ĂƌĞŶĂ ƐŝƐƚĞŵ ƉĞƌƐĂŵĂĂŶ ƚĞƌƐĞďƵƚ ŵĞŶŐŚĂƐŝůŬĂŶ ƉĞƌŶLJĂƚĂĂŶ ƚŝĚĂŬ ďĞŶĂƌ ĂƚĂƵ ŵĞŶŝŵďƵůŬĂŶ ƉĞƌƚĞŶƚĂŶŐĂŶ͕ŝŶŝ ďĞƌĂƌƚŝ ƐŝƐƚĞŵ ƉĞƌƐĂŵĂĂŶ ƚŝĚĂŬŵĞŵŝůŝŬŝ ƐŽůƵƐŝ͘ :ĂĚŝ͕ ƚŝĚĂŬ ĂĚĂ ŵĂƚƌŝŬƐ ^Ͳϭ LJĂŶŐ ŵĞƌƵƉĂŬĂŶ ŝŶǀĞƌƐ ĚĂƌŝ ŵĂƚƌŝŬƐ ^ с » ¼ º « ¬ ª     ͘ <ĞƐŝŵƉƵůĂŶŶLJĂ͕ ƚŝĚĂŬ ƐĞŵƵĂŵĂƚƌŝŬƐƉĞƌƐĞŐŝŵĞŵŝůŝŬŝŝŶǀĞƌƐ͘^ĞďĞůƵŵďĞƌůĂŶũƵƚŬĞƉĞŶŐĞƌƚŝĂŶŵĂƚƌŝŬƐŝŶǀĞƌƐ͕ŬŝƚĂ ďĂŚĂƐĚĞƚĞƌŵŝŶĂŶƐĞďƵĂŚŵĂƚƌŝŬƐLJĂŶŐŵĞŶƵŶũƵŬŬĂŶŝŶǀĞƌƐŵĂƚƌŝŬƐĂĚĂĂƚĂƵƚŝĚĂŬĂĚĂ͘ 'HWHUPLQDQ0DWULNV &DUDPHQJKLWXQJGHWHUPLQDQPDWULNVSHUVHJLWHUJDQWXQJXNXUDQPDWULNVWHUVHEXW&DUD PHQJKLWXQJQLODLGHWHUPLQDQPDWULNVEXMXUVDQJNDUGHQJDQRUGR[DNDQEHUEHGDGHQJDQ FDUDPHQJKLWXQJPDWULNVEXMXUVDQJNDUGHQJDQRUGR[ D 'HWHUPLQDQ0DWULNV2UGR[ 'LNHWDKXLPDWULNVRUGR[GLQ\DWDNDQVHSHUWLEHQWXNGLEDZDK $ ቂ ܽ ܾ ܿ ݀ቃ 1LODLGHWHUPLQDQ$GLVLPERONDQGHQJDQȁܣȁFDUDPHQJKLWXQJQLODLGHWHUPLQDQ$GDSDWGLOLKDW VHSHUWLSDGDFDUDGLEDZDKLQL det$ ȁܣȁ ൌ ܽ݀ െ ܾܿ &RQWRK 7HQWXNDQQLODLGHWHUPLQDQPDWULNV% ቂ ʹ ͳ Ͷ ͷቃ -DZDE ȁܣȁ ൌ ܽ݀ െ ܾܿ ൌ ʹǤͷ െ ͳǤͶ ൌ ͳͲ െ Ͷ ൌ ͸ E 'HWHUPLQDQ0DWULNV2UGR[ 0DWULNV2UGRDGDODKPDWULNVEXMXUVDQJNDUGHQJDQEDQ\DNQ\DNRORPGDQEDULVVDPDGHQJDQWLJD %HQWXNXPXPPDWULNVRUGRDGDODKVHEDJDLEHULNXW $ ൥ ܾܽܿ ݂݀݁ ݄݃ ݅൩ &DUDPHQJKLWXQJGHWHUPLQDQSDGDPDWULNVGHQJDQRUGRWLJDELDVDGLVHEXWGHQJDQAturan Sarrus 8QWXNOHELKMHODVQ\DOLKDWSHQMHODVDQSDGDJDPEDUGLEDZDKLQL &RQWRKffl 7HQWXNDQQLODLGHWHUPLQDQPDWULNV0 ൥ Ͷʹͷ ͵͸͸ ͳ͵ʹ ൩ -DZDEffl ȁܯȁ ൌ ͶǤ͸Ǥʹ ൅ ʹǤ͸Ǥͳ ൅ ͷǤ͵Ǥ͵ െ ͷǤ͸Ǥͳ െ ͶǤ͸Ǥ͵ െ ʹǤ͵Ǥ͵ ൌ Ͷͺ ൅ ͳʹ ൅ Ͷͷ െ ͵Ͳ െ ͹ʹ െ ͳͺ ൌ ͳͲͷ െ ͳʹͲ ൌ െͳͷ fl,QYHUV0DWULNV D ,QYHUVPDWULNVRUGR×  ܾ ܽቂ ൌ ܣܽ݇݅ܬ ܿ ݀ቃ ǡ ݉ܽ݇ܽ A-1 ଵ ୢୣ୲ ஺ ቂ ݀ െܾ െܿ ܽ ቃ &RQWRKffl -LND$ ቂ ͵ െʹ െͷ Ͷ ቃPDND$  ଵ ଷǤସିሺିଶሻǤሺିହሻ ቂ Ͷ ʹ ͷ ͵ቃ   ଵ ଵଶିଵ଴ ቂ Ͷ ʹ ͷ ͵ቃ   ଵ ଶ ቂ Ͷ ʹ ͷ ͵ቃ  ቎ ସ ଶ ଶ ଶ ହ ଶ ଷ ଶ ቏ E ,QYHUVPDWULNVRUGR× 6HEHOXPPHQHQWXNDQLQYHUVPDWULNVSHUVHJL$RUGRWLJDDWDXOHELKSHUOXGLSHUNHQDONDQ NRIDNWRUPLQRUPDWULNV$DWDX0LMGDQDGMRLQPDWULNV$DWDXDGM$-LND » » » ¼ º « « « ¬ ª = g h i d e f a b c A  PDNDffl L 0LQRUGDULPDWULNVA   Mij DGDODKGHWHUPLQDQPDWULN\DQJGLSHUROHKGHQJDQPHQJKDSXV EDULVNH±iGDQNRORPNH±j

2 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 13 -LND » » » ¼ º « « « ¬ ª = g h i d e f a b c A PDND e i f h h i e f g h i d e f a b c M = = = ⋅ − ⋅  d i f g g i d f g h i d e f a b c M = = = ⋅ − ⋅  d h e g g h d e g h i d e f a b c M = = = ⋅ − ⋅  GDQVHWHUXVQ\DVDPSDLM LL .RIDNWRUGDULPDWULNVA ij i j Kij = − ⋅ M +      K =− ⋅M =⋅M    K =− ⋅M =−⋅M    K = − ⋅M =⋅M GDQVHWHUXVQ\DVDPSDLK .LWDSHUROHKPDWULNVNRIDNWRU. ൥ ଵଷܭ ଵଶܭ ଵଵܭ ଶଷܭ ଶଶܭ ଶଵܭ ଷଷܭ ଷଶܭ ଷଵܭ ൩ VHKLQJJDGDULDGM$ WUDQVSRVHGDUL PDWULNVNRIDNWRU. .W  ൥ ଷଵܭ ଶଵܭ ଵଵܭ ଷଶܭ ଶଶܭ ଵଶܭ ଷଷܭ ଶଷܭ ଵଷܭ ൩'LSHUROHKLQYHUVGDULPDWULNV$\DLWX   GHW   Adj A A A = ⋅ −  &RQWRKffl 'LNHWDKXL » » » ¼ º « « « ¬ ª − − − − =     ffi     A WHQWXNDQ − A  3HPEDKDVDQ L 'HWHUPLQDQ                                                    GHW = = − = + + − − − − − ⋅ ⋅ − − ⋅ − ⋅ − − ⋅ ⋅ = ⋅ ⋅ + ⋅ − ⋅ − + − ⋅ ⋅ − − − − − − − A = LL 0LQRU             = ⋅ − − ⋅ − = − = − − M =               = ⋅ − − ⋅ − = − = − − M =            = ⋅ − − ⋅ − = − + = − − M =               = ⋅ − − ⋅ − = − = − − M =               = ⋅ − − ⋅ − = − = − − M =              = ⋅ − − ⋅ − = − + = − − M =            = ⋅ − − − ⋅ = − + = − − M =               = ⋅ − − − ⋅ = − + = − − M =         M = = ⋅ − ⋅ = − = LLL .RIDNWRU        K = − ⋅ = ⋅ =        K = − ⋅ = − ⋅ = −

2 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 13 -LND » » » ¼ º « « « ¬ ª = g h i d e f a b c A PDND e i f h h i e f g h i d e f a b c M = = = ⋅ − ⋅  d i f g g i d f g h i d e f a b c M = = = ⋅ − ⋅  d h e g g h d e g h i d e f a b c M = = = ⋅ − ⋅  GDQVHWHUXVQ\DVDPSDLM LL .RIDNWRUGDULPDWULNVA ij i j Kij = − ⋅ M +      K =− ⋅M =⋅M    K =− ⋅M =−⋅M    K = − ⋅M =⋅M GDQVHWHUXVQ\DVDPSDLK .LWDSHUROHKPDWULNVNRIDNWRU. ൥ ଵଷܭ ଵଶܭ ଵଵܭ ଶଷܭ ଶଶܭ ଶଵܭ ଷଷܭ ଷଶܭ ଷଵܭ ൩ VHKLQJJDGDULDGM$ WUDQVSRVHGDUL PDWULNVNRIDNWRU. .W  ൥ ଷଵܭ ଶଵܭ ଵଵܭ ଷଶܭ ଶଶܭ ଵଶܭ ଷଷܭ ଶଷܭ ଵଷܭ ൩'LSHUROHKLQYHUVGDULPDWULNV$\DLWX   GHW   Adj A A A = ⋅ −  &RQWRK 'LNHWDKXL » » » ¼ º « « « ¬ ª − − − − =         A WHQWXNDQ − A  3HPEDKDVDQffl L 'HWHUPLQDQ                ffi             ffi               ffi       ffi     GHW = = − = + + − − − − − ⋅ ⋅ − − ⋅ − ⋅ − − ⋅ ⋅ = ⋅ ⋅ + ⋅ − ⋅ − + − ⋅ ⋅ − − − − − − − A = LL 0LQRU ffi           ffi   = ⋅ − − ⋅ − = − = − − M =               = ⋅ − − ⋅ − = − = − − M =   ffi         ffi  = ⋅ − − ⋅ − = − + = − − M =               = ⋅ − − ⋅ − = − = − − M =               = ⋅ − − ⋅ − = − = − − M =              = ⋅ − − ⋅ − = − + = − − M =      ffi  fl fl ffi     = ⋅ − − − ⋅ = − + = − − M =               = ⋅ − − − ⋅ = − + = − − M =  ffi   ffi    ffi   M = = ⋅ − ⋅ = − = LLL .RIDNWRU        K = − ⋅ = ⋅ =        K = − ⋅ = − ⋅ = −

4 MatemaƟ a Paket C -etara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 15        K = − ⋅ = ⋅ =        K = − ⋅ =− ⋅ =−        K = − ⋅ = ⋅ =        K = − ⋅ = − ⋅ = −   fl  fl fl  K = − ⋅ = ⋅ =        K = − ⋅ = − ⋅ = −        K = − ⋅ = ⋅ = $GMA .W »»»¼º «««¬ª − − − − =         fl   GHW   Adj A A A = ⋅ − »»»¼º «««¬ª − − − − = »»»¼º «««¬ª − − − − = ⋅ −         fl         fl    A Alternatif lain mencari adjoin matriks A: »»»»»»»¼º «««««««¬ª + − + − + − + − + = d e a b g h a b g h d e d f a c g i a c g i d f e f b c h i b c h i e f Adj  A  &RQWRKffl 'LNHWDKXL »»»¼º «««¬ª − − −− =     ffi     A WHQWXNDQ −  A  3HPEDKDVDQffl                                                             GHW == − = + + − − − − − ⋅ ⋅ − − ⋅ − ⋅ − − ⋅ ⋅ = ⋅ ⋅ + ⋅ − ⋅ − + − ⋅ ⋅ − − − − − −− A = »»»»»»»¼º «««««««¬ª + − − − − − + −− − − − + − − − −− + − − − − − + =                                 Adj  A  »»»¼º «««¬ª + − + − − + + − − − + − − − + + − − − + − + =                                  Adj  A  »»»¼º «««¬ª − − − − = »»»¼º «««¬ª + − + − + − + − + =                                Adj  A  »»»¼º «««¬ª − − − − = »»»¼º «««¬ª − − − − = ⋅ −                    A DĞŶĞŶƚƵŬĂŶ ŝŶǀĞƐ ŵĂƚƌŝŬƐ ĚĂƉĂƚ ƉƵůĂ ĚŝŬĞƌũĂŬĂŶ ĚĞŶŐĂŶ ŵĞŶŐŐƵŶĂŬĂŶ ŽƉĞƌĂƐŝ ďĂƌŝƐ ĞůĞŵĞŶƚĞƌ ;KͿ͘zĂŶŐ ƚĞƌŵĂƐƵŬĚĂůĂŵŽƉĞƌĂƐŝŝŶŝĂĚĂůĂŚ͗ ;ϭͿŵĞŶŐĂůŝŬĂŶďĂƌŝƐ ƐƵĂƚƵŵĂƚƌŝŬƐ ĚĞŶŐĂŶ ƐŬĂůĂƌ ƚŝĚĂŬ ŶŽů͖ ;ϮͿ ŵĞŶƵŬĂƌ ůĞƚĂŬ ďĂƌŝƐ͗ ĂƚĂƵ ;ϯͿ ŵĞŶĂŵďĂŚ ďĂƌŝƐ ƐƵĂƚƵ ŬĞ ďĂƌŝƐ ůĂŝŶŶLJĂ͘DŝƐĂůŬĂŶс »»»¼º «««¬ª − −          ͕ŵĂŬĂĚĞŶŐĂŶŵĞŶŐŐƵŶĂŬĂŶŽƉĞƌĂƐŝďĂƌŝƐĚŝƉĞƌŽůĞŚ͗ »»»¼º «««¬ª − −           ∼ »»»¼º «««¬ª −−          ͕ŵĂƚƌŝŬƐ ϭĚŝďĞŶƚƵŬĚĂƌŝĚĞŶŐĂŶďĂƌŝƐϯĚŝŬĂůŝʹϮ

4 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 15        K = − ⋅ = ⋅ =        K = − ⋅ =− ⋅ =−        K = − ⋅ = ⋅ =        K = − ⋅ = − ⋅ = −     K = − ⋅ = ⋅ =        K = − ⋅ = − ⋅ = −      K = − ⋅ = ⋅ = $GMA .W »»»¼º «««¬ª − − − − =           GHW   Adj A A A = ⋅ − »»»¼º «««¬ª − − − − = »»»¼º «««¬ª − − − − = ⋅ −                    A Alternatif lain mencari adjoin matriks A: »»»»»»»¼º «««««««¬ª + − + − + − + − + = d e a b g h a b g h d e d f a c g i a c g i d f e f b c h i b c h i e f Adj  A  &RQWRK 'LNHWDKXL »»»¼º «««¬ª − − −− =         A WHQWXNDQ −  A  3HPEDKDVDQ                  ffi                ffi                   ffi       ffi     GHW == − = + + − − − − − ⋅ ⋅ − − ⋅ − ⋅ − − ⋅ ⋅ = ⋅ ⋅ + ⋅ − ⋅ − + − ⋅ ⋅ − − − − − −− A = »»»»»»»¼º «««««««¬ª + − − − − − + −− − − − + − − − −− + − − − − − + =  ffi          ffi             ffi          ffi  Adj  A  »»»¼º «««¬ª + − + − − + + − − − + − − − + + − − − + − + =          ffi                       fl  Adj  A  »»»¼º «««¬ª − − − − = »»»¼º «««¬ª + − + − + − + − + =         fl                       fl  Adj  A  »»»¼º «««¬ª − − − − = »»»¼º «««¬ª − − − − = ⋅ −         fl         fl    A DĞŶĞŶƚƵŬĂŶ ŝŶǀĞƌƐ ŵĂƚƌŝŬƐ ĚĂƉĂƚ ƉƵůĂ ĚŝŬĞƌũĂŬĂŶ ĚĞŶŐĂŶ ŵĞŶŐŐƵŶĂŬĂŶ ŽƉĞƌĂƐŝ ďĂƌŝƐ ĞůĞŵĞŶƚĞƌ ;KffiͿ͘zĂŶŐ ƚĞƌŵĂƐƵŬĚĂůĂŵŽƉĞƌĂƐŝŝŶŝĂĚĂůĂŚ͗ ;ϭͿŵĞŶŐĂůŝŬĂŶďĂƌŝƐ ƐƵĂƚƵŵĂƚƌŝŬƐ ĚĞŶŐĂŶ ƐŬĂůĂƌ ƚŝĚĂŬ ŶŽů͖ ;ϮͿ ŵĞŶƵŬĂƌ ůĞƚĂŬ ďĂƌŝƐ͗ ĂƚĂƵ ;ϯͿ ŵĞŶĂŵďĂŚ ďĂƌŝƐ ƐƵĂƚƵ ŬĞ ďĂƌŝƐ ůĂŝŶŶLJĂ͘DŝƐĂůŬĂŶс »»»¼º «««¬ª − −          ͕ŵĂŬĂĚĞŶŐĂŶŵĞŶŐŐƵŶĂŬĂŶŽƉĞƌĂƐŝďĂƌŝƐĚŝƉĞƌŽůĞŚ͗ »»»¼º «««¬ª − −           ∼ »»»¼º «««¬ª −−          ͕ŵĂƚƌŝŬƐ ϭĚŝďĞŶƚƵŬĚĂƌŝĚĞŶŐĂŶďĂƌŝƐϯĚŝŬĂůŝʹϮ

6 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 17 ∼ » » » ¼ º « « « ¬ ª − − −          ͕ŵĂƚƌŝŬƐϮĚŝďĞŶƚƵŬĚĂƌŝϭĚĞŶŐĂŶďĂƌŝƐϭĚŝŬĂůŝϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϮ͘ ∼ » » » ¼ º « « « ¬ ª − − −          ͕ŵĂƚƌŝŬƐϯĚŝďĞŶƚƵŬĚĂƌŝϮĚĞŶŐĂŶŵĞŶƵŬĂƌůĞƚĂŬďĂƌŝƐϭĚĂŶďĂƌŝƐϮ DĂƚƌŝŬƐͲŵĂƚƌŝŬƐLJĂŶŐĚŝƉĞƌŽůĞŚŵĞůĂůƵŝŽƉĞƌĂƐŝďĂƌŝƐĞůĞŵĞŶƚĞƌƚĞƌŚĂĚĂƉŵĂƚƌŝŬƐůĂŝŶĚŝƐĞďƵƚ ĚĞŶŐĂŶŵĂƚƌŝŬƐĞŬŝǀĂůĞŶ͘:ĂĚŝ͕͕ϭ͕Ϯ͕ĚĂŶϯŵĞƌƵƉĂŬĂŶŵĂƚƌŝŬƐͲŵĂƚƌŝŬƐLJĂŶŐĞŬŝǀĂůĞŶ͘ DŝƐĂůŬĂŶ  ŵĂƚƌŝŬƐ ƉĞƌƐĞŐŝ͕ ŵĂŬĂ ĚĞŶŐĂŶ ŵĞůĂŬƵŬĂŶ ƐĞƌĂŶŐŬĂŝĂŶ ŽƉĞƌĂƐŝ ďĂƌŝƐ ĞůĞŵĞŶƚĞƌ ƚĞƌŚĂĚĂƉͮ/ĂŬĂŶĚŝƉĞƌŽůĞŚ/ͮͲϭ͕ƐĞďĂŐĂŝďĞƌŝŬƵƚ͘ ͮ/                   − − ∼                −   ;ďĂƌŝƐϭĚŝŬĂůŝϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϯͿ     ∼                      − − ;ďĂƌŝƐϮĚŝŬĂůŝͲϭͬϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϯͿ     ∼                          − − − − ;ďĂƌŝƐϭ͕Ϯ͕ϯďĞƌƚƵƌƵƚͲƚƵƌƵƚĚŝŬĂůŝʹϭ͕Ъ͕ĚĂŶϮͬϳͿ     ∼            fl                    − − − − − ;ďĂƌŝƐϯĚŝŬĂůŝʹϭͬϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϮ͕ĚĂŶďĂƌŝƐϯĚŝŬĂůŝϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϭͿ     ∼          fl                   − − − − с/ͮͲϭ͘ ;ďĂƌŝƐϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϭͿ :ĂĚŝ͕ŝŶǀĞƌƐĚĂƌŝĂĚĂůĂŚͲϭс » » » ¼ º « « « ¬ ª − − − −                        с   » » » ¼ º « « « ¬ ª − − − −          ͘ .HJLDWDQ +LWXQJODKGHWHUPLQDQGDULPDWULNVPDWULNVGLEDZDKLQL D$ ቀ ʹ ͵ ͸ ͳቁ    F3 ൭ ʹ െ͵ Ͷ ͳ ͳ െͳ ͵ ʹ െͶ ൱ E% ቀ Ͷ െʹ ͳ ͵ቁ    G4 ൭ Ͷ െͳ ʹ ͳ ͵ െͳ ͹ Ͷ ͷ ൱ -LND' ൭ Ͷ ͳ ʹ ͳ ʹ െͳ ͹ ͵ ͷ ൱ KLWXQJODK000... .HJLDWDQ  7HQWXNDQGHWHUPLQDQGDULPDWULNVEHULNXW D & ቂ Ͷ ͹ ͵ ͺቃ E ' ൥ ʹͷ͵ Ͷͳ͸ ͵ʹͷ ൩  7HQWXNDQLQYHUVGDULPDWULNVEHULNXW D 0 ቂ ͷ ʹ Ͷ ͵ቃ E 1 ൥ ͸ͶͶ ͵ͷʹ ͳʹͳ ൩  7HQWXNDQWUDQVSRVHGDULPDWULNVEHULNXW D 2 ൥ ͸ Ͷ ͹ ͷ ͵ െ͵ ൩ E 3 ቂ െʹ ͷ ͵ െͶ ʹ ͸ቃ  'LNHWDKXLVHEXDKPDWULNV$ ቂ ͹ Ͷ ͵ ʹቃPDNDGHWHUPLQDQGDULWUDQVSRVHPDWULNV$DGDODK«  'LNHWDKXLPDWULNV; ቂ െ͵ ͷ ͳ െʹቃLQYHUVGDULWUDQVSRVHPDWULNV;DGDODK«

akeC eaaMMkXM8ena aaDaaeuMr  ƌďƚϭĂďŝ ∼»»»¼º ¬ϯĚĞŝϮĞĂĞŬĞďƌƐϭĂƌDƐĂĚƌƌůĞƚŚĂŵƌƐĂƐƵ ŝ͕ĂĂĂƚͲĂLJŶĞŶDƐŬĂŝ ĞŝĞůƵŶŐŝĞƐ ƌĞ ŚŽϭďĂŐĂŝďĞƌŝŬƵƚ͘ ͮ/с                   − − ∼                −   ;ďĂƌŝƐϭĚŝŬĂůŝϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϯͿ     ∼                     − − ;ďĂƌŝƐϮĚŝŬĂůŝͲϭͬϮĚŝƚĂŵďĂŚŬĂŶŬĞƌŝƐϯͿ     ∼                          − − − − ;ďĂƌŝƐϭ͕Ϯ͕ϯďĞƌƚƵƌƵƚͲƚƵƌƵƚĚŝŬĂůŝʹϭ͕Ъ͕ĚĂŶϮͬϳͿ     ∼                                − − − − − ;ďĂƌŝƐϯĚŝŬĂůŝʹϭͬϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϮ͕ĚĂŶďĂƌŝƐϯĚŝŬĂůŝϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϭͿ     ∼                             − − − − с/ͮͲϭ͘ ;ďĂƌŝƐϮĚŝƚĂŵďĂŚŬĂŶŬĞďĂƌŝƐϭͿ :ĂĚŝ͕ŝŶǀĞƌƐĚĂƌŝĂĚĂůĂŚͲϭс » » » ¼ º « « « ¬ ª − − − −                        с   » » » ¼ º « « « ¬ ª − − − −          ͘ .HJLDWDQffl +LWXQJODKGHWHUPLQDQGDULPDWULNVPDWULNVGLEDZDKLQL D$ ቀ ʹ ͵ ͸ ͳቁ    F3 ൭ ʹ െ͵ Ͷ ͳ ͳ െͳ ͵ ʹ െͶ ൱ E% ቀ Ͷ െʹ ͳ ͵ቁ    G4 ൭ Ͷ െͳ ʹ ͳ ͵ െͳ ͹ Ͷ ͷ ൱ -LND' ൭ Ͷ ͳ ʹ ͳ ʹ െͳ ͹ ͵ ͷ ൱ KLWXQJODKffl0ff0ff0ff.ff.ff. .HJLDWDQ  7HQWXNDQGHWHUPLQDQGDULPDWULNVEHULNXWffl D & ቂ Ͷ ͹ ͵ ͺቃ E ' ൥ ʹͷ͵ Ͷͳ͸ ͵ʹͷ ൩  7HQWXNDQLQYHUVGDULPDWULNVEHULNXWffl D 0 ቂ ͷ ʹ Ͷ ͵ቃ E 1 ൥ ͸ͶͶ ͵ͷʹ ͳʹͳ ൩  7HQWXNDQWUDQVSRVHGDULPDWULNVEHULNXWffl D 2 ൥ ͸ Ͷ ͹ ͷ ͵ െ͵ ൩ E 3 ቂ െʹ ͷ ͵ െͶ ʹ ͸ቃ  'LNHWDKXLVHEXDKPDWULNV$ ቂ ͹ Ͷ ͵ ʹቃPDNDGHWHUPLQDQGDULWUDQVSRVHPDWULNV$DGDODK«  'LNHWDKXLPDWULNV; ቂ െ͵ ͷ ͳ െʹቃLQYHUVGDULWUDQVSRVHPDWULNV;DGDODK«

8 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 19 81,7-$':$/3(5-$/$1$1'$17$%(/.202',7$6%$5$1* -DGZDO3HUMDODQDQ.HUHWD$SL&LUHERQ(NVSUHV33 67$6,81 .$ 67$6,81 .$ '$7$1* %(5$1*.$7 '$7$1* %(5$1*.$7 *$0%,5   &,5(%21   +$85*(8/,6   -$7,%$5$1*   -$7,%$5$1* ffi  -$7,1(*$5$ ffi  &,5(%21   *$0%,5   Jadwal perjalanan kereta api Cirebon Ekspres PP (Stasiun Gambir – Stasiun Cirebon) fl.HVDPDDQ0DWULNV 'XDDWDXOHELKPDWULNVGLNDWDNDQVDPDELODPHPLOLNLRUGRMXPODKEDULVGDQNRORPVDPDGDQ HOHPHQDWDXNRPSRQHQ\DQJEHUVHVXDLDQVDPD'HQJDQNDWDODLQPDWULNVPDWULNVWHUVHEXWDGDODK PDWULNV\DQJVDPDKDQ\DVDMDGHQJDQQDPDEHUEHGD 3ULQVLSNHVDPDDQPDWULNVSDGDXPXPQ\DGLJXQDNDQXQWXNPHQHQWXNDQNRPSRQHQSDGDVHOWHUWHQWX DWDXPHQHQWXNDQYDULDEHO\DQJWHUGDSDWGDODPNRPSRQHQSHQ\XVXQPDWULNV3ULQVLSNHVDPDDQ PDWULNVXPXPQ\DGLKXEXQJNDQGHQJDQSHUVDPDDQPDWHPDWLNDODLQQ\DVHSHUWLSHUVDPDDQOLQHDUGXD YDULDEHOSHUVDPDDQNXDDGUDWHNVSRQHQVLDOORJDULWPDDWDXSXQWULJRQRPHWUL .RQVHS.HVDPDDQ0DWULNV ൥ ܾܽܿ ݂݀݁ ݄݃ ݅൩ ൌቈ ݎݍ݌ ݑݐݏ ݔݓݒ ቉ %LODGXDPDWULNVGLDWDVGLQ\DWDNDQVDPDPDNDEHUODNXffl a = p b = q c = r d = s e = t f =u g =v h = w i = x 0DWULNVPHPLOLNLEDQ\DNNHJXQDDQGLDQWDUDQ\DDGDODKXQWXNPHQ\HOHVDLNDQVLVWHPSHUVDPDDQ OLQHDU8QWXNPHPDKDPLSHQHUDSDDQPDWULNV\DQJOHELKOXDVNLWDSHUOXXQWXNPHQJHWDKXLRSHUDVL RSHUDVLGDODPPDWULNVGDODPSHPEDKDVDQLQLNLWDKDQ\DDNDQPHPEDKDVRSHUDVLSHQMXPODKDQGDQ SHQJXUDQJDQVHUWDNHVDPDDQGDULGXDPDWULNV 8QWXNPHPSHODMDULPDWULNVVHFDUDHIHNWLISHUWDPDNLWDDNDQPHQGHILQLVLNDQPDWULNVVHFDUDXPXP 8QWXNPDWULNVXPXPAVHPXDHOHPHQDQJJRWDQ\DGLQRWDVLNDQVHEDJDLKXUXINHFLO³a´GHQJDQ SRVLVLGDULHOHPHQWHUVHEXWGLWXQMXNNDQGHQJDQLQGHNVUDQJNDSaij+XUXIiGDQjVHFDUDEHUWXUXWWXUXW PHQ\DWDNDQXUXWDQEDULVGDQNRORPGDULHOHPHQPDWULNV\DQJGLPDNVXG0DWULNVAVHFDUDXPXP GDSDWGLWXOLVNDQVHEDJDLEHULNXW ۏ ێ ێ ێ ێ ێ ێ ۍ ܽଵଵ ܽଵଶ ܽଵଷ ڮܽ ଵ௝ ڮܽ ଵ௡ ܽଶଵ ܽଶଶ ܽଶଷ ڮܽ ଶ௝ ڮܽ ଶ௡ ܽଷଵ ܽଷଶ ܽଷଷ ڮܽ ଷ௝ ڮܽ ଷ௡ ڭ ڭ ڭڭڭ ܽ௜ଵ ܽ௜ଶ ܽ௜ଷ ڮ ௝௜ܽ ڮ௡௜ܽ ڭ ڭ ڭڭڭ ے௡௠ܽ ڮ ௝௠ܽ ڮ ଷ ܽ௠ଶ ܽ௠ଵܽ௠ ۑ ۑ ۑ ۑ ۑ ۑ ې 8NXUDQGDULPDWULNVGLVHEXWVHEDJDLRUGRVHKLQJJDNLWDGDSDWPHQJDWDNDQEDKZDPDWULNVAGLDWDV EHURUGRmîn3HUKDWLNDQEDKZDVHPXDHOHPHQHOHPHQ\DQJWHUOHWDNSDGDGLDJRQDOPDWULNV PHPLOLNLELODQJDQNRORPGDQEDULV\DQJVDPDaijGLPDQDi j'HPLNLDQMXJDDSDELODHOHPHQ HOHPHQGDULPDWULNVAGLWXOLVNDQGHQJDQaijPDNDHOHPHQHOHPHQGDULPDWULNVBGDSDWGLWXOLVNDQ VHEDJDLbijHOHPHQHOHPHQPDWULNVCVHEDJDLcijGDQVHWHUXVQ\D &RQWRK0HQJLGHQWLILNDVL2UGRGDQ(OHPHQGDUL6XDWX0DWULNV 1\DWDNDQRUGRGDULPDVLQJPDVLQJPDWULNVEHULNXWGDQHOHPHQHOHPHQ\DQJEHUVHVXDLDQGHQJDQa abbGDQcc ܣൌቂͳ Ͷ ͵ ʹቃ ܤ ൌ ൥ ʹ െ͵ െͳ Ͷ ͷ ͵ ൩ܥ ൌ ൥ ʹ Ͳǡͷ Ͳǡ͵ Ͳǡ͸ െʹ െͲǡͶ ʹǡ͵ ͳǡͷ െ͵ ൩ 3HPEDKDVDQ0DWULNVAPHPLOLNLEDULVGDQNRORPVHKLQJJDPDWULNVAEHURUGRîGHQJDQa HOHPHQ\DQJWHUOHWDNSDGDNRORPNHGDQEDULVNHDGDODKGDQWLGDNDGDHOHPHQaGDODP PDWULNVAAKDQ\DEHURUGRî0DWULNVBPHPLOLNLEDULVGDQNRORPVHKLQJJDRUGRGDUL PDWULNV%DGDODKîGHQJDQb GDQb 0DWULNVCPHPLOLNLRUGRîGHQJDQc  GDQc  &RQWRK0HQHQWXNDQ$SDNDK'XD0DWULNV6DPD 7HQWXNDQDSDNDKSHUQ\DWDDQSHUQ\DWDDQEHULNXWEHQDUVDODKDWDXNRQGLVLRQDO-LNDVDODKMHODVNDQ -LNDNRQGLVLRQDOWHPXNDQQLODL\DQJPHPEXDWSHUQ\DWDDQWHUVHEXWEHQDU ϭ͘ ቂ ͳ ʹ ͵ െͶቃ ൌቂ͵ െͶ ͳ ʹ ቃ Ϯ͘ ൥ െ͵ ʹ ͳ Ͷ െʹ െͳ ൩ ൌቂ ʹ െʹ ͳ െ͵ ͳ Ͷቃ ϯ͘ ቂ ͳ ͵ ʹ Ͷቃ ൌቂܽ െ ͵ ͵ܾ ʹ ʹܿቃ

8 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 19 81,7-$':$/3(5-$/$1$1'$17$%(/.202',7$6%$5$1* -DGZDO3HUMDODQDQ.HUHWD$SL&LUHERQ(NVSUHV33 67$6,81 .$ 67$6,81 .$ '$7$1* %(5$1*.$7 '$7$1* %(5$1*.$7 *$0%,5   &,5(%21   +$85*(8/,6   -$7,%$5$1*   -$7,%$5$1*   -$7,1(*$5$   &,5(%21   *$0%,5   Jadwal perjalanan kereta api Cirebon Ekspres PP (Stasiun Gambir – Stasiun Cirebon) .HVDPDDQ0DWULNV 'XDDWDXOHELKPDWULNVGLNDWDNDQVDPDELODPHPLOLNLRUGRMXPODKEDULVGDQNRORPVDPDGDQ HOHPHQDWDXNRPSRQHQ\DQJEHUVHVXDLDQVDPD'HQJDQNDWDODLQPDWULNVPDWULNVWHUVHEXWDGDODK PDWULNV\DQJVDPDKDQ\DVDMDGHQJDQQDPDEHUEHGD 3ULQVLSNHVDPDDQPDWULNVSDGDXPXPQ\DGLJXQDNDQXQWXNPHQHQWXNDQNRPSRQHQSDGDVHOWHUWHQWX DWDXPHQHQWXNDQYDULDEHO\DQJWHUGDSDWGDODPNRPSRQHQSHQ\XVXQPDWULNV3ULQVLSNHVDPDDQ PDWULNVXPXPQ\DGLKXEXQJNDQGHQJDQSHUVDPDDQPDWHPDWLNDODLQQ\DVHSHUWLSHUVDPDDQOLQHDUGXD YDULDEHOSHUVDPDDQNXDDGUDWHNVSRQHQVLDOORJDULWPDDWDXSXQWULJRQRPHWUL .RQVHS.HVDPDDQ0DWULNV ൥ ܾܽܿ ݂݀݁ ݄݃ ݅൩ ൌቈ ݎݍ݌ ݔݓݒ ቉ %LODGXDPDWULNVGLDWDVGLQ\DWDNDQVDPDPDNDEHUODNX a = p b = q c = r d = s e = t f =u g =v h = w i = x 0DWULNVPHPLOLNLEDQ\DNNHJXQDDQGLDQWDUDQ\DDGDODKXQWXNPHQ\HOHVDLNDQVLVWHPSHUVDPDDQ OLQHDU8QWXNPHPDKDPLSHQHUDSDDQPDWULNV\DQJOHELKOXDVNLWDSHUOXXQWXNPHQJHWDKXLRSHUDVL RSHUDVLGDODPPDWULNVGDODPSHPEDKDVDQLQLNLWDKDQ\DDNDQPHPEDKDVRSHUDVLSHQMXPODKDQGDQ SHQJXUDQJDQVHUWDNHVDPDDQGDULGXDPDWULNV 8QWXNPHPSHODMDULPDWULNVVHFDUDHIHNWLISHUWDPDNLWDDNDQPHQGHILQLVLNDQPDWULNVVHFDUDXPXP 8QWXNPDWULNVXPXPAVHPXDHOHPHQDQJJRWDQ\DGLQRWDVLNDQVHEDJDLKXUXINHFLO³a´GHQJDQ SRVLVLGDULHOHPHQWHUVHEXWGLWXQMXNNDQGHQJDQLQGHNVUDQJNDSaij+XUXIiGDQjVHFDUDEHUWXUXWWXUXW PHQ\DWDNDQXUXWDQEDULVGDQNRORPGDULHOHPHQPDWULNV\DQJGLPDNVXG0DWULNVAVHFDUDXPXP GDSDWGLWXOLVNDQVHEDJDLEHULNXW ۏ ێ ێ ێ ێ ێ ێ ۍ ܽଵଵ ܽଵଶ ܽଵଷ ڮܽ ଵ௝ ڮܽ ଵ௡ ܽଶଵ ܽଶଶ ܽଶଷ ڮܽ ଶ௝ ڮܽ ଶ௡ ܽଷଵ ܽଷଶ ܽଷଷ ڮܽ ଷ௝ ڮܽ ଷ௡ ڭ ڭ ڭڭڭ ܽ௜ଵ ܽ௜ଶ ܽ௜ଷ ڮ ௝௜ܽ ڮ௡௜ܽ ڭ ڭ ڭڭڭ ے௡௠ܽ ڮ ௝௠ܽ ڮ ଷ ܽ௠ଶ ܽ௠ଵܽ௠ ۑ ۑ ۑ ۑ ۑ ۑ ې 8NXUDQGDULPDWULNVGLVHEXWVHEDJDLRUGRVHKLQJJDNLWDGDSDWPHQJDWDNDQEDKZDPDWULNVAGLDWDV EHURUGRmîn3HUKDWLNDQEDKZDVHPXDHOHPHQHOHPHQ\DQJWHUOHWDNSDGDGLDJRQDOPDWULNV PHPLOLNLELODQJDQNRORPGDQEDULV\DQJVDPDaijGLPDQDi j'HPLNLDQMXJDDSDELODHOHPHQ HOHPHQGDULPDWULNVAGLWXOLVNDQGHQJDQaijPDNDHOHPHQHOHPHQGDULPDWULNVBGDSDWGLWXOLVNDQ VHEDJDLbijHOHPHQHOHPHQPDWULNVCVHEDJDLcijGDQVHWHUXVQ\D &RQWRKffl0HQJLGHQWLILNDVL2UGRGDQ(OHPHQGDUL6XDWX0DWULNV 1\DWDNDQRUGRGDULPDVLQJPDVLQJPDWULNVEHULNXWGDQHOHPHQHOHPHQ\DQJEHUVHVXDLDQGHQJDQa affbbffGDQcc ܣൌቂͳ Ͷ ͵ ʹቃ ܤ ൌ ൥ ʹ െ͵ െͳ Ͷ ͷ ͵ ൩ܥ ൌ ൥ ʹ Ͳǡͷ Ͳǡ͵ Ͳǡ͸ െʹ െͲǡͶ ʹǡ͵ ͳǡͷ െ͵ ൩ 3HPEDKDVDQ0DWULNVAPHPLOLNLEDULVGDQNRORPVHKLQJJDPDWULNVAEHURUGRîGHQJDQa HOHPHQ\DQJWHUOHWDNSDGDNRORPNHGDQEDULVNHDGDODKGDQWLGDNDGDHOHPHQaGDODP PDWULNVAAKDQ\DEHURUGRî0DWULNVBPHPLOLNLEDULVGDQNRORPVHKLQJJDRUGRGDUL PDWULNV%DGDODKîGHQJDQb GDQb 0DWULNVCPHPLOLNLRUGRîGHQJDQc  GDQc  &RQWRKffl0HQHQWXNDQ$SDNDK'XD0DWULNV6DPD 7HQWXNDQDSDNDKSHUQ\DWDDQSHUQ\DWDDQEHULNXWEHQDUVDODKDWDXNRQGLVLRQDO-LNDVDODKMHODVNDQ -LNDNRQGLVLRQDOWHPXNDQQLODL\DQJPHPEXDWSHUQ\DWDDQWHUVHEXWEHQDU ϭ͘ ቂ ͳ ʹ ͵ െͶቃ ൌቂ͵ െͶ ͳ ʹ ቃ Ϯ͘ ൥ െ͵ ʹ ͳ Ͷ െʹ െͳ ൩ ൌቂ ʹ െʹ ͳ െ͵ ͳ Ͷቃ ϯ͘ ቂ ͳ ͵ ʹ Ͷቃ ൌቂܽ െ ͵ ͵ܾ ʹ ʹܿቃ

0 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 21 3HPEDKDVDQ  3HUQ\DWDDQSDGDSRLQDGDODKVDODK0DWULNVWHUVHEXWPHPLOLNLRUGR\DQJVDPD\DLWXî GDQHOHPHQHOHPHQ\DQJVDPDWHWDSLHOHPHQHOHPHQ\DQJEHUVHVXDLDQWLGDNODKVDPD3LOLK HOHPHQSDGDEDULVSHUWDPDGDQNRORPSHUWDPD\DLWXSDGDPDWULNVGLUXDVNLULVHGDQJNDQ SDGDPDWULNVUXDVNDQDQHOHPHQWHUVHEXWDGDODK  3HUQ\DWDDQSDGDSRLQMXJDVDODKNDUHQDRUGRGDULPDWULNVPDWULNVWHUVHEXWWLGDNODKVDPD 2UGRGDULPDWULNVGLUXDVNLULDGDODKîVHGDQJNDQPDWULNVGLUXDVNDQDQEHURUGRî  3HUQ\DWDDQSDGDSRLQDGDODKNRQGLVLRQDO$JDUSHUQ\DWDDQWHUVHEXWEHUQLODLEHQDUPDNDa ± a b b c GDQDNDQVDODKMLNDWLGDNPHPHQXKLVDODKVDWXDWDX OHELKGDULV\DUDWWHUVHEXW fl$SOLNDVL0DWULNV fl$SOLNDVL'HWHUPLQDQ0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU D6LVWHP3HUVDPDDQ/LQHDU'XD9DULDEHO ൜ ܽଵݔܾ൅ଵݕൌܿଵ ܽଶݔܾ൅ଶݕൌܿଶǡ GDSDWGLXEDKNHGDODPEHQWXNSHUVDPDDQPDWULNV$; &\DLWXffl ൤ ܽଵ ܾଵ ܽଶ ܾଶ ൨ ቂݔ ݕቃ ቂ ܿଵ ܿଶ ቃ'HQJDQPHQJDOLNDQ$GDULNLULGLSHUROHK$$; $&VHKLQJJD,; $& DWDX; $&-DGL ;  ଵ ௗ௘௧஺ ൤ ܾଶ െܾଵ െܽଶ ܽଵ ൨ ቂܿଵ ܿଶ ቃ   ଵ ௗ௘௧஺ ൤ ܾଶܿଵ െ ܾଵܿଶ ܽଵܿଶ െ ܽଶܿଵ ൨ -DGL [  ଵ ௗ௘௧஺ ሺܾଶܿଵ െ ܾଵܿଶ  ଵ ௗ௘௧஺ ฬ ܿଵ ܾଵ ܿଶ ܾଶ ฬ  ௗ௘௧஺ೣ ௗ௘௧஺  \  ଵ ௗ௘௧஺ ሺܽଵܿଶ െ ܽଶܿଵ  ଵ ௗ௘௧஺ ቚ ܽଵ ܿଵ ܽଶ ܿଶ ቚ  ௗ௘௧஺೤ ௗ௘௧஺  E6LVWHP3HUVDPDDQ/LQHDU7LJD9DULDEHO ൝ ܽͳݔܾ ൅ ͳݕܿ ൅ ͳݖ ൌ ݇ͳ ʹ݇ ൌ ݖʹܿ ൅ ݕʹܾ ൅ ݔʹܽ ͵݇ ൌ ݖ͵ܿ ൅ ݕ͵ܾ ൅ ݔ͵ܽ GDSDWGLVHOHVDLNDQGHQJDQGHWHUPLQDQVHEDJDLEHULNXWffl ' ൥ ܽͳ ܾͳ ܿͳ ܽʹ ܾʹ ܿʹ ܽ͵ ܾ͵ ܿ͵ ൩'[ ൥ ݇ͳ ܾͳ ܿͳ ݇ʹ ܾʹ ܿʹ ݇͵ ܾ͵ ܿ͵ ൩ '\ ൥ ܽͳ ݇ͳ ܿͳ ܽʹ ݇ʹ ܿʹ ܽ͵ ݇͵ ܿ͵ ൩'] ൥ ܽͳ ܾͳ ݇ͳ ܽʹ ܾʹ ݇ʹ ܽ͵ ܾ͵ ݇͵ ൩ [  ஽௫ ஽ \  ஽௬ ஽ GDQ ]  ஽௭ ஽ &RQWRK 6HRUDQJSHGDJDQJPHQMXDOVHPXDEDMXGDQGDVLVHKDUJDGRODU$PHULND+DUJDEDMX DGDODKGRODUGDQVHEXDKGDVLDGDODKGRODU-LNDLDKDQ\DPHQMXDOଵ ଶ GDULMXPODKEDMXGDQଶ ଷ GDUL MXPODKGDVLPDNDLDGDSDWPHQJXPSXONDQXDQJGRODU%HUDSDNDKMXPODKPDVLQJPDVLQJ EDUDQJ\DQJWHODKLDMXDO" -DZDE 0LVDONDQ[ MXPODKEDMX\DQJWHODKGLMXDO  \ MXPODKGDVL\DQJWHODKGLMXDOPDND ቐ ଵ଴ ଷ ݔʹ ൅ ݕ ൌ ͳͲͲͲ ଵ଴ ଷ ቀ ଵ ଶ ݔቁ ൅ ʹ ቀଶ ଷ ݕቁ ൌ ͸ͲͲDWDXቐ ଵ଴ ଷ ݔʹ ൅ ݕ ൌ ͳͲͲͲ ହ ଷ ସ ൅ ݔ ଷ ݕ ൌ ͸ͲͲ ' ቎ ଵ଴ ଷ ʹ ହ ଷ ସ ଷ ቏  ସ଴ ଽ െ ଵ଴ ଷ   ସ଴ ଽ െ ଷ଴ ଽ   ଵ଴ ଽ '[ ቈ ͳͲͲͲ ʹ ͸ͲͲ ସ ଷ ቉  ସ଴଴଴ ଷ െ   ସ଴଴଴ ଷ െ ଷ଺଴଴ ଷ ൌ  ସ଴଴ ଷ '\ ቎ ଵ଴ ଷ ͳͲͲͲ ହ ଷ ͸ͲͲ ቏  ଺଴଴଴ ଷ െ ହ଴଴଴ ଷ ൌ  ଵ଴଴଴  [  ஽௫ ஽ ൌ  ସ଴଴ ଷ  ׷ ଵ଴ ଽ ൌ  ସ଴଴ ଷ š ଽ ଵ଴ ൌ  GDQ\ ஽௬ ஽ ൌ  ଵ଴଴଴ ଷ  ׷ ଵ଴ ଽ ൌ ଵ଴଴଴ ଷ š ଽ ଵ଴ ൌ  -DGLMXPODKDMXGDQGL\DQJWHODKLDMXDOEHUWXUXWWXUXWDGDODKGDQ 7HQWXNDQKLPSXQDQSHQ\HOHVDLDQVLVWHPSHUVDPDDQEHULNXW ൝ ͷ ൌ ݖ െ ݕ ൅ ݔʹ ͵െ  ൌ ݖʹ ൅ ݕʹ െ ݔ͵ ݔ െ ͵ݕ െ ͵ݖ ൌ  െʹ -DZDE ൝ ͷ ൌ ݖ െ ݕ ൅ ݔʹ ͵െ  ൌ ݖʹ ൅ ݕʹ െ ݔ͵ ݔ െ ͵ݕ െ ͵ݖ ൌ  െʹ

Ɵ aArnejiaakD\DGSDDVWVVEHNGQV\D HPXLDHHDDGOUWUNVLXVQDWQWGDOK \DDRDNHLUWLNDULXDNLNHQQKNRQGLVLRQDO$JDUSHUQ\DWDDQWHUVHEXWEHUQLODLEHQDUPDNDa ± a b b c GDQDNDQVDODKMLNDWLGDNPHPHQXKLVDODKVDWXDWDX OHELKGDULV\DUDWWHUVHEXW $SOLNDVL0DWULNV $SOLNDVL'HWHUPLQDQ0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU D6LVWHP3HUVDPDDQ/LQHDU'XD9DULDEHO ൜ ܽଵݔܾ൅ଵݕൌܿଵ ܽଶݔܾ൅ଶݕൌܿଶǡ GDSDWGLXEDKNHGDODPEHQWXNSHUVDPDDQPDWULNV$; &\DLWX ൤ ܽଵ ܾଵ ܽଶ ܾଶ ൨ ቂݔ ݕቃ ቂ ܿଵ ܿଶ ቃ'HQJDQPHQJDOLNDQ$GDULNLULGLSHUHK$$; $&VHKLQJJD,; $& DWDX; $&-DGL;  ଵ ௗ௘௧஺ ൤ ܾଶ െܾଵ െܽଶ ܽଵ ൨ ቂܿଵ ܿଶ ቃ   ଵ ௗ௘௧஺ ൤ ܾଶܿଵ െ ܾଵܿଶ ܽଵܿଶ െ ܽଶܿଵ ൨ -DGL [  ଵ ௗ௘௧஺ ሺܾଶܿଵ െ ܾଵܿଶ  ଵ ௗ௘௧஺ ฬ ܿଵ ܾଵ ܿଶ ܾଶ ฬ  ௗ௘௧஺ೣ ௗ௘௧஺  \  ଵ ௗ௘௧஺ ሺܽଵܿଶ െ ܽଶܿଵ  ଵ ௗ௘௧஺ ቚ ܽଵ ܿଵ ܽଶ ܿଶ ቚ  ௗ௘௧஺೤ ௗ௘௧஺  E6LVWHP3HUVDPDDQ/LQHDU7LJD9DULDEHO ൝ ܽͳݔܾ ൅ ͳݕܿ ൅ ͳݖ ൌ ݇ͳ ʹ݇ ൌ ݖʹܿ ൅ ݕʹܾ ൅ ݔʹܽ ͵݇ ൌ ݖ͵ܿ ൅ ݕ͵ܾ ൅ ݔ͵ܽ GDSDWGLVHOHVDLNDQGHQJDQGHWHUPLQDQVHEDJDLEHULNXW ' ൥ ܽͳ ܾͳ ܿͳ ܽʹ ܾʹ ܿʹ ܽ͵ ܾ͵ ܿ͵ ൩'[ ൥ ݇ͳ ܾͳ ܿͳ ݇ʹ ܾʹ ܿʹ ݇͵ ܾ͵ ܿ͵ ൩ '\ ൥ ܽͳ ݇ͳ ܿͳ ܽʹ ݇ʹ ܿʹ ܽ͵ ݇͵ ܿ͵ ൩'] ൥ ܽͳ ܾͳ ݇ͳ ܽʹ ܾʹ ݇ʹ ܽ͵ ܾ͵ ݇͵ ൩ [  ஽௫ ஽ ff\  ஽௬ ஽ ffGDQ ]  ஽௭ ஽ &RQWRKffl 6HRUDQJSHGDJDQJPHQMXDOVHPXDEDMXGDQGDVLVHKDUJDGRODU$PHULND+DUJDEDMX DGDODKGRODUGDQVHEXDKGDVLDGDODKGRODU-LNDLDKDQ\DPHQMXDOଵ ଶ GDULMXPODKEDMXGDQଶ ଷ GDUL MXPODKGDVLPDNDLDGDSDWPHQJXPSXONDQXDQJGRODU%HUDSDNDKMXPODKPDVLQJPDVLQJ EDUDQJ\DQJWHODKLDMXDO" -DZDEffl 0LVDONDQffl[ MXPODKEDMX\DQJWHODKGLMXDO  \ MXPODKGDVL\DQJWHODKGLMXDOPDNDffl ቐ ଵ଴ ଷ ݔʹ ൅ ݕ ൌ ͳͲͲͲ ଵ଴ ଷ ቀ ଵ ଶ ݔቁ ൅ ʹ ቀଶ ଷ ݕቁ ൌ ͸ͲͲDWDXቐ ଵ଴ ଷ ݔʹ ൅ ݕ ൌ ͳͲͲͲ ହ ଷ ସ ൅ ݔ ଷ ݕ ൌ ͸ͲͲ ' ቎ ଵ଴ ଷ ʹ ହ ଷ ସ ଷ ቏  ସ଴ ଽ െ ଵ଴ ଷ   ସ଴ ଽ െ ଷ଴ ଽ   ଵ଴ ଽ '[ ቈ ͳͲͲͲ ʹ ͸ͲͲ ସ ଷ ቉  ସ଴଴଴ ଷ െ   ସ଴଴଴ ଷ െ ଷ଺଴଴ ଷ ൌ  ସ଴଴ ଷ '\ ቎ ଵ଴ ଷ ͳͲͲͲ ହ ଷ ͸ͲͲ ቏  ଺଴଴଴ ଷ െ ହ଴଴଴ ଷ ൌ  ଵ଴଴଴ ଷ  [  ஽௫ ஽ ൌ  ସ଴଴ ଷ  ׷ ଵ଴ ଽ ൌ  ସ଴଴ ଷ š ଽ ଵ଴ ൌ  GDQ\ ஽௬ ஽ ൌ  ଵ଴଴଴ ଷ  ׷ ଵ଴ ଽ ൌ ଵ଴଴଴ ଷ š ଽ ଵ଴ ൌ  -DGLMXPODKEDMXGDQGDVL\DQJWHODKLDMXDOEHUWXUXWWXUXWDGDODKGDQ 7HQWXNDQKLPSXQDQSHQ\HOHVDLDQVLVWHPSHUVDPDDQEHULNXW ൝ ͷ ൌ ݖ െ ݕ ൅ ݔʹ ͵െ  ൌ ݖʹ ൅ ݕʹ െ ݔ͵ ݔ െ ͵ݕ െ ͵ݖ ൌ  െʹ -DZDEffl ൝ ͷ ൌ ݖ െ ݕ ൅ ݔʹ ͵െ  ൌ ݖʹ ൅ ݕʹ െ ݔ͵ ݔ െ ͵ݕ െ ͵ݖ ൌ  െʹ

2 MatemaƟ a Paket C -etara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 23 ' ൥ ʹ ͳ െͳ ͵ െʹ ʹ ͳ െ͵ െ͵ ൩ ൥ ʹ ͳ െͳ ͵ െʹ ʹ ͳ െ͵ െ͵ ൩ ʹ ͳ ͵ െʹ ͳ െ͵   [[[[[[±[[±[[ ±[[  ffi±±±ffi  ffiffi   '[ ൥ ͷ ͳ െͳ െ͵ െʹ ʹ െʹ െ͵ െ͵ ൩ ൥ ͷ ͳ െͳ െ͵ െʹ ʹ െʹ െ͵ െ͵ ൩ ͷ ͳ െ͵ െʹ െʹ െ͵  [[[[[[±[[± [[±[[ ffi±±±ffi ±±ffi±ffi ±  '\ ൥ ʹ ͷ െͳ ͵ െ͵ ʹ ͳ െʹ െ͵ ൩ ൥ ʹ ͷ െͳ ͵ െ͵ ʹ ͳ െʹ െ͵ ൩ ʹ ͷ ͵ െ͵ ͳ െʹ  [[[[[[±[[±[ [±[[    fl±±fl±    fl±fl    fl±    fl '] ൥ ʹ ͳ ͷ ͵ െʹ െ͵ ͳ െ͵ െʹ ൩ ൥ ʹ ͳ ͷ ͵ െʹ െ͵ ͳ െ͵ െʹ ൩ ʹ ͳ ͵ െʹ ͳ െ͵  [[[[[[±[[±[[ ±[[    ±±±    ±±±  ±   6HKLQJJD[ ஽௫ ஽   ସଶ ସଶ  \  ஽௬ ஽   ଼ସ ସଶ  ] ஽௭ ஽   ିସଶ ସଶ   -DGL+3 ሼሺͳǡʹǡ െͳሻሽ $SOLNDVL,QYHUV0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU 6XDWXVLVWHPSHUVDPDDQ൜ ܽͳݔܾ ൅ ͳݕ ൌ ܿͳ ܽʹݔܾ ൅ ͳݕ ൌ ܿʹGDSDWGLWXOLVVHEDJDLSHUNDOLDQGDULPDWULNV NRHLVLHQGHQJDQYDULDEHOQ\D\DLWX ቂ ܽͳ ܾͳ ܽʹ ܾʹቃ ቂ ݔ ݕቃ ቂ ܿͳ ܿʹቃGHQJDQቂ ܽͳ ܾͳ ܽʹ ܾʹቃGLVHEXWmatriks koefisien 8QWXNPHQ\HOHVDLNDQVLVWHPSHUDPDDQLQLNHGXDUXDVGLNDOLNDQGHQJDQLQYHUVGDULPDWULNV NRHILVLHQQ\D &RQWRK +LWXQJODKKDUJD[GDQ\\DQJPHPHQXKLV\VWHPSHUVDPDDQEHULNXW ൜ ͻ ൌ ݕ͵ ൅ ݔʹ ʹ ൌ ݕ ൅ ݔ -DZDE ൜ ͻ ൌ ݕ͵ ൅ ݔʹ ݔ ൅ ݕ ൌ ʹDWDXቂ ʹ ͵ ͳ ͳቃ ቂ ݔ ݕቃ ቂ ͻ ʹ ቃ 0DWULNV.RHILVLHQ$ ቂ ʹ ͵ ͳ ͳቃPDND$  ଵ ଶሺଵሻିଷሺଵሻ ቂ ͳ െ͵ െͳ ʹቃ $  ଵ ଶିଷ ቂ ͳ െ͵ െͳ ʹቃ $  ଵ ିଵ ቂ ͳ െ͵ െͳ ʹቃ $ ቂ െͳ ͵ ͳ െʹቃ

2 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 23 ' ൥ ʹ ͳ െͳ ͵ െʹ ʹ ͳ െ͵ െ͵ ൩ ൥ ʹ ͳ െͳ ͵ െʹ ʹ ͳ െ͵ െ͵ ൩ ʹ ͳ ͵ െʹ ͳ െ͵   [[[[[[±[[±[[ ±[[  ±±±    '[ ൥ ͷ ͳ െͳ െ͵ െʹ ʹ െʹ െ͵ െ͵ ൩ ൥ ͷ ͳ െͳ െ͵ െʹ ʹ െʹ െ͵ െ͵ ൩ ͷ ͳ െ͵ െʹ െʹ െ͵  [[[[[[±[[± [[±[[ ±±± ±±± ±  '\ ൥ ʹ ͷ െͳ ͵ െ͵ ʹ ͳ െʹ െ͵ ൩ ൥ ʹ ͷ െͳ͵ െ͵ ʹ ͳ െʹ െ͵ ൩ ͷ ͵ െ͵ ͳ െʹ  [[[[[[±[[±[ [±[[    ±±±    ±    ±     '] ൥ ʹ ͳ ͷ ͵ െʹ െ͵ ͳ െ͵ െʹ ൩ ൥ ʹ ͳ ͷ ͵ െʹ െͳ െ͵ െʹ ൩ ʹ ͳ ͵ െʹ ͳ െ͵  [[[[[[±[[±[[ ±[[    fl±±fl±    fl±±±fl  ±   6HKLQJJDffl[ ஽௫ ஽   ସଶ ସଶ  ff\  ஽௬ ஽   ଼ସ ସଶ  ff] ஽௭ ஽   ିସଶ ସଶ   -DGL+3 ሼሺͳǡʹǡ െͳሻሽ fl$SOLNDVL,QYHUV0DWULNVGDODP3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU 6XDWXVLVWHPSHUVDPDDQffl൜ ܽͳݔܾ ൅ ͳݕ ൌ ܿͳ ܽʹݔܾ ൅ ͳݕ ൌ ܿʹGDSDWGLWXOLVVHEDJDLSHUNDOLDQGDULPDWULNV NRHILVLHQGHQJDQYDULDEHOQ\D\DLWXffl ቂ ܽͳ ܾͳ ܽʹ ܾʹቃ ቂ ݔ ݕቃ ቂ ܿͳ ܿʹቃGHQJDQቂ ܽͳ ܾͳ ܽʹ ܾʹቃGLVHEXWmatriks koefisien 8QWXNPHQ\HOHVDLNDQVLVWHPSHUVDPDDQLQLNHGXDUXDVGLNDOLNDQGHQJDQLQYHUVGDULPDWULNV NRHILVLHQQ\D &RQWRKffl +LWXQJODKKDUJD[GDQ\\DQJPHPHQXKLV\VWHPSHUVDPDDQEHULNXW ൜ ͻ ൌ ݕ͵ ൅ ݔʹ ʹ ൌ ݕ ൅ ݔ -DZDEffl ൜ ͻ ൌ ݕ͵ ൅ ݔʹ ݔ ൅ ݕ ൌ ʹDWDXቂ ʹ ͵ ͳ ͳቃ ቂ ݔ ݕቃ ቂ ͻ ʹ ቃ 0DWULNV.RHILVLHQ$ ቂ ʹ ͵ ͳ ͳቃPDND$  ଵ ଶሺଵሻିଷሺଵሻ ቂ ͳ െ͵ െͳ ʹቃ $  ଵ ଶିଷ ቂ ͳ െ͵ െͳ ʹቃ $  ଵ ିଵ ቂ ͳ െ͵ െͳ ʹቃ $ ቂ െͳ ͵ ͳ െʹቃ

4 MatemaƟ ka Paket C - Setara SMA/MAlas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 25 6HKLQJJDffl ቂ ʹ ͵ ͳ ͳቃ ቂ ݔ ݕቃ ቂ ͻ ʹ ቃ ቂ െͳ ͵ ͳ െʹቃ ቂ ͵ ͳ ͳቃ ݔ ݕቃ ቂ െͳ ͵ ͳ െʹቃ ቂͻ ʹ ቃ ቈ ሺെͳݔʹሻ ൅ ሺ͵ݔͳሻ ൫ሺെͳሻݔ͵൯ ൅ ሺ͵ݔͳሻ ሺͳݔʹሻ ൅ ሺሺെʹሻݔͳ ሺͳݔ͵ሻ ൅ ሺሺെʹሻݔͳ ቉ቂ ݔ ݕቃ ൤ ሺെͳݔͻሻ ൅ ሺ͵ݔʹሻ ሺͳݔͻሻ ൅ ሺሺെʹሻݔʹ൨ ቂ ͳ Ͳ Ͳ ͳቃ ቂݔ ݕቃ ቂ െ͵ ͷቃ ቂ ݔ ݕቃ ቂ െ͵ ͷቃ -DGL[ GDQ\  /DWLKDQffl 'HQJDQGHHUPLQDQPDWULNVWHQWXNDQQLODLYDULDEHOGDULVLVWHPSHUVDPDDQEHULNXW D൜ Ͷݔʹ ൅ ݕ ൌ ͷ ͵ݔ ൅ Ͷݕ ൌ ͳEቄ ͵ݑʹ ൅ ݒ െ ͳͺ ൌ Ͳ ͷݑ െ ݒ െ ͳʹ ൌ Ͳ  'HQJDQLQYHUVPDWULNVHQWXNDQQLODLYDULDEHOGDULVLVWHPSHUVDPDDQEHULNXW D൜ Ͷݔʹ ൅ ݕ ൌ ͷ ͵ݔ ൅ Ͷݕ ൌ ͳEቄ ͵ݑʹ ൅ ݒ െ ͳͺ ൌ Ͳ ͷݑ െ ݒ െ ͳʹ ൌ Ͳ  'HQJDQGHWHUPLQDQPDWULNVWHQWXNDQQLODL[\GDQ]GDULVLVWHPSHUVDPDDQEHULNXW D൝ ͳ ൌ ݖʹ െ ݕ ൅ ݔʹ ʹ ൌ ݖ െ ͵ ൅ ݔʹ െͳͲ  ൌ ݖʹ ൅ ݕʹ െ ݔ E൝ ʹെ ൌ ݕ͵ ൅ ݔʹ ͷݕ െ ʹݖ ൌ Ͷ Ͷݔʹ ൅ ݖ ൌ  െ͹ 5$1*.80$1 ͳǤ —ŽƒŠƒ–ƒ—•‡Ž‹•‹Š†—ƒƒ–”‹•›ƒ‰•ƒƒ——”ƒ›ƒ•ƒƒ†‡‰ƒƒ–”‹•„ƒ”—†‡‰ƒ ‡Œ—ŽƒŠƒƒ–ƒ—‡‰—”ƒ‰ƒ‡Ž‡‡Ǧ‡Ž‡‡•‡Ž‡–ƒǤ ʹǤ ‡Œ—ŽƒŠƒ†ƒ’‡‰—”ƒ‰ƒ†—ƒƒ–”‹•†ƒ†ƒ’ƒ–†‹Žƒ—ƒƒ’ƒ„‹Žƒǣ • ‘”†‘α‘”†‘ • ܣ േ ܤαሺܣ௝௜ሻേሺܤ௤௣Ȍǡ—–—•‡–‹ƒ’i = p†ƒj = q ͵Ǥ ‹ƒǡǡ†ƒƒ–”‹•›ƒ‰‡’—›ƒ‹‘”†‘›ƒ‰•ƒƒǡƒƒ„‡”Žƒ—•‹ˆƒ–ǣ • †‡–‹–ƒ•ǣA ൅ O = AǢ†‡‰ƒO αቀͲ Ͳ Ͳ Ͳቁ • ‘—–ƒ–‹ˆǣA ൅ B = B ൅ A ሻܥ ൅ ܤሺ ൅ ܣ ൌ ܥ ൅ ሻܤ൅ܣሺǣ• •‘•‹ƒ–‹ˆ ͶǤ ‡”ƒŽ‹ƒ†—ƒƒ–”‹•ǡ›ƒ‹–—ƒ–”‹•„ƒ”‹•ͳš†ƒšͳƒƒ‡‰Šƒ•‹Žƒƒ–”‹•ͳšͳ ‡”ƒŽ‹ƒ†—ƒƒ–”‹•ǡ›ƒ‹–—ƒ–”‹•„ƒ”‹•š’αሺܽ௜௝ሻ†ƒ’šαሺܾ௜௝ሻƒƒ ‡‰Šƒ•‹Žƒƒ–”‹•šαሺܿ௜௝ሻ ƒŽƒ’‡”ƒŽ‹ƒ†—ƒƒ–”‹•ǡŒ‹ƒ„ƒ›ƒ‘Ž‘ƒ–”‹•–‹†ƒ•ƒƒ†‡‰ƒ„ƒ›ƒ „ƒ”‹•ƒ–”‹•ǡƒƒ’‡”ƒŽ‹ƒƒ–”‹•Ǥ–‹†ƒ–‡”†‡ˆ‹‹•‹Ǥ ͷǤ ‹ƒ’‡”ƒŽ‹ƒƒ–”‹•–‡”†‡ˆ‹‹•‹ǡƒƒ•‡ŽƒŽ—‡‡—Š‹‡–‡–—ƒ„‡”‹—–ǣ Ǥ •‘•‹ƒ–‹ˆǣȋǤȌǤαǤȋǤȌ Ǥ †‡–‹–ƒ•ǣǤαǤα Ǥ ‹•–”‹„—–‹ˆǣ A(ܤ േ ܥ(αሺܣǤ ܤሻ േ ሺܣǤ ܥሻ (A േ B)C = ሺܣǤ ܥሻ േ ሺܤǤ ܥሻ ͸Ǥ ‡–‡”‹ƒƒ–”‹•’‡”•‡‰‹„‡”‘”†‘ʹšʹ ܣൌቀܽଵଵ ܽଵଶ ܽଶଵ ܽଶଶቁฺ†‡–ȋȌαa11 . a22 Ȃ a21 . a12 ‡–‡”‹ƒƒ–”‹•’‡”•‡‰‹„‡”‘”†‘͵š͵ ܣ ൌ ൭ ܽଵଵ ܽଵଶ ܽଵଷ ܽଶଵ ܽଶଶ ܽଶଷ ܽଷଵ ܽଷଶ ܽଷଷ ൱ǡ—–—‡…ƒ”‹†‡–ȋȌ†ƒ’ƒ–†‹•‡Ž‡•ƒ‹ƒ†‡‰ƒ†—ƒ…ƒ”ƒǣ ‡–‘†‡ƒ””—•ǣ ‡–‘†‡‡•’ƒ•‹‘ˆƒ–‘” ‹‘”ȋ‹ŒȌ•—ƒ–——•—”ƒ†ƒŽƒŠ•—ƒ–—†‡–‡”‹ƒ›ƒ‰†‹Šƒ•‹Žƒ•‡–‡ŽƒŠ–‡”Œƒ†‹ ’‡‰Šƒ’—•ƒ„ƒ”‹•‡Ǧ†ƒ‘Ž‘‡ǦŒ†‹ƒƒ—•—”‹–—–‡”Ž‡–ƒǤ ‘–‘Šǣ‹‘”†ƒ”‹ܽଶଶαܯଶଶαቀܽଵଵ ܽଵଷ ܽଷଵ ܽଷଷቁαܽଵଵ .ܽଷଷ Ȃ ܽଷଵǤܽଵଷ    ƒ’—•‘Ž‘‡Ǧʹ ൭ ܽଵଵ ࢇܽ ૛૚ଵଷ ૜૛ࢇ ૛૛ࢇ ૚૛ࢇ ܽଷଵ ࢇܽ ૛૜ଷଷ ൱    ƒ’—•„ƒ”‹•‡Ǧʹ ‘ˆƒ–‘”†ƒ”‹•—ƒ–——•—”ƒ†ƒŽƒŠ‹‘”—•—”‹–—„‡”‹—––ƒ†ƒ›ƒܭ௝௜αሺെͳሻ௜ା௝Ǥܯ௝௜ ‡‡–—ƒ†‡–‡”‹ƒ†‡‰ƒ‡•’ƒ•‹‡—”—–„ƒ”‹•‡Ǧ” ȁ ȁ ൌ෍ܽ௥௝ ଷ ௝ୀଵ ௝௥ܭǤ ‡‡–—ƒ†‡–‡”‹ƒ†‡‰ƒ‡•’ƒ•‹‡—”—–‘Ž‘‡Ǧ” ȁ ȁ ൌ෍ܽ௥௝ ଷ ௝ୀଵ ௝௥ܭǤ  ,QYHUVPDWULNVSHUVHJLEHURUGR[ ܾ ܽൌቀܣ ܿ ݀ቁฺܣିଵ  ଵ ୢୣ୲ ሺ஺ሻ ቀ ݀ െܾ െܿ ܽ ቁ

aeCeM eM ra naaDtnk ͳቂݔ ʹቃ ͳ ʹ͵ͳቂݔݕ ቂͳ ቃͻʹቃሺͳݔെ͵൅͵ሻሺʹሺ͵൅ሺሻ ቃሺ ሺʹͻ൅ሺሻ൨ቂͳ ݕ െ ቃቃ DQ HDGHLQDLHXQLLDDODPHDDELW D൜Ͷ ݕ ͶͳE͵ ݒ Ͳͷെ  QLHWNWHWDLDDODVPHDDELW D൜Ͷ ݕ Ͷͳ ͵ʹൌʹൌ QQHULQLHXQLLD]VHSDEHULNXW D൝ ͳ ൌ ݖʹ െ ݕ ൅ ݔʹ ʹ ൌ ݖ െ ݕ͵ ൅ ݔʹ െͳͲ  ൌ ݖʹ ൅ ݕʹ െ ݔ E൝ ʹെ ൌ ݕ͵ ൅ ݔʹ ͷݕ െ ʹݖ ൌ Ͷ Ͷݔʹ ൅ ݖ ൌ  െ͹ 5$1*.80$1 ͳǤ —ŽƒŠƒ–ƒ—•‡Ž‹•‹Š†—ƒƒ–”‹•”ƒƒ‡ƒ•„‰‡—”ƒ‡‡–Ǥ’‰—ƒ‰ƒƒ‹Ž—’‹†” ܣܤȌ——•‹ƒǡǡƒƒ†›‰ǡƒ”ƒǣ–ǣ O  •–‹ Bሻ൅ሺ ൅ǣ‘Ǥ‡ƒƒ†–ǡƒ—ƒ‹”†ƒŽƒ‹ͳ‹ƒƒ‹›–”•ƒ•ሺ௝௜ƒ ‡Š‹–š௝ƒ‡ƒƒ†–‘”•–‹ƒ•ƒƒ ƒ•ƒ‹’‹––ƒ–†‹•ͷ ƒ‡ƒƒ”•‡•ƒ•ŽŠ”—ǣ ‘ƒˆǤ Ǥ†–ƒα Ǥ‹‹ǣ Ǥܤሻേ ሺܣǤ ܥሻ (A േ B)C = ሺܣǤ ܥሻ േ ሺܤǤ ܥሻ ͸Ǥ ‡–‡”‹ƒƒ–”‹•’‡”•‡‰‹„‡”‘”†‘ʹšʹ ܣൌቀܽଵଵ ܽଵଶ ܽଶଵ ܽଶଶቁฺ†‡–ȋȌαa11 . a22 Ȃ a21 . a12 ‡–‡”‹ƒƒ–”‹•’‡”•‡‰‹„‡”‘”†‘͵š͵ ܣ ൌ ൭ ܽଵଵ ܽଵଶ ܽଵଷ ܽଶଵ ܽଶଶ ܽଶଷ ܽଷଵ ܽଷଶ ܽଷଷ ൱ǡ—–—‡…ƒ”‹†‡–ȋȌ†ƒ’ƒ–†‹•‡Ž‡•ƒ‹ƒ†‡‰ƒ†—ƒ…ƒ”ƒǣ ‡–‘†‡ƒ””—•ǣ ‡–‘†‡‡•’ƒ•‹‘ˆƒ–‘” ‹‘”ȋ‹ŒȌ•—ƒ–——•—”ƒ†ƒŽƒŠ•—ƒ–—†‡–‡”‹ƒ›ƒ‰†‹Šƒ•‹Žƒ•‡–‡ŽƒŠ–‡”Œƒ†‹ ’‡‰Šƒ’—•ƒ„ƒ”‹•‡Ǧ†ƒ‘Ž‘‡ǦŒ†‹ƒƒ—•—”‹–—–‡”Ž‡–ƒǤ ‘–‘Šǣ‹‘”†ƒ”‹ܽଶଶαܯଶଶαቀܽଵଵ ܽଵଷ ܽଷଵ ܽଷଷቁαܽଵଵ .ܽଷଷ Ȃ ܽଷଵǤܽଵଷ    ƒ’—•‘Ž‘‡Ǧʹ ൭ ܽଵଵ ࢇܽ ૛૚ଵଷ ૜૛ࢇ ૛૛ࢇ ૚૛ࢇ ܽଷଵ ࢇܽ ૛૜ଷଷ ൱    ƒ’—•„ƒ”‹•‡Ǧʹ ‘ˆƒ–‘”†ƒ”‹•—ƒ–——•—”ƒ†ƒŽƒŠ‹‘”—•—”‹–—„‡”‹—––ƒ†ƒ›ƒܭ௝௜αሺെͳሻ௜ା௝Ǥܯ௝௜ ‡‡–—ƒ†‡–‡”‹ƒ†‡‰ƒ‡•’ƒ•‹‡—”—–„ƒ”‹•‡Ǧ” ȁ ȁ ൌ෍ܽ௥௝ ଷ ௝ୀଵ ௝௥ܭǤ ‡‡–—ƒ†‡–‡”‹ƒ†‡‰ƒ‡•’ƒ•‹‡—”—–‘Ž‘‡Ǧ” ȁ ȁ ൌ෍ܽ௥௝ ଷ ௝ୀଵ ௝௥ܭǤ  ,QYHUVPDWULNVSHUVHJLEHURUGR[ ܾ ܽൌቀܣ ܿ ݀ቁฺܣିଵ  ଵ ୢୣ୲ ሺ஺ሻ ቀ ݀ െܾ െܿ ܽ ቁ

6 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 27 ,QYHUVPDWULNVSHUVHJLEHURUGR[ ܣ ൌ ൭ ܽଵଵ ࢇܽ ૛૚ଵଷ ૜૛ࢇ ૛૛ࢇ ૚૛ࢇ ܽଷଵ ࢇܽ ૛૜ଷଷ ൱ ฺ ܣିଵ  ଵ ୢୣ୲ ሺ஺ሻ†Œ‘‹ȋȌǡ†‡‰ƒ†Œ‘‹ȋȌƒ†ƒŽƒŠƒ–”‹• ‘ˆƒ–‘”†ƒ”‹•‡–‹ƒ’‡Ž‡‡ƒ–”‹•αሺܽ௜௝ሻ 6DUDQ5HIHUHQVL • ——–‡•ƒ–‡ƒ–‹ƒ—”‹—Ž—ʹͲͳ͵ȀȀȀ‡Žƒ•flǡ”Žƒ‰‰ƒǡʹͲͳͶ .ULWHULD3LQGDK/XOXV0RGXO †ƒ †‹›ƒ–ƒƒ ‡ƒŠƒ‹ ‘†—Ž ‹‹ ƒ–ƒ— †ƒ’ƒ– „‡”’‹†ƒŠ ‡ ‘†—Ž „‡”‹—–›ƒ ƒ’ƒ„‹Žƒ –‡ŽƒŠ‡‡—Š‹•ƒŽƒŠ•ƒ–—’‡”•›ƒ”ƒ–ƒ„‡”‹—–Ǥ ͳǤ  ƒ’— ‡‰‡”Œƒƒ –—‰ƒ• †ƒ •‘ƒŽ Žƒ–‹Šƒ •‡…ƒ”ƒ Ž‡‰ƒ’ǡ „‡ƒ”ǡ ƒ—”ƒ– †ƒ •‡•—ƒ‹ ’”‘•‡†—”’‡‰‡”Œƒƒ ʹǤƒ’—‡‰‡”Œƒƒ–—‰ƒ•†ƒ•‘ƒŽŽƒ–‹Šƒ†‡‰ƒ„‡ƒ”ǡƒ—”ƒ–†ƒ•‡•—ƒ‹’”‘•‡†—” ’‡‰‡”Œƒƒǡ‹‹ƒŽ•‡„‡•ƒ”͹ͷΨ ͵Ǥƒ’—‡‰‡”Œƒƒ–‡•–’‡‡’ƒ–ƒ—–—‘†—Ž‹‹†‡‰ƒ„‡ƒ”ǡƒ—”ƒ–†ƒ•‡•—ƒ‹ ’”‘•‡†—”’‡‰‡”Œƒƒǡ‹‹ƒŽ•‡„‡•ƒ”͹ͷΨ †ƒ†‹›ƒ–ƒƒ„‡Ž—‡ƒŠƒ‹†ƒ‡‰—ƒ•ƒ‹‘†—Ž‹‹†ƒ„‡Ž—†ƒ’ƒ–„‡”’‹†ƒŠ‡ ‘†—Ž„‡”‹—–›ƒƒ’ƒ„‹Žƒǣ ͳǤƒ’—‡‰‡”Œƒƒ–—‰ƒ•†ƒ•‘ƒŽŽƒ–‹Šƒ†‡‰ƒ„‡ƒ”ǡƒ—”ƒ–†ƒ•‡•—ƒ‹’”‘•‡†—” ’‡‰‡”Œƒƒǡ†‹„ƒ™ƒŠ•‡„‡•ƒ”͹ͷΨ ʹǤ‡‰‹—–‹–‡•–’‡‡’ƒ–ƒ†‡‰ƒŠƒ•‹Ž†‹„ƒ™ƒŠ͹ͷΨ 3HQLODLDQ .XQFL-DZDEDQ Latihan 1: ͳǤ ƒǤflΪffiα൥ ͳͳ ͹ ͳͳ ͳͳ ͳʹ ͳͳ ൩„ǤflȂffiα൥ െ͵ െ͵ െͷ െͳ ͸ ͵ ൩ ʹǤ ଵ ଷ ቂ ͳʹ ͵ ͻ ͸ ͳͷ ͸ቃαቂͶͳ͵ ʹͷʹቃ ͵Ǥ Ǥα൥ ͵ʹ ʹ͸ ͳͲ ͵Ͷ ͵Ͳ ͳͲ ͳͶ ͳͳ Ͷ ൩ ͶǤ ƒǤαቂʹ െͷ ͵ Ͷ ቃ„Ǥαቂ ͵ ʹ െͳ ͵ቃ…Ǥαቂʹ ͳ ͳ Ͷቃ ͷǤ ƒǤΪαቂെͳ ͳ Ͳ Ͷቃ „Ǥαቂ ͹ Ͷ െͺ ͳቃ …ǤȋΪȌαቂെͶ ʹͶ െͳ ͻ ቃ†ǤΪαቂെ͵ െ͵ െͶ െͺቃ Kegiatan 1: 'HWHUPLQDQGDULPDWULNVPDWULNVGLEDZDKLQLDGDODK D$ ቀ ʹ ͵ ͸ ͳቁ GHW$ ൫ሺʹݔͳሻ െ ሺ͸ݔ͵ሻ൯ ൌ ሺʹ െ ͳͺሻ ൌ െͳ͸ E% ቀ Ͷ െʹ ͳ ͵ቁ GHW% ൫ሺͶݔ͵ሻ െ ሺͳݔሺെʹሻሻ൯ ൌ ሺͳʹ െ ሺെʹሻሻ ൌ ሺͳʹ ൅ ʹሻ ൌ ͳͶ F3 ൭ ʹ െ͵ Ͷ ͳ ͳ െͳ ͵ ʹ െͶ ൱ GHW3 ൫ሺ൫ʹݔͳݔሺെͶሻ൯൅൫ሺെ͵ሻݔሺെͳሻݔ͵൯ ൅ ሺͶݔͳݔʹሻ െ ሺ͵ݔͳݔͶሻ െ ሺʹݔሺെͳሻݔʹሻ െ ሺെͶݔͳݔሺെ͵ሻሻ൯  ൫ሺെͺ ൅ ͻ ൅ ͺሻ െ ሺͳʹሻ െ ሺെͶሻ െ ሺͳʹሻ൯  ሺͻ െ ʹͲሻ െͳͳ G4 ൭ Ͷ െͳ ʹ ͳ ͵ െͳ ͹ Ͷ ͷ ൱ GHW4 ቀሺͶݔ͵ݔͷሻ ൅ ൫ሺെͳሻݔሺെͳሻݔ͹൯ ൅ ሺʹݔͳݔͶሻ െ ሺ͹ݔ͵ݔʹሻ െ ሺͶݔሺെͳሻݔͶሻെ ሺͷݔͳݔሺെͳሻቁ  ሺ͸Ͳ ൅ ͹ ൅ ͺ െ ሺͶʹሻ െ ሺെͳ͸ሻ െ ሺെͷሻሻ  ሺ͹ͷ െ ʹͳሻ  -LND' ൭ Ͷ ͳ ʹ ͳ ʹ െͳ ͹ ͵ ͷ ൱PDND000...DGDODK

6 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 27 ,QYHUVPDNVSHUVHJLEHURUGR[ ܣ ൌ ൭ ܽଵଵ ࢇܽ ૛૚ଵଷ ૜૛ࢇ ૛૛ࢇ ૚૛ࢇ ܽଷଵ ࢇܽ ૛૜ଷଷ ൱ ฺ ܣିଵ  ଵ ୢୣ୲ ሺ஺ሻ†Œ‘‹ȋȌǡ†‡‰ƒ†Œ‘‹ȋȌƒ†ƒŽƒŠƒ–”‹• ‘ˆƒ–‘”†ƒ”‹•‡–‹ƒ’‡Ž‡‡ƒ–”‹•αሺܽ௜௝ሻ 6DUDQ5HIHUHQVL • ——–‡•ƒ–‡ƒ–‹ƒ—”‹—Ž—ʹͲͳ͵ȀȀȀ‡Žƒ•ǡ”Žƒ‰‰ƒǡʹͲͳͶ .ULWHULD3LQGDK/XOXV0RGXO †ƒ †‹›ƒ ‡ƒŠƒ‹ ‘†—Ž ‹‹ ƒ–ƒ— †ƒ’ƒ– „‡”’‹†ƒŠ ‡ ‘†—Ž „‡”‹—–›ƒ ƒ’ƒ„‹Žƒ –‡ŽƒŠ‡‡—Š‹•ƒŽƒŠ•ƒ–—’‡”•›ƒ”ƒ–ƒ„‡”‹—–Ǥ ͳǤ  ƒ’— ‡‰‡”Œƒƒ –—‰ƒ• †ƒ •‘ƒŽ Žƒ–‹Šƒ •‡…ƒ”ƒ Ž‡‰ƒ’ǡ „‡ƒ”ǡ ƒ—”ƒ– †ƒ •‡•—ƒ‹ ’”‘•‡†—”’‡‰‡”Œƒƒ ʹǤƒ’—‡‰‡”Œƒƒ–—‰ƒ•†ƒ•‘ƒŽŽƒ–‹Šƒ†‡‰ƒ„‡ƒ”ǡƒ—”ƒ–†ƒ•‡•—ƒ‹’”‘•‡†—” ’‡‰‡”Œƒƒǡ‹‹ƒŽ•‡„‡•ƒ”͹ͷΨ ͵Ǥƒ’—‡‰‡”Œƒƒ–‡•–’‡‡’ƒ–ƒ—–—‘†—Ž‹‹†‡‰ƒ„‡ƒ”ǡƒ—”ƒ–†ƒ•‡•—ƒ‹ ’”‘•‡†—”’‡‰‡”Œƒƒǡ‹‹ƒŽ•‡„‡•ƒ”͹ͷΨ †ƒ†‹›ƒ–ƒƒ„‡Ž—‡ƒŠƒ‹†ƒ‡‰—ƒ•ƒ‹‘†—Ž‹‹†ƒ„‡Ž—†ƒ’ƒ–„‡”’‹†ƒŠ‡ ‘†—Ž„‡”‹–›ƒƒ’ƒ„‹Žƒǣ ͳǤƒ’—‡‰‡”Œƒƒ–—‰ƒ•†ƒ•‘ƒŽŽƒ–‹Šƒ†‡‰ƒ„‡ƒ”ǡƒ—”ƒ–†ƒ•‡•—ƒ‹’”‘•‡†—” ’‡‰‡”Œƒƒǡ†‹„ƒ™ƒŠ•‡„‡•ƒ”͹ͷΨ ʹǤ‡‰‹—–‹–‡•–’‡‡’ƒ–ƒ†‡‰ƒŠƒ•‹Ž†‹„ƒ™ƒŠ͹ͷΨ 3HQLODLDQ .XQFL-DZDEDQ Latihan 1: ͳǤ ƒǤΪα൥ ͳͳ ͹ ͳͳ ͳͳ ͳʹ ͳͳ ൩„ǤȂα൥ െ͵ െ͵ െͷ െͳ ͸ ͵ ൩ ʹǤ ଵ ଷ ቂ ͳʹ ͵ ͻ ͸ ͳͷ ͸ቃαቂͶͳ͵ ʹͷʹቃ ͵Ǥ Ǥα൥ ͵ʹ ʹ͸ ͳͲ ͵Ͷ ͵Ͳ ͳͲ ͳͶ ͳͳ Ͷ ൩ ͶǤ ƒǤαቂʹ െͷ ͵ Ͷ ቃ„Ǥαቂ ͵ ʹ െͳ ͵ቃ…Ǥαቂʹ ͳ ͳ Ͷቃ ͷǤ ƒǤΪαቂെͳ ͳ Ͳ Ͷቃ „Ǥαቂ ͹ Ͷ െͺ ͳቃ …ǤȋΪȌαቂെͶ ʹͶ െͳ ͻ ቃ†ǤΪαቂെ͵ െ͵ െͶ െͺቃ Kegiatan 1: 'HWHUPLQDQGDULPDWULNVPDWULNVGLEDZDKLQLDGDODKffl D$ ቀ ʹ ͵ ͸ ͳቁ GHW$ ൫ሺʹݔͳሻ െ ሺ͸ݔ͵ሻ൯ ൌ ሺʹ െ ͳͺሻ ൌ െͳ͸ E% ቀ Ͷ െʹ ͳ ͵ቁ GHW% ൫ሺͶݔ͵ሻ െ ሺͳݔሺെʹሻሻ൯ ൌ ሺͳʹ െ ሺെʹሻሻ ൌ ሺͳʹ ൅ ʹሻ ൌ ͳͶ F3 ൭ ʹ െ͵ Ͷ ͳ ͳ െͳ ͵ ʹ െͶ ൱ GHW3 ൫ሺ൫ʹݔͳݔሺെͶሻ൯൅൫ሺെ͵ሻݔሺെͳሻݔ͵൯ ൅ ሺͶݔͳݔʹሻ െ ሺ͵ݔͳݔͶሻ െ ሺʹݔሺെͳሻݔʹሻ െ ሺെͶݔͳݔሺെ͵ሻሻ൯  ൫ሺെͺ ൅ ͻ ൅ ͺሻ െ ሺͳʹሻ െ ሺെͶሻ െ ሺͳʹሻ൯  ሺͻ െ ʹͲሻ െͳͳ G4 ൭ Ͷ െͳ ʹ ͳ ͵ െͳ ͹ Ͷ ͷ ൱ GHW4 ቀሺͶݔ͵ݔͷሻ ൅ ൫ሺെͳሻݔሺെͳሻݔ͹൯ ൅ ሺʹݔͳݔͶሻ െ ሺ͹ݔ͵ݔʹሻ െ ሺͶݔሺെͳሻݔͶሻെ ሺͷݔͳݔሺെͳሻቁ  ሺ͸Ͳ ൅ ͹ ൅ ͺ െ ሺͶʹሻ െ ሺെͳ͸ሻ െ ሺെͷሻሻ  ሺ͹ͷ െ ʹͳሻ  -LND' ൭ Ͷ ͳ ʹ ͳ ʹ െͳ ͹ ͵ ͷ ൱PDNDffl0ff0ff0ff.ff.ff.DGDODKffl

8 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 29 ͳͳαቀʹ െͳ ͵ ͷ ቁ ൌ ሺʹݔͷ ሻ െ ሺ͵ݔ ሺെͳ ሻሻ ൌ ͳͲ ൅ ͵ ൌ ͳ͵ ʹʹαቀͶ ʹ ͹ ͷቁ ൌ ሺͶݔͷ ሻ െ ሺ͹ݔʹሻ ൌ ʹͲ െ ͳͶ ൌ ͸ ͵ͳαቀͳ ʹ ʹ െͳቁ ൌ ሺͳݔሺെͳሻ ሻ െ ሺʹݔʹሻ ൌ ሺെͳ ሻ െ Ͷ ൌ െͷ ͳʹαሺെͳሻଵାଶǤͳʹ αሺെͳሻ ଷǤቀͳ െͳ ͹ ͷ ቁ αሺെͳሻǤ൫ ሺͳݔͷ ሻ െ ሺ͹ݔሺെͳሻ൯ αሺെͳሻǤ ሺͷ ൅ ͹ ሻ αሺെͳሻǤͳʹ αെͳʹ ʹ͵αሺെͳሻଶାଷǤʹ͵ αሺെͳሻ ହǤቀͶ ͳ ͹ ͵ቁ αሺെͳሻǤ൫ ͵ݔሺͶ ሻ െ ሺ͹ݔͳ൯ αሺെͳሻǤ ሺͳʹ െ ͹ ሻ αሺെͳሻǤͷ αെͷ ͵ʹαሺെͳሻଷାଶǤ͵ʹ αሺെͳሻ ହǤቀͶ ʹ ͳ െͳቁ αሺെͳሻǤ൫ ሺͶݔሺെͳሻ ሻ െ ሺͳݔʹሻ൯ αሺെͳሻǤ൫ ሺെͶ ሻ െ ʹ൯ αሺെͳሻǤሺെ͸ሻ α͸ Kegiatan :  'HHUPLQDQGULPWULNVEHULNXWDKffl ͹ ቃ H&൫ͺെ ͶH'ͷሻݔሺ൫ሺͳͲ ൅ ͻͲ ൅ ʹͶ ሻ െ ሺͻሻ െ ሺʹͶሻ െ ሺͳͲͲሻ൯   ሺͳʹͶ െ ͳ͵͵ ሻ  െͻ 7HHX ଵሺ௫ଶሻ ቂ ͵ െʹ െͶ ͷ ቃ   ଵ ଵ଴ି଼ ቂ ͵ െʹ െͶ ͷ ቃ    ଵଶ ቂ ͵ െʹ െͶ ͷ ቃ   ଶହଶ ቏   ቎ ଷଶ െͳ െʹ ହଶ ቏ E 1  ൥ ͸ͶͶ ͵ͷʹ ͳʹͳ ൩ 1  ଵ ୢୣ୲ ே$GM1 'LFDULPLQRUQ\DWHUOHELKGDKXOX  0  ቀ ͷ ʹ ʹ ͳቁ ൌ ሺͷݔͳ ሻ െ ʹݔʹሺ ሻ ൌͷെͶൌͳ 0  ቀ ͵ ʹ ͳ ͳቁ ൌ ሺ͵ݔͳ ሻ െ ʹݔሺͳ ሻ ൌ͵െʹൌͳ 0  ቀ ͵ ͷ ͳ ʹቁ ൌ ʹݔ͵ሺ ሻ െ ሺͳݔͷ ሻ ൌ͸െͷൌͳ 0  ቀ Ͷ Ͷ ʹ ͳቁ ൌ ሺͶݔͳ ሻ െ ሺʹݔͶ ሻ ൌ Ͷ െ ͺ ൌ െͶ 0  ቀ ͸ Ͷ ͳ ͳቁ ൌ ሺ͸ݔͳ ሻ െ ሺͳݔͶ ሻ ൌ͸െͶൌʹ

8 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 29 ͳͳαቀʹ െͳ ͵ ͷ ቁ ൌ ሺʹݔͷ ሻ െ ሺ͵ݔ ሺെͳ ሻሻ ൌ ͳͲ ൅ ͵ ൌ ͳ͵ ʹʹαቀͶ ʹ ͹ ͷቁ ൌ ሺͶݔͷ ሻ െ ሺ͹ݔʹሻ ൌ ʹͲ െ ͳͶ ൌ ͸ ͵ͳαቀͳ ʹ ʹ െͳቁ ൌ ሺͳݔሺെͳሻ െ ሺʹݔʹሻ ൌ ሺെͳ ሻ െ Ͷ ൌ െͷ ͳʹαሺെͳሻଵାଶǤͳʹ αሺെͳሻ ଷǤቀͳ െͳ ͹ ͷ ቁ αሺെͳሻǤ൫ ሺͳݔͷ ሻ െ ሺ͹ݔሺെͳሻ൯ αሺെͳሻǤ ሺͷ ൅ ͹ ሻ αሺെͳሻǤͳʹ αെͳʹ ʹ͵αሺെͳሻଶାଷǤʹ͵ αሺെͳሻ ହǤቀͶ ͳ ͹ ͵ቁ αሺെͳሻǤ൫ ͵ݔሺͶ ሻ െ ሺ͹ݔͳ൯ αሺെͳሻǤ ሺͳʹ െ ͹ ሻ αሺെͳሻǤͷ αെͷ ͵ʹαሺെͳሻଷାଶǤ͵ʹ αሺെͳሻ ହǤቀͶ ʹ ͳ െͳቁ αሺെͳሻǤ൫ ሺͶݔሺെͳሻ ሻ െ ሺͳݔʹሻ൯ αሺെͳሻǤ൫ ሺെͶ ሻ െ ʹ൯ αሺെͳሻǤሺെ͸ሻ α͸ Kegiatan 2:  'HWHUPLQDQGDULPDWULNVEHULNXWDGDODK D & ቂ Ͷ ͹ ͵ ͺ ቃ GHW&  ൫ ሺͶݔͺ ሻ െ ሺ͵ݔ͹ሻ൯  ±   E ' ൥ ʹͷ͵ Ͷͳ͸ ͵ʹͷ ൩ GHW'  ൫ ሺʹݔͳݔͷ ሻ ൅ ͵ݔ͸ݔሺͷ ሻ ൅ ʹݔͶݔ͵ሺ ሻ െ ͵ݔͳݔ͵ሺ ሻ െ ʹݔ͸ݔʹሺ ሻ െ ሺͷݔͶݔͷሻ൯   ൫ ሺͳͲ ൅ ͻͲ ൅ ʹͶ ሻ െ ሺͻሻ െ ሺʹͶሻ െ ሺͳͲͲ൯  ሺͳʹͶ െ ͳ͵͵ ሻ  െͻ 7HQWDQHUVGDULPDWULNVEHULNXWffl D 0  ቂ ͷ ʹ Ͷ ͵ ቃ 0  ଵ ሺହ௫ଶ ሻିሺସ௫ଶሻ ቂ ͵ െʹ െͶ ͷ ቃ   ଵ ଵ଴ି଼ ቂ ͵ െʹ െͶ ͷ ቃ    ଵଶ ቂ ͵ െʹ െͶ ͷ ቃ    ቎ ଷଶ ିଶଶ ିସଶ ହଶ ቏   ቎ ଷଶ െͳ െʹ ହଶ ቏ E 1  ൥ ͸ͶͶ ͵ͷʹ ͳʹͳ ൩ 1  ଵ ୢୣ୲ ே$GM1 'LFDULPLQRUQ\DWHUOHELKGDKXOXffl  0  ቀ ͷ ʹ ʹ ͳቁ ൌ ሺͷݔͳ ሻ െ ʹݔʹሺ ሻ ൌͷെͶൌͳ 0  ቀ ͵ ʹ ͳ ͳቁ ൌ ሺ͵ݔͳ ሻ െ ʹݔሺͳ ሻ ൌ͵െʹൌͳ 0  ቀ ͵ ͷ ͳ ʹቁ ൌ ʹݔ͵ሺ ሻ െ ሺͳݔͷ ሻ ൌ͸െͷൌͳ 0  ቀ Ͷ Ͷ ʹ ͳቁ ൌ ሺͶݔͳ ሻ െ ሺʹݔͶ ሻ ൌ Ͷ െ ͺ ൌ െͶ 0  ቀ ͸ Ͷ ͳ ͳቁ ൌ ሺ͸ݔͳ ሻ െ ሺͳݔͶ ሻ ൌ͸െͶൌʹ

0 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 31 0 ቀ ͸ Ͷ ͳ ʹቁ ൌ ሺ͸ݔʹሻ െ ሺͳݔͶሻ ൌ ͳʹ െ Ͷ ൌ ͺ 0 ቀ Ͷ Ͷ ͷ ʹቁ ൌ ሺͶݔʹሻ െ ሺͷݔͶሻ ൌ ͺ െ ʹͲ ൌ െͳʹ 0 ቀ ͸ Ͷ ͵ ʹቁ ൌ ሺ͸ݔʹሻ െ ሺ͵ݔͶሻ ൌ ͳʹ െ ͳʹ ൌ Ͳ 0 ቀ ͸ Ͷ ͵ ͷቁ ൌ ሺ͸ݔͷሻ െ ሺ͵ݔͶሻ ൌ ͵Ͳ െ ͳʹ ൌ ͳͺ 0LQRU1 ൥ ͳ ͳͳ െͶ ʹ ͺ െͳʹ Ͳ ͳͺ ൩ .RIDNWRU1 ቎ ൅ሺͳሻ െሺͳሻ ൅ሺͳሻ െሺെͶሻ ൅ሺʹሻ െሺͺሻ ൅ሺെͳʹሻ െሺͲሻ ൅ሺͳͺሻ቏ ൥ ͳ െͳ ͳ Ͷ ʹ െͺ െͳʹ Ͳ ͳͺ ൩ $GM1 ൥ ͳ Ͷ െͳʹ െͳ ʹ Ͳ ͳ െͺ ͳͺ ൩ GHW1 ൥ ͸ͶͶ ͵ͷʹ ͳʹͳ ൩ ൫ሺ͸ݔͷݔͳሻ ൅ ሺͶݔʹݔͳሻ ൅ ሺͶݔ͵ݔʹሻ െ ሺͳݔͷݔͶሻ െ ሺʹݔʹݔ͸ሻ െ Ͷሻ൯ݔ͵ݔሺͳ    ൫ሺ͵Ͳ ൅ ͺ ൅ ʹͶሻ െ ሺʹͲሻ െ ሺʹͶሻ െ ሺͳʹሻ൯    ሺ͸ʹ െ ͷ͸ሻ     -DGL1  ଵ ୢୣ୲ ே$GM1    ଵ ଺  ൥ ͳ Ͷ െͳʹ െͳ ʹ Ͳ ͳ െͺ ͳͺ ൩    ۏ ێ ێ ێ ۍ ଵ ଺ ସ ଺ ିଵଶ ଺ ିଵ ଺ ଶ ଺ Ͳ ଵ ଺ ି଼ ଺ ଵ଼ ے ଺ ۑ ۑ ۑ ې  7UDQVSRVHGDULPDWULNVEHULNXWDGDDKffl D 2 ൥ ͸Ͷ͹ ͷ ͵ െ͵  ͸͹ͷ ቃ3 െ͸െ •ƒǤ   αʹ ͷǤ ƒ–”‹•αቂെ͵ ͷ ͳ െʹቃǡ‹˜‡”•†ƒ”‹–”ƒ•’‘•‡ƒ–”‹•ƒ†ƒŽƒŠǡ•–‹െ†‡–αሺെ͵ݔሺെʹሻሻ െ ሺͷݔͳሻ α͸Ȃͷ αͳ Latihan 2: ͳǤ‡‰ƒ†‡–‡”‹ƒƒ–”‹•ǡ‹Žƒ‹˜ƒ”‹ƒ„‡Ž‹•‹•–‡’‡”•ƒƒƒ„‡”‹—–ƒ†ƒŽƒŠǣ ƒǤ൜Ͷݔʹ ൅ ݕ ൌ ͷ ͵ݔ ൅ Ͷݕ ൌ ͳ  αቀͶ ʹ ͵ ͶቁαሺͶݔͶሻ െ ሺ͵ݔʹሻ    αͳ͸Ȃ͸    αͳͲ šαቀͷ ʹ ͳ ͶቁαሺͷݔͶሻ െ ሺͳݔʹሻ   αʹͲȂʹ   αͳͺ ›αቀͶ ͷ ͵ ͳቁαሺͶݔͳሻ െ ሺ͵ݔš஽ 

0 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 31 0 ቀ ͸ Ͷ ͳ ʹቁ ൌ ሺ͸ݔʹሻ െ ሺͳݔͶሻ ൌ ͳʹ െ Ͷ ൌ ͺ 0 ቀ Ͷ Ͷ ͷ ʹቁ ൌ ሺͶݔʹሻ െ ሺͷݔͶሻ ൌ ͺ െ ʹͲ ൌ െͳʹ 0 ቀ ͸ Ͷ ͵ ʹቁ ൌ ሺ͸ݔʹሻ െ ሺ͵ݔͶሻ ൌ ͳʹ െ ͳʹ ൌ Ͳ 0 ቀ ͸ Ͷ ͵ ͷቁ ൌ ሺ͸ݔͷሻ െ ሺ͵ݔͶሻ ൌ ͵Ͳ െ ͳʹ ൌ ͳͺ 0LQRU1 ൥ ͳ ͳͳ െͶ ʹ ͺ െͳʹ Ͳ ͳͺ ൩ .RIDNWRU1 ቎ ൅ሺͳሻ െሺͳሻ ൅ሺͳሻ െሺെͶሻ ൅ሺʹሻ െሺͺሻ ൅ሺെͳʹሻ െሺͲሻ ൅ሺͳͺሻ቏ ൥ ͳ െͳ ͳ Ͷ ʹ െͺ െͳʹ Ͳ ͳͺ ൩ $GM1 ൥ ͳ Ͷ െͳʹ െͳ ʹ Ͳ ͳ െͺ ͳͺ ൩ GHW1 ൥ ͸ͶͶ ͵ͷʹ ͳʹͳ ൩ ൫ሺ͸ݔͷݔͳሻ ൅ ሺͶݔʹͳሻ ൅ ሺͶݔ͵ݔʹሻ െ ሺͳݔͷݔͶሻ െ ሺʹݔʹݔ͸ሻ െ Ͷሻ൯ݔ͵ݔሺͳ    ൫ሺ͵Ͳ ൅ ͺ ൅ ʹͶሻ െ ሺʹͲሻ െ ሺʹͶሻ െ ሺͳʹሻ൯    ሺ͸ʹ െ ͷ͸ሻ     -DGL1  ଵ ୢୣ୲ ே$GM1    ଵ ଺  ൥ ͳ Ͷ െͳʹ െͳ ʹ Ͳ ͳ െͺ ͳͺ ൩    ۏ ێ ێ ێ ۍ ଵ ଺ ସ ଺ ିଵଶ ଺ ିଵ ଺ ଶ ଺ Ͳ ଵ ଺ ି଼ ଺ ଵ଼ ے ଺ ۑ ۑ ۑ ې  7UDQVSRVHGDULPDWULNVEHULNXWDGDODK D 2 ൥ ͸ Ͷ ͹ ͷ ͵ െ͵ ൩  ቂ ͸͹ ͵ Ͷ ͷ െ͵ቃ E 3 ቂ െʹ െͶ ʹ ͸ቃ  ൥ െʹ െͶ ͷ ʹ ͵ ͸ ൩ ͶǤ ƒ–”‹•αቂ͹ Ͷ ͵ ʹቃǡƒƒ†‡–‡”‹ƒ†ƒ”‹–”ƒ•’‘•‡ƒ–”‹•ƒ†ƒŽƒŠǥǤ αቂ͹ Ͷ ͵ ʹቃǡ–”ƒ•’‘•‡ƒ–”‹•αቂ͹ ͵ Ͷ ʹቃ    †‡–αሺ͹ݔʹሻ െ ሺͶݔ͵ሻ  αͳͶȂͳʹ  αʹ ͷǤ ƒ–”‹•flαቂെ͵ ͷ ͳ െʹቃǡ‹˜‡”•†ƒ”‹–”ƒ•’‘•‡ƒ–”‹•flƒ†ƒŽƒŠǥǤ flαቂെ͵ ͷ ͳ െʹቃǡ–ƒ•’‘•‡ƒ–”‹•flαቂെ͵ ͳ ͷ െʹቃ †‡–flαሺെ͵ݔሺെʹሻሻ െ ሺͷݔͳሻ α͸Ȃͷ αͳ Latihan 2: ͳǤ‡‰ƒ†‡–‡”‹ƒƒ–”‹•ǡ‹Žƒ‹˜ƒ”‹ƒ„‡Ž†ƒ”‹•‹•–‡’‡”•ƒƒƒ„‡”‹—–ƒ†ƒŽƒŠǣ ƒǤ൜Ͷݔʹ ൅ ݕ ൌ ͷ ͵ݔ ൅ Ͷݕ ൌ ͳ  αቀͶ ʹ ͵ ͶቁαሺͶݔͶሻ െ ሺ͵ݔʹሻ    αͳ͸Ȃ͸    αͳͲ šαቀͷ ʹ ͳ ͶቁαሺͷݔͶሻ െ ሺͳݔʹሻ   αʹͲȂʹ   αͳͺ ›αቀͶ ͷ ͵ ͳቁαሺͶݔͳሻ െ ሺ͵ݔͷሻ   αͶȂͳͷ   αȂͳͷ šα ஽௫ ஽ α ଵ଼ ଵ଴ α ଽ ହ

2 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 33 ›α஽௬஽ α ିଵହ ଵ଴ α ିଷଶ ƒ†‹šα ଽହ †ƒ›αିଷଶ ܾǤ ቄ͵ݑʹ ൅ ݒ െ ͳͺ ൌ Ͳ ͷݑ െ ݒ െ ͳʹ ൌ Ͳ  '  ቀ ͵ ʹ ͷ െͳ ቁ  ሺ͵ݔሺെͳሻ ሻ െ ሺͷݔʹሻ   Ȃ͵ȂͳͲ   αȂͳ͵ 'X  ቀ ͳͺ ʹ ͳʹ െͳ ቁ  ሺͳͺݔሺെͳሻ ሻ െ ሺͳʹݔʹሻ    ȂͳͺȂʹͶ    ȂͶʹ 'Y  ቀ ͵ ͳͺ ͷ ͳʹ ቁ  ሺ͵ݔͳʹ ሻ െ ሺͷݔͳͺሻ    ͵͸ȂͻͲ    Ȃ͸Ͷ —α ஽௨஽ α ିସଶ ିଵଷ ˜α ஽௩஽ α ି଺ସ ିଵଷ ƒ†‹—αିସଶ ିଵଷ †ƒ˜αି଺ସ ିଵଷ 'HQJDQLQYHUVPDWULNVQLODLYDULDEHOGDULVLVWHPSHUVDPDDQEHULNXWDGDODKffl D ൜ Ͷݔʹ ൅ ݕ ൌ ͷ ͵ݔ ൅ Ͷݕ ൌ ͳ ቀ Ͷ ʹ ͵ Ͷቁ ቀ ݕݔ ቁ  ቀ ͷͳ ቁ PDWULNVNRHILVLHQ$  ቀ Ͷ ʹ ͵ Ͷ ቁ $  ଵ ଵ଺ି଺ ቀ Ͷ െʹ െ͵ Ͷ ቁ     $  ଵ ଵ଴ ቀ Ͷ െʹ െ͵ Ͷ ቁ     $  ቌ ସ ଵ ିଶ ଵ଴ ିଷ ଵ଴ ସଵ଴ ቍ   ቌ ସ ିଶ ଵ଴ଵ଴଴ ቀ Ͷቀ ଵି ଴ ଷଵቁ଴ ቀ ଵ଺ ଵ଴ቁ൅ቀି଺ ଵ଴ቁ ቀ ଼ ଵ଴ቁ൅଼ ଵ଴ ቁ ቀ ିଵଶ ଵ଴ ቁ൅ቀଵଶ ଵ଴ቁ ቀି଺ ଵ଴ቁ൅ቀଵ଺ ଵ଴ ቁ ቀ ݕݔ ଴൅ଵ ͳቁ ቌ ቀ ଵ଼ ଵ଴ ቁ ቀ ିଵଵ ଵ଴ ቁ ቍ   ቀ ݕݔ ቁ  ቌ ቀ ଵ଼ ଴ ቁ ቀ ିଵଵ ଵ଴ ቁ ቍ  -DGG ିଵଵ ଵ଴ E ቄ ͵ݑʹ ൅ ݒ െ ͳͺ ൌ Ͳ ͷݑ െ ݒ െ ͳʹ ൌ Ͳ   ቀ ͵ ʹ ͷ െͳቁ ቀ ݒݑ ቁ  ቀ ͳͺ ͳʹ ቁ PDWULNVNRHILVLHQ%  ቀ ͵ ʹ െͳ ቁ %  ଵ ሺିଷሻିଵ଴ ቀ െͳ െʹ െͷ ͵ ቁ     %  ଵ ିଵଷ ቀ െͳ െʹ െͷ ͵ ቁ     %  ቌ ିଵ ିଵଷ ିଶ ିଵଷ ିହ ିଵଷ ଷ ିଵଷ ቍ ቌ ିଵ ିଵଷ ିଶ ିଵଷ ିହ ିଵଷ ଷ ିଵଷ ቍ ቀ ͵ ʹ ͷ െͳቁ ቀ  ቁݒݑ ቌ ିଵ ିଵଷ ିଶ ିଵଷ ିହ ିଵଷ ଷ ିଵଷ ቍ ቀ ͳͺ ͳʹ ቁ ିଷ ቁሺିሻ ቁቀቁିିሻሺቀ ݒିିͳቀଵቁʹ ቀଵቁ ଵͳ

2 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 33 ›α஽௬஽ α ିଵହ ଵ଴ α ିଷଶ ƒ†‹šα ଽହ †ƒ›αିଷଶ ܾǤ ቄ͵ݑʹ ൅ ݒ െ ͳͺ ൌ Ͳ ͷݑ െ ݒ െ ൌ Ͳ  '  ቀ ͵ ʹ ͷ െͳ ቁ  ሺ͵ݔሺെͳሻ ሻ െ ሺͷݔʹሻ   Ȃ͵ȂͳͲ   αȂͳ͵ 'X  ቀ ͳͺ ʹ ͳʹ െͳ ቁ  ሺͳͺݔሺെͳሻ ሻ െ ሺͳʹݔʹሻ    ȂͳͺȂʹͶ    ȂͶʹ 'Y  ቀ ͵ ͳͺ ͷ ͳʹ ቁ  ሺ͵ݔͳʹ ሻ െ ሺͷݔͳͺሻ    ͵͸ȂͻͲ    Ȃ͸Ͷ —α ஽௨஽ α ିସଶ ିଵଷ ˜α ஽௩஽ α ି଺ସ ିଵଷ ƒ†‹—αିସଶ ିଵଷ †ƒ˜αି଺ସ ିଵଷ 'HQJDQLQYHUVPDWULNVQLODLYDULDEHOGDULVLVWHPSHUVDPDDQEHULNXWDGDODK D ൜ Ͷݔʹ ൅ ݕ ൌ ͷ ͵ݔ ൅ Ͷݕ ൌ ͳ ቀ Ͷ ʹ ͵ Ͷቁ ቀ ݕݔ ቁ  ቀ ͷͳ ቁ PDWULNVNRHILVLHQ$  ቀ Ͷ ʹ ͵ Ͷ ቁ $  ଵ ଵ଺ି଺ ቀ Ͷ െʹ െ͵ Ͷ ቁ     $  ଵ ଵ଴ ቀ Ͷ െʹ െ͵ Ͷ ቁ     $  ቌ ସ ଵ଴ ିଶ ଵ଴ ିଷ ଵ଴ ସ ଵ଴ ቍ   ቌ ସ ଵ଴ ିଶ ଵ଴ ିଷ ଵ଴ ସ ଵ଴ ቍ ቀ Ͷ ʹ ͵ Ͷቁ ቀ ݕݔ ቁ  ቌ ସ ଵ଴ ିଶ ଵ଴ ିଷ ଵ଴ ସ ଵ଴ ቍ ቀ ͷͳ ቁ   ቌ ቀ ସ ଵ଴ቁͶ൅ቀିଶ ଵ଴ቁ͵ ቀ ସ ଵ଴ቁʹ൅ቀିଶ ଵ଴ቁ Ͷ ቀ ିଷ ଵ଴ቁͶ൅ቀ ସ ଵ଴ቁ͵ ቀିଷ ଵ଴ቁʹ൅ቀ ସ ଵ଴ቁ Ͷ ቍ ቀ ݕݔ ቁ  ቌ ቀ ସ ଵ଴ቁͷ൅ቀିଶ ଵ଴ቁ ͳ ቀ ିଷ ଵ଴ቁͷ൅ቀ ସ ଵ଴ቁ ͳ ቍ   ቌ ቀ ଵ଺ ଵ଴ቁ൅ቀି଺ ଵ଴ቁ ቀ ଼ ଵ଴ቁ൅ቀି଼ ଵ଴ ቁ ቀ ିଵଶ ଵ଴ ቁ൅ቀଵଶ ଵ଴ቁ ቀି଺ ଵ଴ቁ൅ቀଵ଺ ଵ଴ ቁ ቍ ቀ ݕݔ ቁ  ቌ ቀ ଶ଴ ଵ଴ቁ൅ቀିଶ ଵ଴ ቁ ቀ ିଵହ ଵ଴ ቁ൅ቀ ସ ଵ଴ ቁ ቍ   ቀ ͳ Ͳ Ͳ ͳቁ ቀ ݕݔ ቁ  ቌ ቀ ଵ଼ ଵ଴ ቁ ቀ ିଵଵ ଵ଴ ቁ ቍ   ቀ ݕݔ ቁ  ቌ ቀ ଵ଼ ଵ଴ ቁ ቀ ିଵଵ ଵ଴ ቁ ቍ  -DGL[ ଵ଼ ଵ଴GDQ\ ିଵଵ ଵ଴ E ቄ ͵ݑʹ ൅ ݒ െ ͳͺ ൌ Ͳ ͷݑ െ ݒ െ ͳʹ ൌ Ͳ   ቀ ͵ ʹ ͷ െͳቁ ቀ ݒݑ ቁ  ቀ ͳͺ ͳʹ ቁ PDWULNVNRHILVLHQ%  ቀ ͵ ʹ ͷ െͳ ቁ %  ଵ ሺିଷሻିଵ଴ ቀ െͳ െʹ െͷ ͵ ቁ     %  ଵ ିଵଷ ቀ െͳ െʹ െͷ ͵ ቁ     %  ቌ ିଵ ିଵଷ ିଶ ିଵଷ ିହ ିଵଷ ଷ ିଵଷ ቍ ቌ ିଵ ିଵଷ ିଶ ିଵଷ ିହ ିଵଷ ଷ ିଵଷ ቍ ቀ ͵ ʹ ͷ െͳቁ ቀ  ቁݒݑ ቌ ିଵ ିଵଷ ିଶ ିଵଷ ିହ ିଵଷ ଷ ିଵଷ ቍ ቀ ͳͺ ͳʹ ቁ ቌ ቀ ିଵ ିଵଷቁ͵൅ቀ ିଶ ିଵଷቁͷ ቀ ିଵ ିଵଷቁʹ൅ሺ ିଶ ିଵଷሻሺെͳሻ ቀ ିହ ିଵଷቁ͵൅ቀ ଷ ିଵଷቁͷ ቀ ିହ ିଵଷቁʹ൅ሺ ଷ ିଵଷሻሺെͳሻ ቍ ቀ ݒݑ ቁ  ቌ ቀ ିଵ ିଵଷቁ ͳͺ ൅ ቀ ିଶ ିଵଷቁ ͳʹ ቀ ିହ ିଵଷቁ ͳͺ ൅ ሺ ଷ ିଵଷሻͳʹ ቍ

4 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 35  'HQJDQGHWHUPLQDQPDWULNVQLODL[\GDQ]GDULVLVWHPSHUVDPDDQEHULNXWDGDODKffl D൝ ͳ ൌ ݖʹ െ ݕ ൅ ݔʹ ʹ ൌ ݖ െ ݕ͵ ൅ ݔʹ െͳͲ  ݖʹ ൅ ݕʹ െ ݔ  ' ൭ ʹ ͳ െʹ ʹ ͵ െͳ ͳ െʹ ʹ ൱ ʹ ͳ ʹ ͵ ͳ െʹ  ሺʹǤ͵Ǥʹ ൅ ͳǤ ሺെͳሻǤͳ൅ ሺെʹሻǤ ʹǤ ሺെʹሻ െ ͳǤ͵Ǥ ሺെʹሻ െ ሺെʹሻǤ ሺെͳሻǤʹെ ʹǤʹǤͳሻ     ሺͳʹ െ ͳ ൅ ͺ ൅ ͸ െ Ͷ െ Ͷሻ      ሺͳʹ ൅ ͺ ൅ ͸ െ ͳ െ Ͷ െ Ͷሻ      ሺʹ͸ െ ͻሻ      '[ ൭ ͳ ͳ െʹ ʹ ͵ െͳ െͳͲ െʹ ʹ ൱ ͳ ͳ ʹ ͵ െͳͲ െʹ  ሺͳǤ͵Ǥʹ ൅ ͳǤ ሺെͳሻǤ ሺെͳͲሻ ൅ ሺെʹሻǤ ʹǤ ሺെʹሻ െ ሺെͳͲሻǤ ͵Ǥ ሺെʹሻ െ ሺെʹሻǤ ሺെͳሻǤ ͳ െ ʹǤʹǤͳሻ    ሺ͸ ൅ ͳͲ ൅ ͺ െ ͸Ͳ െ ʹ ൅ Ͷሻ    ሺʹͺ െ ͸Ͳሻ   െ͵ʹ '\ ൭ ʹ ͳ െʹ ʹ ʹ െͳ ͳ െͳͲ ʹ ൱ ʹ ͳ ʹ ʹ ͳ െͳͲ  ሺʹǤʹǤʹ ൅ ͳǤ ሺെͳሻǤͳ൅ ሺെʹሻǤ ʹǤ ሺെͳͲሻ െ ͳǤʹǤ ሺെʹሻ െ  ሺെͳͲሻǤ ሺെͳሻǤ ʹ െ ʹǤʹǤͳሻ    ሺͺ െ ͳ ൅ ͶͲ ൅ Ͷ ൅ ʹͲ െ Ͷሻ    ሺ͹ʹ െ ͷሻ    '] ൭ ʹͳ ͳ ʹ͵ ͳ ͳ െʹ െͳͲ ൱ ʹ ͳ ʹ ͵ ͳ െʹ  ሺʹǤ͵Ǥ ሺെͳͲሻ ൅ ͳǤͳǤͳ ൅ ͳǤʹǤ ሺെʹሻ െ ͳǤ͵Ǥͳ െ ʹǤͳǤʹ െ ͳͲǤʹǤͳሻ       ሺെ͸Ͳ ൅ ͳ െ Ͷ െ ͵ െ Ͷ െ ʹͲሻ      െͻͲ [  ஽௫ ஽   ିଷଶ ଵ଻   \ ஽௬ ஽   ଺଻ ଵ଻  ]  ஽௭ ஽   ିଽ଴ ଵ଻ E൝ ͵െ ൌ ݖ െ ݕ͵ ൅ ݔʹ ͸ ൌ ݖ ൅ ݕ ൅ ݔ ͳ ൌ ݖʹ ൅ ݕ െ ݔ͵ α൭ ʹ ͵ െͳ ͳͳ ͳ ͵ െͳ ʹ ൱ ʹ ͵ ͳ ͳ ͵ െͳ αሺʹǤͳǤʹ ൅ ͵ǤͳǤ͵ ൅ ሺെͳሻǤͳǤ ሺെͳሻ െ ሺ͵ǤͳǤ ሺെͳሻሻ െ ሺሺെͳሻǤͳǤʹሻ െ ሺʹǤͳǤ͵ሻሻ αሺͶ൅ͻ൅ͳെ ሺെ͵ሻ െ ሺെʹሻ െ ሺ͸ሻሻ αሺͳͻ െ ͸ሻ αͳ͵ šα൭͵ ͵ െͳ ͸ͳ ͳ ͳ െͳ ʹ ൱ ͵ ͵ ͸ ͳ ͳ െͳ α൫͵ǤͳǤʹ ൅ ͵ǤͳǤͳ ൅ ሺെͳሻǤ ͸Ǥ ሺെͳሻ െ ሺͳǤͳǤ ሺെͳሻሻ െ ൫ሺെͳሻǤ ͳǤ͵൯ െ ሺʹǤ͸Ǥ͵ሻ൯ αሺ͸൅͵൅͸െ ሺെͳሻ െ ሺെ͵ሻ െ ͵͸ሻ αሺͳͻ െ ͵͸ሻ αെͳ͹ ›α൭ʹ െ͵ െͳ ͳ͸ ͳ ͵ͳ ʹ ൱ ʹ െ͵ ͳ ͳ ͵ െͳ αሺሺʹǤ͸Ǥʹሻ ൅ ሺሺെ͵ሻǤͳǤ͵ ൅ ሺሺെͳሻǤ ͳǤ ሺെͳሻሻ െ ሺሺ͵Ǥ͸Ǥ ሺെͳሻሻ െ ሺͳǤͳǤʹሻ െ ሺʹǤͳǤ ሺെ͵ሻሻ αሺʹͶ ൅ ሺെͻሻ ൅ͳെ ሺെͳͺሻ െ ʹ െ ሺെ͸ሻሻ αሺʹͶ ൅ ͳ ൅ ͳͺ ൅ ͸ െ ͻ െ ʹሻ αሺͶͻ െ ͳͳሻ α͵ͺ '] ൭ ʹ ͵ െ͵ ͳͳ ͸ ͵ െͳ ͳ ൱ ʹ ͵ ͳ ͳ ͵ െͳ ൫ሺʹǤͳǤͳሻ ൅ ሺ͵Ǥ͸Ǥ͵ሻ ൅ ሺെ͵ሻǤ ͳǤ ሺെͳሻ െ ሺሺ͵ǤͳǤ ሺെ͵ሻሻ െ ൫ሺെͳሻǤ ͸Ǥʹ൯ െ ሺͳǤͳǤ͵ሻ൯  ሺʹ ൅ ͷͶ ൅ ͵ ൅ ͻ ൅ ͳʹ െ ͵ሻ  ሺͺͲ െ ͵ሻ   -DGLQLODL[ ஽௫ ஽   ିଵ଻ ଵଷ \ ஽௬ ஽   ଷ଼ ଵଷ]  ஽௭ ஽   ଻଻ ଵଷ

4 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 Keteraturan Barisan dan Penyajian Data dalam Bentuk Matriks 35  'HQJDQGHWHUPLQDQPDWULNVQLODL[\GDQ]GDULVLVWHPSHUVDPDDQEHULNXWDGDODK D൝ ͳ ൌ ݖʹ െ ݕ ൅ ݔʹ ʹ ൌ ݖ െ ݕ͵ ൅ ݔʹ െͳͲ  ൌ ݖʹ ൅ ݕʹ െ ݔ  ' ൭ ʹ ͳ െʹ ʹ ͵ െͳ ͳ െʹ ʹ ൱ ʹ ͳ ʹ ͵ ͳ െʹ  ሺʹǤ͵Ǥʹ ൅ ͳǤ ሺെͳሻǤͳ൅ ሺെʹሻǤ ʹǤ ሺെʹሻ െ ͳǤ͵Ǥ ሺെʹሻ െ ሺെʹሻǤ ሺെͳሻǤʹെ ʹǤʹǤͳሻ   ሺͳʹ െ ͳ ൅ ͺ ൅ ͸ െ Ͷ െ Ͷሻ      ሺͳʹ ൅ ͺ ൅ ͸ െ ͳ െ Ͷ െ Ͷሻ      ሺʹ͸ െ ͻሻ      '[ ൭ ͳ ͳ െʹ ʹ ͵ െͳ െͳͲ െʹ ʹ ൱ ͳ ͳ ʹ ͵ െͳͲ െʹ  ሺͳǤ͵Ǥʹ ൅ ͳǤ ሺെͳሻǤ ሺെͳͲሻ ൅ ሺെʹሻǤ ʹǤ ሺെʹሻ െ ሺെͳͲሻǤ ͵Ǥ ሺെʹሻ െ ሺെʹሻǤ ሺെͳሻǤ ͳ െ ʹǤʹǤͳሻ    ሺ͸ ൅ ͳͲ ൅ ͺ െ ͸Ͳ െ ʹ ൅ Ͷሻ    ሺʹͺ െ ͸Ͳሻ   െ͵ʹ '\ ൭ ʹ ͳ െʹ ʹ ʹ െͳ ͳ െͳͲ ʹ ൱ ʹ ͳ ʹ ʹ ͳ െͳͲ  ሺʹǤʹǤʹ ൅ ͳǤ ሺെͳሻǤͳ൅ ሺെʹሻǤ ʹǤ ሺെͳͲሻ െ ͳǤʹǤ ሺെʹሻ െ  ሺെͳͲሻǤ ሺെͳሻǤ ʹ െ ʹǤʹǤͳሻ    ሺͺ െ ͳ ൅ ͶͲ ൅ Ͷ ൅ ʹͲ െ Ͷሻ    ሺ͹ʹ െ ͷሻ    '] ൭ ʹͳ ͳ ʹ͵ ͳ ͳ െʹ െͳͲ ൱ ʹ ͳ ʹ ͵ ͳ െʹ  ሺʹǤ͵Ǥ ሺെͳͲሻ ൅ ͳǤͳǤͳ ൅ ͳǤʹǤ ሺെʹሻ െ ͳǤ͵Ǥͳ െ ʹǤͳǤʹ െ ͳͲǤʹǤͳሻ       ሺെ͸Ͳ ൅ ͳ െ Ͷ െ ͵ െ Ͷ െ ʹͲሻ      െͻͲ [  ஽௫ ஽   ିଷଶ ଵ଻   \ ஽௬ ஽   ଺଻ ଵ଻  ]  ஽௭ ஽   ିଽ଴ ଵ଻ E൝ ͵െ ൌ ݖ െ ݕ͵ ൅ ݔʹ ͸ ൌ ݖ ൅ ݕ ൅ ݔ ͳ ൌ ݖʹ ൅ ݕ െ ݔ͵ α൭ ʹ ͵ െͳ ͳͳ ͳ ͵ െͳ ʹ ൱ ʹ ͵ ͳ ͳ ͵ െͳ αሺʹǤͳǤʹ ൅ ͵ǤͳǤ͵ ൅ ሺെͳሻǤͳǤ ሺെͳሻ െ ሺ͵ǤͳǤ ሺെͳሻሻ െ ሺሺെͳሻǤͳǤʹሻ െ ሺʹǤͳǤ͵ሻሻ αሺͶ൅ͻ൅ͳെ ሺെ͵ሻ െ ሺെʹሻ െ ሺ͸ሻሻ αሺͳͻ െ ͸ሻ αͳ͵ šα൭͵ ͵ െͳ ͸ͳ ͳ ͳ െͳ ʹ ൱ ͵ ͵ ͸ ͳ ͳ െͳ α൫͵ǤͳǤʹ ൅ ͵ǤͳǤͳ ൅ ሺെͳሻǤ ͸Ǥ ሺെͳሻ െ ሺͳǤͳǤ ሺെͳሻሻ െ ൫ሺെͳሻǤ ͳǤ͵൯ െ ሺʹǤ͸Ǥ͵ሻ൯ αሺ͸൅͵൅͸െ ሺെͳሻ െ ሺെ͵ሻ െ ͵͸ሻ αሺͳͻ െ ͵͸ሻ αെͳ͹ ›α൭ʹ െ͵ െͳ ͳ͸ ͳ ͵ͳ ʹ ൱ ʹ െ͵ ͳ ͳ ͵ െͳ αሺሺʹǤ͸Ǥʹሻ ൅ ሺሺെ͵ሻǤͳǤ͵ ൅ ሺሺെͳሻǤ ͳǤ ሺെͳሻሻ െ ሺሺ͵Ǥ͸Ǥ ሺെͳሻሻ െ ሺͳǤͳǤʹሻ െ ሺʹǤͳǤ ሺെ͵ሻሻ αሺʹͶ ൅ ሺെͻሻ ൅ͳെ ሺെͳͺሻ െ ʹ െ ሺെ͸ሻሻ αሺʹͶ ൅ ͳ ൅ ͳͺ ൅ ͸ െ ͻ െ ʹሻ αሺͶͻ െ ͳͳሻ α͵ͺ '] ൭ ʹ ͵ െ͵ ͳͳ ͸ ͵ െͳ ͳ ൱ ʹ ͵ ͳ ͳ ͵ െͳ ൫ሺʹǤͳǤͳሻ ൅ ሺ͵Ǥ͸Ǥ͵ሻ ൅ ሺെ͵ሻǤ ͳǤ ሺെͳሻ െ ሺሺ͵ǤͳǤ ሺെ͵ሻሻ െ ൫ሺെͳሻǤ ͸Ǥʹ൯ െ ሺͳǤͳǤ͵ሻ൯  ሺʹ ൅ ͷͶ ൅ ͵ ൅ ͻ ൅ ͳʹ െ ͵ሻ  ሺͺͲ െ ͵ሻ   -DGLQLODL[ ஽௫ ஽   ିଵ଻ ଵଷ \ ஽௬ ஽   ଷ଼ ଵଷ]  ஽௭ ஽   ଻଻ ଵଷ

36 MatemaƟ ka Paket C - Setara SMA/MA kelas XI Modul 8 'DIWDU3XVWDND %XNX0DWHPDWLNDNDUDQJDQ'UV6XWDPD 0HQ\HOHVDLNDQ3HUVDPDDQ/LQHDUGHQJDQ0DWULNVROHK0XML6XZDUQR %XNX0DWHPDWLND3URJUDP3DNHW&3HQHUELW$U\D'XWDNDUDQJDQ'UV$JXV+LGD\DW KWWSfflUXPXVPDWHPDWLNDFRPPDWHULPDWULNVOHQJNDSGDQFRQWRKQ\D KWWSVfflLGZLNLERRNVRUJZLNL6XEMHNffl0DWHPDWLND0DWHULffl0DWULNV KWWSVfflZZZNRQVHSPDWHPDWLNDFRPffiGHWHUPLQDQGDQLQYHUVPDWULNVKWPO KWWSVfflLGVFKRROQHWVPDRSHUDVLKLWXQJSHQMXPODKDQSHQJXUDQJDQSHUNDOLDQPDWULNV flKWWSVffl\RVSUHQVZRUGSUHVVFRPNHVDPDDQSHQMXPODKDQGDQSHQJXUDQJDQPDWULNV  WZK&/>WffiEh>/^ 1DPD/HQJNDS ffl1XUVDQWR 7HOS.DQWRU+3 fflflffiH[Wflflfl (0DLO  fflQXUVDQWR#JPDLOFRP    $ODPDW.DQWRU ffl-O.REHU3HGDWL5W5Z .HOXUDKDQ%DOLPHVWHU.HFDPDWDQ-DWLQHJDUD .RWD$GPLQLVWUDVL-DNDUWD7LPXU %LGDQJ.HDKOLDQffl 5LZD\DW3HNHUMDDQ3URIHVLGDODP7DKXQ7HUDNKLU 0HQJDMDUGL3.%0),=$57DKXQ±VHNDUDQJ 0HQJDMDUGL3.%0$ZZDOL\DK5RKLLP7DKXQ±VHNDUDQJ 5LZD\DW3HQGLGLNDQ7LQJJLGDQ7DKXQ%HODMDU 60,3$-XUXVDQ0DWHPDWLNDOXOXVWDKXQffiffi « «GVW -XGXO%XNXGDQ7DKXQ7HUELW7DKXQ7HUDNKLU -XGXO3HQHOLWLDQGDQ7DKXQ7HUELW7DKXQ7HUDNKLU