{"id":289,"date":"2023-07-06T19:13:46","date_gmt":"2023-07-06T19:13:46","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/"},"modified":"2023-07-06T19:13:46","modified_gmt":"2023-07-06T19:13:46","slug":"contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/","title":{"rendered":"Minor, asisten dan matriks pelengkap asisten"},"content":{"rendered":"<p>Pada bagian ini kita akan melihat apa itu dan bagaimana cara menghitung <strong>minor komplementer, adjoint, dan matriks adjoint<\/strong> . Selain itu, Anda akan menemukan contoh agar Anda memahaminya dengan sempurna, dan latihan diselesaikan langkah demi langkah, sehingga Anda dapat berlatih.<\/p>\n<h2 class=\"wp-block-heading\"> Apa yang dimaksud dengan minor komplementer?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Ini disebut <strong>komplemen minor<\/strong> suatu elemen.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41d4a89db3722950dc94351832a1bcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> ke determinan yang diperoleh dengan menghapus garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-695d9d59bd04859c6c99e7feb11daab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan kolom<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43c82d5bb00a7568d935a12e3bd969dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"j\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> dari sebuah matriks.<\/p>\n<h2 class=\"wp-block-heading\"> Bagaimana cara menghitung minor komplementer suatu unsur?<\/h2>\n<p> Mari kita lihat bagaimana minor komplementer suatu unsur dihitung menggunakan beberapa contoh:<\/p>\n<h3 style=\"color:#00B0FF\"> Contoh 1:<\/h3>\n<p> Hitung <strong>komplemen minor dari 1<\/strong> matriks persegi 3 \u00d7 3 berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a9db280911827ab5d64507cfe71aed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\left( \\begin{array}{ccc} 6 &amp; 1 &amp; 7 \\\\[1.1ex] 3 &amp; 2 &amp; 0 \\\\[1.1ex] 5 &amp; 8 &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>Minor komplementer dari 1<\/strong> adalah determinan matriks yang tersisa setelah baris dan kolom tempat angka 1 dihilangkan. Artinya, menghapus baris pertama dan kolom kedua:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cb0021e61d4a3779378734771071bdfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{ccc} \\cellcolor[HTML]{F5B7B1}6 &amp; \\cellcolor[HTML]{F5B7B1}1 &amp; \\cellcolor[HTML]{F5B7B1}7 \\\\ &amp; \\cellcolor[HTML]{F5B7B1} &amp; \\\\[-2ex] 3 &amp; \\cellcolor[HTML]{F5B7B1}2 &amp; 0 \\\\ &amp; \\cellcolor[HTML]{F5B7B1} &amp; \\\\[-2ex] 5 &amp;  \\cellcolor[HTML]{F5B7B1}8 &amp; 4                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"486\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a38c134fa8e592ff15956701ce4521c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 1} =  \\begin{vmatrix} 3 &amp; 0 \\\\[1.1ex] 5 &amp; 4 \\end{vmatrix} = \\bm{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"331\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 style=\"color:#00B0FF\"> Contoh 2:<\/h3>\n<p> Kali ini kita akan menghitung <strong>minor komplementer 0<\/strong> dari matriks yang sama seperti sebelumnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a9db280911827ab5d64507cfe71aed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\left( \\begin{array}{ccc} 6 &amp; 1 &amp; 7 \\\\[1.1ex] 3 &amp; 2 &amp; 0 \\\\[1.1ex] 5 &amp; 8 &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>Minor komplementer 0<\/strong> adalah determinan matriks dengan menghilangkan baris dan kolom yang bernilai 0:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eeeb42496216ad8689d1a70807b56644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{ccc} 6 &amp; 1 &amp; \\cellcolor[HTML]{F5B7B1}7 \\\\ &amp;  &amp; \\cellcolor[HTML]{F5B7B1} \\\\[-2ex] \\cellcolor[HTML]{F5B7B1} 3 &amp; \\cellcolor[HTML]{F5B7B1}2 &amp; \\cellcolor[HTML]{F5B7B1}0 \\\\ &amp; &amp;\\cellcolor[HTML]{F5B7B1} \\\\[-2ex] 5 &amp;  8 &amp; \\cellcolor[HTML]{F5B7B1}4                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"492\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd1eff11f2081d56b20c97203fc053c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 0} =  \\begin{vmatrix} 6 &amp; 1 \\\\[1.1ex] 5 &amp; 8 \\end{vmatrix} = \\bm{43}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"332\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Latihan terpecahkan untuk anak di bawah umur yang saling melengkapi<\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Hitung komplemen terkecil dari 3 matriks 3\u00d73 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16dac836fa9d63465e46dd35e2f36249_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 5 &amp; 1 &amp; 2 \\\\[1.1ex] 3 &amp; 4 &amp; 7 \\\\[1.1ex] -1 &amp; 6 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Minor komplementer dari 3 adalah determinan matriks yang tersisa setelah baris dan kolom yang berisi 3 dihilangkan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23b957e07aa004db36332997e906169f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 3} = \\begin{vmatrix} 1 &amp; 2 \\\\[1.1ex] 6 &amp; 7 \\end{vmatrix} = \\bm{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"328\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Tentukan minor komplementer dari 5 matriks orde 3 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-870e864969258f55a07ecd82c68c3132_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -2 &amp; 4 &amp; -2 \\\\[1.1ex] 1 &amp; 3 &amp; 4 \\\\[1.1ex] 5 &amp; 8 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"108\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Minor komplementer dari 5 adalah determinan matriks yang diperoleh dengan menghapus baris dan kolom yang mengandung 5: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f9fc980c8adf2b46e6bcfea0ef69737a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 5} = \\begin{vmatrix} 4 &amp; -2 \\\\[1.1ex] 3 &amp; 4 \\end{vmatrix} = \\bm{22}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"344\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Hitung komplemen minor dari 6 matriks 4\u00d74 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c61e20d710e35ab2b27c94ca720e01a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 1 &amp; 3 &amp; 4 \\\\[1.1ex] 2 &amp; 6 &amp; -1 &amp; 8 \\\\[1.1ex] 3 &amp; 9 &amp; -1 &amp; 4 \\\\[1.1ex] 5 &amp; 4 &amp; 1 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"119\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Minor komplementer dari 6 adalah determinan matriks yang tersisa setelah baris dan kolom yang bertempat 6 dihilangkan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60150a09c3023b5f1e147bf437df719c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 6} = \\begin{vmatrix} 1 &amp; 3 &amp; 4 \\\\[1.1ex] 3 &amp; -1 &amp; 4 \\\\[1.1ex] 5&amp; 1 &amp; 3 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"325\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menyelesaikan determinan dengan aturan Sarrus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f331c9c3723df34235d8f172f5f41750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; 3 &amp; 4 \\\\[1.1ex] 3 &amp; -1 &amp; 4 \\\\[1.1ex] 5 &amp; 1 &amp; 3 \\end{vmatrix}=-3+60+12+20-4-27 = \\bm{58}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"359\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\">Apa adjoin dari elemen array? <\/h2>\n<div style=\"background-color:#dff6ff;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p align=\"LEFT\"> <strong>Wakil<\/strong> dari<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41d4a89db3722950dc94351832a1bcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> , yaitu item baris<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-695d9d59bd04859c6c99e7feb11daab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan kolom<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43c82d5bb00a7568d935a12e3bd969dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"j\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> , diperoleh dengan rumus berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dcce4b79a3549da03df7c78b678add31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } a_{ij} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"430\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h2 class=\"wp-block-heading\"> Bagaimana cara mendapatkan gabungan elemen array?<\/h2>\n<p> Mari kita lihat bagaimana adjoint suatu elemen dihitung melalui beberapa contoh:<\/p>\n<h3 style=\"color:#00B0FF\"> Contoh 1:<\/h3>\n<p> Hitung <strong>adjoin dari 4<\/strong> matriks berorde 3 berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0acdd22355294e7c19583b1538c9070d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 1 &amp; 2 &amp; 3 \\\\[1.1ex] 4 &amp; 5 &amp; 6 \\\\[1.1ex] 7 &amp; 8 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32a95816558c4ad5b48cb3e6b06eb8c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } 4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Angka 4 ada di <strong>baris 2<\/strong> dan <strong>kolom 1<\/strong> , jadi dalam kasus ini<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16ec1d81dc1a7d422c1985f813b6603b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb4d87f6d5922c8ff5cf03f1ea28faaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"j = 1 :\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aea771762912a2598233c359dabc88e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 = \\displaystyle (-1)^{2+1} \\bm{\\cdot} \\text{Menor complementario de } 4\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"409\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan, seperti yang kita lihat sebelumnya, <strong>komplemen minor dari 4<\/strong> adalah determinan matriks, menghilangkan baris dan kolom tempat 4 berada. Karena itu:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1cdd0dac0607a955fcfb19849c05276_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de} 4 = \\displaystyle(-1)^{2+1} \\bm{\\cdot}  \\begin{vmatrix}  2 &amp; 3  \\\\[1.1ex]  8 &amp; 9 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"241\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sekarang kita selesaikan determinannya dan <strong>temukan adjoint dari 4:<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9522581f22ca9b6b750bb9e3e7b0a60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 = (-1)^{3} \\bm{\\cdot}  (-5) = -1 \\cdot (-6) = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"339\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div style=\"background-color:#fffde7;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p align=\"LEFT\"> <strong>Ingatlah<\/strong> bahwa bilangan negatif yang dipangkatkan menjadi eksponen genap adalah bilangan positif. Oleh karena itu, jika -1 dipangkatkan menjadi bilangan genap maka menjadi positif.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5044fab01a117e78360f8982b1d37d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\longrightarrow}(-1)^2=\\bm{+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p align=\"LEFT\"> Sebaliknya, jika suatu bilangan negatif dipangkatkan menjadi eksponen ganjil, maka bilangan tersebut negatif. Oleh karena itu, jika -1 dipangkatkan ke bilangan ganjil maka selalu negatif.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8b51896f8d21b327891018914418bf6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\longrightarrow}(-1)^3=\\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<h3 style=\"color:#00B0FF\"> Contoh 2:<\/h3>\n<p> Kita akan mencari <strong>wakil dari 5<\/strong> matriks yang sama seperti sebelumnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0acdd22355294e7c19583b1538c9070d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 1 &amp; 2 &amp; 3 \\\\[1.1ex] 4 &amp; 5 &amp; 6 \\\\[1.1ex] 7 &amp; 8 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-330e8801d4047cb9970efea37bb1eb8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 5 = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } 5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"405\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3e47d30b12e053b3f5950033640b662_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de} 5 = \\displaystyle(-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 3  \\\\[1.1ex]  7 &amp; 9 \\end{vmatrix} = 1 \\cdot (-12) = \\bm{-12}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"388\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 style=\"color:#00B0FF\"> Contoh 3:<\/h3>\n<p> Mari kita buat <strong>wakil dari 3<\/strong> matriks yang sama: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0acdd22355294e7c19583b1538c9070d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 1 &amp; 2 &amp; 3 \\\\[1.1ex] 4 &amp; 5 &amp; 6 \\\\[1.1ex] 7 &amp; 8 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bb298a5166e562f6a168addd0d1450a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 3 = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } 3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-954d6137c753a58e91682334addc5345_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de} 3 \\displaystyle =  (-1)^{1+3} \\bm{\\cdot} \\begin{vmatrix} 4 &amp; 5  \\\\[1.1ex]  7 &amp; 8 \\end{vmatrix} = 1 \\cdot (-3) = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"370\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Adjoint suatu elemen digunakan untuk menghitung determinan, seperti yang akan kita lihat nanti, dan untuk menghitung matriks adjoint, yang akan kita lihat sekarang.<\/p>\n<h2 class=\"wp-block-heading\"> Latihan terpecahkan untuk asisten<\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Hitung adjoin 2 matriks 3\u00d73 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-340d5ef9265b33c7a6ad4ac7d72633f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 3 &amp; 1 \\\\[1.1ex] -1 &amp; -3 &amp; 5 \\\\[1.1ex] 5 &amp; 3 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"108\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mendapatkan hasil adjoint 2, cukup terapkan rumus adjoint suatu elemen: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27e737fcb3ffe43ab7b1ee30a091bfb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de 2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"405\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74e69b36278f7b0518a20be2e02aea4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} \\displaystyle = (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} -3 &amp; 5 \\\\[1.1ex] 3 &amp; 1 \\end{vmatrix} = 1 \\cdot (-18) = \\bm{-18}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"402\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Tentukan adjoin dari 4 matriks orde 3 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e21733cd834cdbeed5ca8fc433068ccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 3 &amp; 1 &amp; -1 \\\\[1.1ex] 2 &amp; 9 &amp; 4 \\\\[1.1ex] 6 &amp; 5 &amp; -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mendapatkan wakil dari 4, kita harus menggunakan rumus wakil suatu unsur: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-58a3653b2ec21f65f85689ffbe978079_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 4} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de 4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4a2228588aeef08594e7f3cc93c53ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 4} \\displaystyle = (-1)^{2+3} \\bm{\\cdot} \\begin{vmatrix} 3 &amp; 1 \\\\[1.1ex] 6 &amp; 5 \\end{vmatrix} = -1 \\cdot 9 = \\bm{-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"356\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\"> Latihan 3<\/h3>\n<p> Tentukan wakil dari 7 matriks 4\u00d74 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64b3cf6b9f34fce5f66d24502f2434a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 2 &amp; 5 &amp; -2 \\\\[1.1ex] 3 &amp; 1 &amp; -3 &amp; 3 \\\\[1.1ex] 2 &amp; -1 &amp; 4 &amp; 0 \\\\[1.1ex] 2 &amp; 7 &amp; 9 &amp; -4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"147\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk membuat tambahan 7 kita menerapkan rumus tambahan suatu elemen: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b62c0cebb18f5b2ae6d01078babc00b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 7}=(-1)^{4+2} \\bm{\\cdot} \\text{Menor complementario de 7}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"409\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54f5200bb9a57df8b0aa73271ec26c7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 7} \\displaystyle = (-1)^{4+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 5 &amp; -2 \\\\[1.1ex] 3 &amp; -3 &amp; 3 \\\\[1.1ex] 2 &amp; 4 &amp; 0\\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"293\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menerapkan aturan Sarrus untuk menyelesaikan determinan orde ketiga: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34d456bf805c4a6d8673d00febc983dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = (-1)^{6} \\bm{\\cdot} \\bigl[0+30-24-12-12-0\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"276\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b228f8cd5f96cfdbd7e80138cb109e3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = 1 \\bm{\\cdot} \\bigl[-18 \\bigr] = \\bm{-18}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\">Apa matriks terlampir?<\/h2>\n<p> <strong>Array terlampir<\/strong> adalah array yang semua elemennya telah digantikan oleh wakilnya.<\/p>\n<h2 class=\"wp-block-heading\"> Bagaimana cara menghitung matriks adjoin?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Untuk menghitung <strong>wakil matriks<\/strong> , kita perlu mensubstitusi semua elemen matriks untuk wakilnya.<\/p>\n<p> Mari kita lihat bagaimana matriks gabungan dibuat melalui contoh: <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-119\"><\/div>\n<\/div>\n<h3 style=\"color:#00B0FF\"> Contoh:<\/h3>\n<p> Hitung matriks adjoin matriks persegi berdimensi 2\u00d72 berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e1d84d025062b24cb6a7ef021cb55de1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 4 &amp; -1 \\\\[1.1ex] 3 &amp; 2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"109\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Untuk menghitung adjoint matriks, kita harus <strong>menghitung adjoint setiap elemen matriks<\/strong> . Oleh karena itu, pertama-tama kita akan menyelesaikan persamaan semua elemen dengan rumus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dcce4b79a3549da03df7c78b678add31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } a_{ij} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"430\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30683bf4304e3072c4fcf46610e06e05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 =\\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} 2 \\end{vmatrix} = 1 \\cdot 2 = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"302\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-04af89fae8a9060940f892f5d1e0c51d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -1} =\\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix} 3 \\end{vmatrix} = -1 \\cdot 3 = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"336\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-042a24b0f0896742500d7455e8f944ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 3 =\\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} -1 \\end{vmatrix} = -1 \\cdot (-1) = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"357\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0d3e6017c878bc47df1c509936fbcf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 2 =\\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 4 \\end{vmatrix} = 1 \\cdot 4 = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"303\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Sekarang kita hanya perlu mengganti setiap elemen dalam array<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> oleh wakilnya untuk mencari <strong>matriks wakilnya<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1372441aae26d85aebdcbe3baf70cf56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{A} :\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c4c2583218c84e184a1911972dca72b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{2} &amp; \\bm{-3} \\\\[1.1ex] \\bm{1} &amp; \\bm{4}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan dengan cara ini wakil dari sebuah matriks ditemukan. Tapi Anda mungkin bertanya-tanya untuk apa semua perhitungan ini? Nah, salah satu kegunaan penggabungan matriks adalah menghitung <a href=\"https:\/\/mathority.org\/id\/matriks-terbalik\/\">invers suatu matriks<\/a> . Sebenarnya metode yang paling umum untuk mencari matriks invers adalah metode matriks adjoin.<\/p>\n<h2 class=\"wp-block-heading\"> Memecahkan masalah matriks adjoin<\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Hitung matriks adjoin dari matriks persegi 2\u00d72 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5fbfc1c22345724f35d7208214f8592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 3  \\\\[1.1ex] -4 &amp; 1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menghitung adjoint matriks, kita harus menghitung adjoint setiap elemen matriks. Oleh karena itu, pertama-tama kita akan menyelesaikan persamaan semua elemen dengan rumus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86e59cf1a404062a425e15fde85090cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} =\\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} 1 \\end{vmatrix} = 1 \\cdot 1 = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"302\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74a9e31be5bf93b62a51c1bf23200f48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 3} =\\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix} -4 \\end{vmatrix} = -1 \\cdot (-4) = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"358\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25393a1a057c92d2eea1f57ac2ae914f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -4} =\\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} 3 \\end{vmatrix} = -1 \\cdot 3 = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"336\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f05aa937b693794438cf7c04b75fc924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 1} =\\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 2 \\end{vmatrix} = 1 \\cdot 2 = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"302\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita hanya perlu mengganti setiap elemen dalam array<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> oleh wakilnya untuk mencari matriks wakilnya <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed7f99fecb7719c7108eaecc0a21dad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A :\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d3fdee2506136365c141a81596f1d22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{1} &amp; \\bm{4} \\\\[1.1ex] \\bm{-3} &amp; \\bm{2}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Tentukan matriks adjoin dari matriks orde kedua berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b95133fbf999cb6585b3a32f4b1b906b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 6 &amp; -2  \\\\[1.1ex] 3 &amp; -7  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menghitung adjoint matriks, kita harus menghitung adjoint setiap elemen matriks. Oleh karena itu, pertama-tama kita akan menyelesaikan persamaan semua elemen dengan rumus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35b5b261848474e8eb940bee9147c21b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 6} =\\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} -7 \\end{vmatrix} = 1 \\cdot (-7) = \\bm{-7}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"358\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0f1e6a5a5c504b3b6d06e5d3d8e0862e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -2} =\\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix} 3 \\end{vmatrix} = -1 \\cdot 3 = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"336\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05a49201adc9cef4d1e9903157860e4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 3} =\\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} -2 \\end{vmatrix} = -1 \\cdot (-2) = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"357\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e936a7e026d5fc05b60e032170c85c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -7} =\\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 6 \\end{vmatrix} = 1 \\cdot 6 = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"309\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita hanya perlu mengganti setiap elemen dalam array<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> oleh wakilnya untuk mencari matriks wakilnya <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed7f99fecb7719c7108eaecc0a21dad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A :\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-604112d6e7d95ca76dd5266dc2eceb86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{-7} &amp; \\bm{-3} \\\\[1.1ex] \\bm{2} &amp; \\bm{6}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"173\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 3<\/h3>\n<p> Hitung matriks adjoin dari matriks 3\u00d73 berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0072b68810f2662ae9f4ec3d11902f97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 3 &amp; -1 \\\\[1.1ex] 2 &amp; 4 &amp; 0 \\\\[1.1ex] 5 &amp; 0 &amp; -2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menghitung adjoint matriks, kita harus menghitung adjoint setiap elemen matriks. Oleh karena itu, pertama-tama kita akan menyelesaikan persamaan semua elemen dengan rumus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68e2bee7e07b5749033cdf67d90684a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 1} = \\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} 4 &amp; 0 \\\\[1.1ex] 0 &amp; -2\\end{vmatrix} = 1 \\cdot (-8) = \\bm{-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"385\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88120e3a6fa0e6ba43c654ce7884eb41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 3} = \\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix}  2 &amp; 0 \\\\[1.1ex] 5 &amp; -2\\end{vmatrix} = -1 \\cdot (-4) = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"385\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49c170f202956d9571fcce88cd389889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -1} = \\displaystyle (-1)^{1+3} \\bm{\\cdot} \\begin{vmatrix} 2 &amp; 4 \\\\[1.1ex] 5 &amp; 0\\end{vmatrix} = 1 \\cdot (-20) = \\bm{-20}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"395\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9dd9f81ddb6bd58f2a4e1241c3fbfdb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} = \\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} 3 &amp; -1 \\\\[1.1ex] 0 &amp; -2\\end{vmatrix} = -1 \\cdot (-6) = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"385\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee11d10a5ef1719e3eee0d1de8e2fd1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 4} = \\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; -1 \\\\[1.1ex] 5 &amp; -2\\end{vmatrix} = 1 \\cdot 3 = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"343\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-327cba2dd78055703b66b887083d3a50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 0} = \\displaystyle (-1)^{2+3} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 3  \\\\[1.1ex] 5 &amp; 0 \\end{vmatrix} = -1 \\cdot (-15) = \\bm{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"388\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5df97c790e24f1257c7d1073c4e2af8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 5} = \\displaystyle (-1)^{3+1} \\bm{\\cdot} \\begin{vmatrix} 3 &amp; -1 \\\\[1.1ex] 4 &amp; 0 \\end{vmatrix} = 1 \\cdot 4 = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"343\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d0cd9b3ea07312942362d52f07c04bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 0} = \\displaystyle (-1)^{3+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; -1 \\\\[1.1ex] 2 &amp; 0\\end{vmatrix} = -1 \\cdot 2 = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"370\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00f3983f64257be282584209b8f2d842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -2} = \\displaystyle (-1)^{3+3} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 3 \\\\[1.1ex] 2 &amp; 4 \\end{vmatrix} = 1 \\cdot (-2) = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"376\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita hanya perlu mengganti setiap elemen dalam array<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> oleh wakilnya untuk mencari matriks wakilnya <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed7f99fecb7719c7108eaecc0a21dad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A :\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01e49ffda72034d74b18ecdd37d1e3b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{-8} &amp; \\bm{4} &amp; \\bm{-20} \\\\[1.1ex] \\bm{6} &amp; \\bm{3} &amp; \\bm{15} \\\\[1.1ex] \\bm{4} &amp; \\bm{-2} &amp; \\bm{-2}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"223\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Pada bagian ini kita akan melihat apa itu dan bagaimana cara menghitung minor komplementer, adjoint, dan matriks adjoint . Selain itu, Anda akan menemukan contoh agar Anda memahaminya dengan sempurna, dan latihan diselesaikan langkah demi langkah, sehingga Anda dapat berlatih. Apa yang dimaksud dengan minor komplementer? Ini disebut komplemen minor suatu elemen. ke determinan yang &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\"> <span class=\"screen-reader-text\">Minor, asisten dan matriks pelengkap asisten<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[63],"tags":[],"class_list":["post-289","post","type-post","status-publish","format-standard","hentry","category-matriks-terbalik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Minor, asisten dan asisten matriks pelengkap - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Minor, asisten dan asisten matriks pelengkap - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada bagian ini kita akan melihat apa itu dan bagaimana cara menghitung minor komplementer, adjoint, dan matriks adjoint . Selain itu, Anda akan menemukan contoh agar Anda memahaminya dengan sempurna, dan latihan diselesaikan langkah demi langkah, sehingga Anda dapat berlatih. Apa yang dimaksud dengan minor komplementer? Ini disebut komplemen minor suatu elemen. ke determinan yang &hellip; Minor, asisten dan matriks pelengkap asisten Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T19:13:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41d4a89db3722950dc94351832a1bcd9_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Minor, asisten dan matriks pelengkap asisten\",\"datePublished\":\"2023-07-06T19:13:46+00:00\",\"dateModified\":\"2023-07-06T19:13:46+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\"},\"wordCount\":747,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Matriks terbalik\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\",\"url\":\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\",\"name\":\"Minor, asisten dan asisten matriks pelengkap - 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