{"id":298,"date":"2023-07-06T16:17:35","date_gmt":"2023-07-06T16:17:35","guid":{"rendered":"https:\/\/mathority.org\/id\/metode-jordan-gauss-dengan-contoh-dan-latihan-yang-diselesaikan\/"},"modified":"2023-07-06T16:17:35","modified_gmt":"2023-07-06T16:17:35","slug":"metode-jordan-gauss-dengan-contoh-dan-latihan-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/metode-jordan-gauss-dengan-contoh-dan-latihan-yang-diselesaikan\/","title":{"rendered":"Metode gaussian \u2013 yordania"},"content":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa itu metode Gauss-Jordan dan cara menyelesaikan sistem persamaan menggunakan metode Gauss. Selain itu, Anda juga akan menemukan contoh dan penyelesaian latihan sistem dengan metode Gauss sehingga Anda dapat mempraktikkan dan memahaminya dengan sempurna.<\/p>\n<h2 class=\"wp-block-heading\"> Apa metode Gauss?<\/h2>\n<p> <strong>Metode Gauss-Jordan<\/strong> adalah prosedur yang digunakan untuk menyelesaikan sistem persamaan dengan 3 hal yang tidak diketahui, yaitu seperti 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-088146ef83bbd007e82aca8189434c25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 3x-4y+5z=10 \\\\[2ex] x+5y-2z=4 \\\\[2ex] -x+4y+2z=-1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"170\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Tujuan dari metode Gauss adalah untuk mengubah sistem persamaan awal menjadi <strong>sistem bertahap<\/strong> , yaitu sistem yang setiap persamaannya memiliki satu persamaan yang kurang diketahui dibandingkan persamaan 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-10926b0856ae512c737ae924bd9413a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} a_1x+b_1y+c_1z=d_1 \\\\[2ex] a_2x+b_2y+c_2z=d_2 \\\\[2ex] a_3x+b_3y+c_3z=d_3 \\end{array} \\right\\} \\ \\bm{\\longrightarrow}   \\left. \\begin{array}{r} A_1x+B_1y+C_1z=D_1 \\\\[2ex] B_2y+C_2z=D_2 \\\\[2ex] C_3z=D_3 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"436\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Namun, untuk melakukannya, Anda harus terlebih dahulu mengetahui cara <strong>menyatakan sistem persamaan dalam bentuk matriks<\/strong> dan <strong>transformasi yang diperbolehkan<\/strong> pada matriks tersebut. Jadi kita akan menjelaskan kedua hal ini sebelumnya, dan kemudian kita akan melihat bagaimana <strong>prosedur menggunakan metode Gauss<\/strong> .<\/p>\n<h2 class=\"wp-block-heading\"> Matriks yang diperluas sistem<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Sebelum melihat bagaimana sistem diselesaikan, Anda harus mengetahui bahwa <strong>sistem persamaan dapat dinyatakan dalam bentuk matriks:<\/strong> koefisien 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-891f4f92ba63784e78eefc68d49377b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> dimasukkan ke dalam kolom pertama, koefisien dari<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f731d739f7ff6bfef57b5a830dbe13aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> di kolom kedua, koefisien dari<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4586e340cb83d5b642972e97a288fec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> di kolom ketiga dan angka tanpa diketahui di kolom keempat.<\/p>\n<p> Misalnya: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/resoudre-un-systeme-d-equations-par-la-methode-de-gauss.webp\" alt=\"metode Gaussian\" class=\"wp-image-4379\" width=\"422\" height=\"415\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Transformasi baris diperbolehkan<\/h2>\n<p> Untuk mengubah sistem persamaan menjadi sistem berskala, salah satu operasi berikut dapat dilakukan pada matriks yang terkait dengan sistem:<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2\">Mengubah urutan<\/span><\/strong> baris dalam matriks.<\/li>\n<\/ul>\n<p> Misalnya, kita dapat mengubah urutan baris 2 dan 3 suatu matriks:<\/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-ee0e251559ef9dfd02c9b0105f934af8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 3 &amp; 5 &amp; -2 &amp; 1 \\\\[2ex] -2 &amp; 4 &amp; -1 &amp; 2 \\\\[2ex] 6 &amp; 1 &amp; -3 &amp; 10 \\end{array} \\right)  \\begin{array}{c} \\\\[2ex] \\xrightarrow{ f_2 \\rightarrow f_3}} \\\\[2ex] \\xrightarrow{ f_3 \\rightarrow f_2}} \\end{array} \\left( \\begin{array}{ccc|c} 3 &amp; 5 &amp; -2 &amp; 1 \\\\[2ex] 6 &amp; 1 &amp; -3 &amp; 10 \\\\[2ex] -2 &amp; 4 &amp; -1 &amp; 2 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2\">Kalikan atau bagi<\/span><\/strong> semua suku dalam satu baris dengan angka selain 0.<\/li>\n<\/ul>\n<p> Misalnya, kita mengalikan baris 1 dengan 4 dan membagi baris 3 dengan 2:<\/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-0e1f081c9056075ede064b2e5c9e4193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; 3 &amp; 1 \\\\[2ex] 3 &amp; -1 &amp; 5 &amp; -3 \\\\[2ex] 2 &amp; -4 &amp; -2 &amp; 6 \\end{array} \\right) \\begin{array}{c}  \\xrightarrow{4  f_1} \\\\[2ex]  \\\\[2ex] \\xrightarrow{ f_3 \/ 2} \\end{array} \\left( \\begin{array}{ccc|c} 4 &amp; -8 &amp; 12 &amp; 4 \\\\[2ex] 3 &amp; -1 &amp; 5 &amp; -3 \\\\[2ex] 1 &amp; -2 &amp; -1 &amp; 3 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2\">Ganti sebuah baris<\/span><\/strong> dengan jumlah baris yang sama ditambah baris lainnya dikalikan dengan sebuah angka.<\/li>\n<\/ul>\n<p> Misalnya, pada matriks berikut, kita menambahkan baris 2 ke baris 3 dikalikan 1:<\/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-04417e2094ac05c7a374334c55197f36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} -1 &amp; -3 &amp; 4 &amp; 1 \\\\[2ex] 2 &amp; 4 &amp; 1 &amp; -5 \\\\[2ex] 1 &amp; -2 &amp; 3 &amp; -1 \\end{array} \\right) \\begin{array}{c}   \\\\[2ex]  \\xrightarrow{f_2 + 1 \\cdot f_3}  \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c} -1 &amp; -3 &amp; 4 &amp; 1 \\\\[2ex] 3 &amp; 2 &amp; 4 &amp; -6 \\\\[2ex] 1 &amp; -2 &amp; 3 &amp; -1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"417\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Bagaimana cara menyelesaikan sistem persamaan menggunakan metode Gauss?<\/h2>\n<p> Sekarang kita akan melihat melalui contoh prosedur <strong>penyelesaian sistem persamaan dengan metode Gauss:<\/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-61e6e829301e6730c9e27f9c0a30de2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} -x+2y+2z=-24 \\\\[2ex] x+y+z=48 \\\\[2ex] 2x-6y+4z=12 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"179\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Hal pertama yang harus dilakukan adalah <strong>matriks yang diperluas dari sistem<\/strong> : <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-de-systeme-dequations-par-la-methode-de-gauss.webp\" alt=\"Contoh sistem persamaan yang diselesaikan dengan metode Gauss\" class=\"wp-image-913\" width=\"541\" height=\"175\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Seperti yang akan kita lihat nanti, <strong>sebaiknya digit pertama pada baris pertama adalah 1.<\/strong> Oleh karena itu, kita akan mengubah urutan baris 1 dan 2:<\/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-b45e0f757ca2880442314f6a4800697b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} -1 &amp; 2 &amp; 2 &amp;-24 \\\\[2ex] 1 &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\end{array} \\right)  \\begin{array}{c} \\xrightarrow{ f_1 \\rightarrow f_2} \\\\[2ex] \\xrightarrow{ f_2 \\rightarrow f_1} \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c}   \\color{blue}\\boxed{\\color{black}1} &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] -1 &amp; 2 &amp; 2 &amp;-24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12  \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"496\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Tujuan metode Gauss adalah membuat <strong>bilangan di bawah diagonal utama menjadi 0<\/strong> . Artinya, kita perlu mengubah angka merah menjadi 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-28164ac6b48d32c09b4725548c0633f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] \\color{red}\\bm{-1} &amp; 2 &amp; 2 &amp;-24 \\\\[2ex] \\color{red}\\bm{2} &amp; \\color{red}\\bm{-6} &amp; 4 &amp; 12  \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"224\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Untuk menghilangkan angka-angka ini, kita perlu melakukan transformasi baris yang sesuai.<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p> Misalnya, -1 yang merupakan elemen pertama baris kedua adalah negatif dari 1, elemen pertama baris pertama. Oleh karena itu, jika <strong>kita menambahkan baris pertama ke baris kedua,<\/strong> -1 akan 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-8b22cdc60e02d30a4ed31073c9ad47c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lccc|c}  &amp; -1  &amp; 2 &amp; 2 &amp; -24  \\\\ + &amp; \\phantom{-}1  &amp; 1 &amp; 1 &amp; \\phantom{-}48   \\\\ \\hline &amp; \\phantom{-}0 &amp; 3 &amp; 3 &amp; \\phantom{-}24  \\end{array} \\begin{array}{l} \\color{blue}\\bm{\\leftarrow f_2} \\\\ \\color{blue}\\bm{\\leftarrow f_1} \\\\ \\phantom{hline} \\\\ \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"245\" style=\"vertical-align: -29px;\"><\/p>\n<\/p>\n<p> Jadi jika kita melakukan penjumlahan ini, kita akan mendapatkan matriks 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-1b106306b92bfc3e99d602c22d5198bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] -1 &amp; 2 &amp; 2 &amp; -24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\end{array} \\right) \\begin{array}{c}   \\\\[2ex]  \\xrightarrow{f_2 + f_1}  \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  \\color{blue}\\boxed{\\color{black}0} &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"479\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dengan cara ini kami berhasil mengubah -1 menjadi 0.<\/p>\n<p> Sekarang kita akan mentransformasikan 2. Jika Anda perhatikan, 2, yang merupakan elemen pertama pada baris ketiga, adalah dua kali lipat dari 1, elemen pertama pada baris pertama. Oleh karena itu, jika <strong>kita menambahkan baris pertama dikalikan -2 ke baris ketiga, maka<\/strong> angka 2 akan 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-50716b37fe5c1ff45dc2e4b05300e3da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lccc|c}    &amp;  \\phantom{-}2 &amp; -6 &amp; \\phantom{-}4 &amp; \\phantom{-}12  \\\\ + &amp; -2  &amp; -2 &amp; -2 &amp; -96 \\\\ \\hline &amp;  \\phantom{-}0 &amp; -8 &amp; \\phantom{-}2 &amp; -84  \\end{array} \\begin{array}{l} \\color{blue} \\bm{\\leftarrow f_3} \\\\ \\color{blue} \\bm{\\leftarrow -2 f_1} \\\\ \\phantom{hline} \\\\ \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"295\" style=\"vertical-align: -29px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, kami mendapatkan matriks 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-36b2fdf8de855cf35049ecefcf7c1da5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\end{array} \\right) \\begin{array}{c}   \\\\[2ex]    \\\\[2ex] \\xrightarrow{f_3-2f_1} \\end{array} \\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] \\color{blue}\\boxed{\\color{black}0} &amp; -8 &amp; 2 &amp; -84 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"472\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dengan cara ini kami berhasil mengubah angka 2 menjadi 0.<\/p>\n<p> Yang harus kita lakukan sekarang adalah mengubah -8 menjadi 0. Caranya, <strong>kita kalikan baris ketiga dengan 3 dan tambahkan baris kedua dikalikan 8:<\/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-156b06e383e387edd24cf4be09d98fe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lccc|r} &amp; 0  &amp; -24 &amp; \\phantom{2}6 &amp; -252  \\\\ + &amp; 0  &amp; \\phantom{-}24 &amp; 24 &amp; \\phantom{-}192  \\\\ \\hline  &amp; 0 &amp; \\phantom{-2}0 &amp; 30 &amp; -60  \\end{array} \\begin{array}{l}\\color{blue}\\bm{ \\leftarrow 3f_3} \\\\\\color{blue}\\bm{ \\leftarrow 8f_2} \\\\ \\phantom{hline} \\\\ \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"281\" style=\"vertical-align: -29px;\"><\/p>\n<\/p>\n<p> Oleh karena itu kami memperoleh matriks 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-6e2324629222c746a9021ce05ba7d54d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 0 &amp; -8 &amp; 2 &amp; -84 \\end{array} \\right) \\begin{array}{c}   \\\\[2ex]  \\\\[2ex] \\xrightarrow{3f_3 + 8f_2} \\end{array} \\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 0 &amp; \\color{blue}\\boxed{\\color{black}0} &amp; 30 &amp; -60 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"488\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan dengan transformasi ini, kita mendapatkan <strong>semua bilangan di bawah diagonal utama menjadi 0.<\/strong> Jadi sekarang kita bisa menyelesaikan sistem persamaannya.<\/p>\n<p> Sekarang kita harus <strong>mengubah matriks tersebut menjadi sistem persamaan yang tidak diketahui<\/strong> . Untuk melakukan ini, ingatlah bahwa kolom pertama berhubungan dengan<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> , kolom kedua dari<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> , kolom ketiga dari<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4586e340cb83d5b642972e97a288fec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan kolom terakhir adalah angka-angka yang tidak diketahui:<\/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-6f90de9d9f5a06959a2d4aebf05f4758_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 0 &amp; 0 &amp; 30 &amp; -60 \\end{array} \\right) \\  \\longrightarrow \\ \\left. \\begin{array}{r} 1x+1y+1z=48 \\\\[2ex] 3y+3z=24 \\\\[2ex] 30z=-60 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"379\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan terakhir, untuk menyelesaikan sistem ini, kita perlu <strong>menyelesaikan persamaan yang tidak diketahui dari bawah ke atas.<\/strong> Karena persamaan terakhir hanya mempunyai satu hal yang tidak diketahui, kita dapat menyelesaikannya dan mencari nilainya: <\/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-f609bf44e2a363aca5008fec95c678dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"30z=-60\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" 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-18c467d7caa0bb171c5b1590f9caa694_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z = \\cfrac{-60}{30}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"75\" style=\"vertical-align: -12px;\"><\/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-9881bf11e418247b881ffbb7de1f0565_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{z=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sekarang kita sudah mengetahui apa itu z, jika kita substitusikan nilainya ke dalam persamaan kedua, kita dapat mencari nilai 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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> : <\/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-47af5f5709e3e010efe9fb6f9ab0e8c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y+3z=24 \\ \\xrightarrow{z \\ = \\ -2} \\ 3y+3(-2)=24\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"305\" 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-da13228341b35d3040ae42078cabd99a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y-6=24\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" 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-8587739ff9abd17db5f6c4c51f4201dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y=24+6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" 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-8e6cb4d9575b53c3eafb342482f0dd28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y=30\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" 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-d5e353e1b4b02441dfcb4258ee4b5480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{30}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"53\" style=\"vertical-align: -12px;\"><\/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-819c20ffb8ea217c6f5fe196d891beec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=10}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Dan kita melakukan hal yang sama dengan persamaan pertama: kita mengganti nilai-nilai yang tidak diketahui lainnya dan menghapusnya<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> : <\/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-16197bd2e6cc012ef57ffb9e5dc77e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1x+1y+1z=48 \\ \\xrightarrow{y \\ = \\ 10 \\ ; \\ z \\ = \\ -2} \\ 1x+1(10)+1(-2)=48\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"467\" 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-a333e16025e12b5a3220e3673b32cfbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+10-2=48\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"122\" style=\"vertical-align: -2px;\"><\/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-11b343d96345b46d6686d9531c5ed39a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=48-10+2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"121\" style=\"vertical-align: -2px;\"><\/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-5c64ae2e78dc27d215fff9629c45a07d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=40}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, penyelesaian sistem persamaan tersebut adalah: <\/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-edf75d5dd0f035a459aaa69d22286a89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=40} \\quad \\bm{y=10} \\quad \\bm{z=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> Menyelesaikan masalah sistem persamaan dengan metode Gauss-Jordan<\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Selesaikan sistem persamaan berikut dengan menggunakan metode Gauss: <\/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-854043b0e7e3e2166593dcf5c645bfa0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} x+y-z=2 \\\\[2ex] x-2y+3z=0 \\\\[2ex] 2x-y+3z=3 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"143\" 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\"> Hal pertama yang perlu kita lakukan adalah matriks yang diperluas dari sistem:<\/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-1b6369a58b91f31bf4c8bc212ccf68c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} x+y-z=2 \\\\[2ex] x-2y+3z=0 \\\\[2ex] 2x-y+3z=3 \\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  1 &amp; -2 &amp; 3 &amp; 0 \\\\[2ex] 2 &amp; -1 &amp; 3 &amp; 3 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"339\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita perlu membuat semua angka di bawah array utama menjadi 0.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami melakukan operasi baris untuk membatalkan dua suku terakhir dari kolom pertama:<\/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-cd42dcf61aebc4c67de13e09dff72f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  1 &amp; -2 &amp; 3 &amp; 0 \\\\[2ex] 2 &amp; -1 &amp; 3 &amp; 3 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -f_1} \\\\[2ex] \\xrightarrow{f_3-2f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  0 &amp; -3 &amp; 4 &amp; -2  \\\\[2ex] 0 &amp; -3 &amp; 5 &amp; -1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita menghapus elemen terakhir dari 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-13945337848a6f1badf6efe249951124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  0 &amp; -3 &amp; 4 &amp; -2 \\\\[2ex] 0 &amp; -3 &amp; 5 &amp; -1 \\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{f_3-f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex] 0 &amp; -3 &amp; 4 &amp; -2 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"406\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah semua bilangan di bawah diagonal utama adalah 0, sekarang kita dapat menyelesaikan sistem persamaannya. Untuk melakukan ini, kita nyatakan kembali matriks tersebut dalam bentuk sistem persamaan dengan yang tidak diketahui:<\/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-f068c276aae018a668cc005bcad3e641_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex] 0 &amp; -3 &amp; 4 &amp; -2 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 1 \\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} x+y-z=2 \\\\[2ex] -3y+4z=-2 \\\\[2ex] 1z=1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"367\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami memecahkan persamaan yang tidak diketahui dari bawah ke atas. Pertama-tama kita selesaikan persamaan terakhir: <\/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-96b4633173cfb05c06e2c5bdc995d68c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1z= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" 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-be8e058ccee5d0aa33ffcce09cd28f98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita substitusikan nilai z ke dalam persamaan kedua untuk mencari nilai y: <\/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-be96e507b80d44350c96abb013cdcaf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y+4z=-2 \\ \\xrightarrow{z \\ = \\ 1} \\ -3y+4(1)=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"316\" 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-8e9d92c48f937b8bffa678a761acee72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y+4=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"107\" 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-23ff1832dcecc68a83d1e6afdf07a08a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y=-2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"108\" 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-27cf5638a108b52a34c74053b099361e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y=-6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" 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-1c9efb6ee00d7b62fd3f436c1037feb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-6}{-3} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"97\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita melakukan hal yang sama dengan persamaan pertama: kita mengganti nilai-nilai yang tidak diketahui lainnya dan menyelesaikan x: <\/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-63f719497b296c95e6e9cf43651598c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+y-z=2 \\ \\xrightarrow{y \\ = \\ 2 \\ ; \\ z \\ = \\ 1} \\  x+(2)-(1)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"356\" 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-56845b4eb32748e1842b62d558249eb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"72\" style=\"vertical-align: -2px;\"><\/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-02e03b55e65a6262280f3d3e592443ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"72\" 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-df0486e1bf5773e392faebda4843f515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, penyelesaian sistem persamaan tersebut adalah: <\/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-3acc67c77d6f5f92d9a684f87a5def90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=1} \\qquad \\bm{y=2} \\qquad \\bm{z=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"196\" style=\"vertical-align: -4px;\"><\/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> Temukan solusi sistem persamaan berikut dengan menggunakan metode Gauss: <\/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-7d0595899b8137f769c74fce1b21286b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+y+2z=-3 \\\\[2ex] x+3y+2z=5 \\\\[2ex] 4x+2y-z=-1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"157\" 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\"> Hal pertama yang perlu kita lakukan adalah matriks yang diperluas dari sistem:<\/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-5e2a16b6d1451520bd8898675c022dc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+y+2z=-3 \\\\[2ex] x+3y+2z=5 \\\\[2ex] 4x+2y-z=-1 \\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex] 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 4 &amp; 2 &amp; -1 &amp; -1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"352\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Untuk menerapkan metode Gauss, akan lebih mudah jika bilangan pertama pada baris pertama adalah 1. Oleh karena itu, kita akan mengubah urutan baris 1 dan 2:<\/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-ef7e2e42d0eecb0395afb7c8311b2ade_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex] 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 4 &amp; 2 &amp; -1 &amp; -1 \\end{array} \\right) \\begin{array}{c} \\xrightarrow{f_1\\rightarrow f_2} \\\\[2ex] \\xrightarrow{f_2\\rightarrow f_1} \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c}1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex]  4 &amp; 2 &amp; -1 &amp; -1\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"101\" width=\"381\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita perlu membuat semua angka di bawah array utama menjadi 0.<\/p>\n<p class=\"has-text-align-left\"> Jadi kita melakukan operasi baris untuk mengganti dua elemen terakhir dari kolom pertama:<\/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-40baaee3bbde9ed1577e00bc1c3b338f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex] 4 &amp; 2 &amp; -1 &amp; -1 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -2f_1} \\\\[2ex] \\xrightarrow{f_3-4f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex] 0 &amp; -10 &amp; -9 &amp; -21 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"417\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita mengubah elemen terakhir kolom kedua menjadi nol:<\/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-f328906485bfe6ee77833c04869e1240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex] 0 &amp; -10 &amp; -9 &amp; -21\\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{f_3-2f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex]  0 &amp; 0 &amp; -5 &amp; 5 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"439\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah semua bilangan di bawah diagonal utama adalah 0, kita dapat menyelesaikan sistem persamaannya. Untuk melakukan ini, kita nyatakan kembali matriks tersebut dalam bentuk sistem persamaan dengan yang tidak diketahui:<\/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-a7e129715c720218a5cb25ef07442442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex]  0 &amp; 0 &amp; -5 &amp; 5 \\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} x+3y+2z=5 \\\\[2ex] -5y-2z=-13 \\\\[2ex] -5z=5 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"384\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami memecahkan persamaan yang tidak diketahui dari bawah ke atas. Pertama-tama kita selesaikan persamaan terakhir: <\/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-a52023bf513299dc6e11f3f0b83478cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5z= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" 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-8c401bac44e84469a254eca182dbaaf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\cfrac{5}{-5}=\\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"103\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita substitusikan nilai z ke dalam persamaan kedua untuk mencari nilai y: <\/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-802f76b9a10de545be30d16421b0a476_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y-2z=-13 \\ \\xrightarrow{z \\ = \\ -1} \\ -5y-2(-1)=-13\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"360\" 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-dba702d28248bdc1928df387178232a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y+2=-13\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"117\" 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-00b2616ea47a24b0c533514cbad0074b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=-13-2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"116\" 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-7f23dbeb21681cd1e0a85a6e980d578d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=-15\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" 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-aa2c8d4e1526976ef2450ec835412a4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-15}{-5} = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita melakukan hal yang sama dengan persamaan pertama: kita mengganti nilai-nilai yang tidak diketahui lainnya dan menyelesaikan x: <\/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-664205a7f0b30720a191edc7ac6b5d4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+3y+2z=5 \\ \\xrightarrow{y \\ = \\ 3 \\ ; \\ z \\ = \\ -1} \\  x+3(3)+2(-1)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"416\" 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-e08c94f818594a2e81185baa1b81c59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+9-2=5\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" style=\"vertical-align: -2px;\"><\/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-9e21aa5a70c92b8a72ef4c9a374d5acf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5-9+2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" style=\"vertical-align: -2px;\"><\/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-6505a1b32f86c9deb3ab0716f13c3949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, penyelesaian sistem persamaan tersebut adalah: <\/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-1be1c5f4156b37412c9e19a63190d45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-2} \\qquad \\bm{y=3} \\qquad \\bm{z=-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"224\" style=\"vertical-align: -4px;\"><\/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-119\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\"> Latihan 3<\/h3>\n<p> Hitung penyelesaian sistem persamaan berikut dengan metode Gauss: <\/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-4301eae3179543fbdee7568e8f88aa4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+3y+z=-1 \\\\[2ex] 6x+4y+4z=0 \\\\[2ex] -4x+2y-z=5 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"157\" 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\"> Hal pertama yang perlu kita lakukan adalah matriks yang diperluas dari sistem:<\/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-c0d96160d6670e817dd39f61816e1e6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+3y+z=-1 \\\\[2ex] 6x+4y+4z=0 \\\\[2ex] -4x+2y-z=5\\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 6 &amp; 4 &amp; 4 &amp; 0 \\\\[2ex] -4 &amp; 2 &amp; -1 &amp; 5 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"366\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita perlu membuat semua angka di bawah array induk menjadi 0.<\/p>\n<p class=\"has-text-align-left\"> Jadi kita melakukan operasi baris untuk mengganti dua elemen terakhir dari kolom pertama:<\/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-87853177b6be449178c24e414dc0865a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 6 &amp; 4 &amp; 4 &amp; 0 \\\\[2ex] -4 &amp; 2 &amp; -1 &amp; 5\\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -3f_1} \\\\[2ex] \\xrightarrow{f_3+2f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 8 &amp; 1 &amp; 3\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita mengubah elemen terakhir kolom kedua menjadi nol:<\/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-c4105ceb64b201c532109f8639bdefde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 8 &amp; 1 &amp; 3\\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{5f_3+8f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 0 &amp; 13 &amp; 39 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"401\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah semua bilangan di bawah diagonal utama adalah 0, kita dapat menyelesaikan sistem persamaannya. Untuk melakukan ini, kita nyatakan kembali matriks tersebut dalam bentuk sistem persamaan dengan yang tidak diketahui:<\/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-faae83295a3f7b3d8b6d76f78d56fac6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 0 &amp; 13 &amp; 39\\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} 2x+3y+1z=-1 \\\\[2ex] -5y+z=3 \\\\[2ex] 13z=39 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami memecahkan persamaan yang tidak diketahui dari bawah ke atas. Pertama-tama kita selesaikan persamaan terakhir: <\/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-4ce4c9f218fa1bd1448e77039773f7d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"13z= 39\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" 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-2b17181241c9203cad7e9e776a3e4fbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\cfrac{39}{13}=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"85\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita substitusikan nilai z ke dalam persamaan kedua untuk mencari nilai y: <\/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-60d5784aa102e6db8696ba9bf79e1da5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y+z=3 \\ \\xrightarrow{z \\ = \\ 3} \\ -5y+(3)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"272\" 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-48fbd56cf56ffcfb7d9c676eecf02550_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=3-3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"94\" 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-8ee955981979845afcdca2dfbefe7fca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"64\" 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-720b6716d584d822d06446bcc18382e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{0}{-5} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"90\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita melakukan hal yang sama dengan persamaan pertama: kita mengganti nilai-nilai yang tidak diketahui lainnya dan menyelesaikan x: <\/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-ed92c6b5eec53094b5ff47ff6274f113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+3y+1z=-1 \\ \\xrightarrow{y \\ = \\ 0 \\ ; \\ z \\ = \\ 3} \\  2x+3(0)+1(3)=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"437\" 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-d7df18713df47399b523eb5025194be6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+0+3=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"126\" style=\"vertical-align: -2px;\"><\/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-994c82dc1b5d22d408db4477e0964fec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=-1-3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"96\" 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-8bb8c1283df065c83c44b7fe484324a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"66\" 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-d9dd0f99977b1208f94006aaa348d060_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-4}{2}=\\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, penyelesaian sistem persamaan tersebut adalah: <\/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-93fd2b17430c25b9d44e5afc2e099e0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-2} \\qquad \\bm{y=0} \\qquad \\bm{z=3}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"211\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Selesaikan sistem persamaan berikut dengan 3 yang tidak diketahui menggunakan metode Gauss: <\/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-b005b2eda0d63c7130f2f5531c2ae4a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r}  2x-6=4y+6z \\\\[2ex] -y-3z=1-3x \\\\[2ex] -4x-y=6-3z \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"156\" 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\"> Sebelum menerapkan metode Gauss, kita perlu menyusun sistem persamaannya sehingga semua yang tidak diketahui berada di sebelah kiri persamaan dan angka-angkanya berada di sebelah kanan:<\/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-1e0ca77b625e8f9e235ce8da4e4008df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r}2x-6=4y+6z \\\\[2ex] -y-3z=1-3x \\\\[2ex] -4x-y=6-3z \\end{array} \\right\\} \\longrightarrow \\left.  \\begin{array}{r} 2x-4y-6z=6 \\\\[2ex] 3x-y-3z=1 \\\\[2ex] -4x-y+3z=6\\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"364\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah sistem diurutkan, kami membangun matriks sistem yang dikembangkan:<\/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-b88e3ff141b847028a55ba4b46b8e870_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x-4y-6z=6 \\\\[2ex] 3x-y-3z=1 \\\\[2ex] -4x-y+3z=6 \\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 2 &amp; -4 &amp; -6 &amp; 6 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"365\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Karena semua bilangan pada baris pertama adalah bilangan genap, sebelum mengerjakan baris-baris tersebut kita akan membagi baris pertama dengan 2. Karena ini akan mempermudah penghitungan:<\/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-b05235526cd8e44c16749606bfe8976c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}2 &amp; -4 &amp; -6 &amp; 6 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6 \\end{array} \\right) \\begin{array}{c} \\xrightarrow{f_1\/2} \\\\[2ex] \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"99\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita perlu membuat semua angka di bawah array utama menjadi 0.<\/p>\n<p class=\"has-text-align-left\"> Jadi kita melakukan operasi baris untuk mengganti dua elemen terakhir dari kolom pertama:<\/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-3da82815d14fdfae0f61a8e1747fb9fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -3f_1} \\\\[2ex] \\xrightarrow{f_3+4f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -9 &amp; -9 &amp; 18\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Seperti sebelumnya, karena semua angka pada baris terakhir adalah kelipatan 9, maka kita akan membaginya dengan 9 agar perhitungannya lebih mudah:<\/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-342000d19a7bd19e055a39695c79cb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -9 &amp; -9 &amp; 18 \\end{array} \\right) \\begin{array}{c}  \\\\[2ex] \\\\[2ex]\\xrightarrow{f_3\/9} &amp; \\end{array} \\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -1 &amp; -1 &amp; 2\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita mengubah elemen terakhir kolom kedua menjadi nol:<\/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-2158e7f439f677617bb8a40695fb5711_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -1 &amp; -1 &amp; 2\\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{5f_3+f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 2 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah semua bilangan di bawah diagonal utama adalah 0, kita dapat menyelesaikan sistem persamaannya. Untuk melakukan ini, kita nyatakan kembali matriks tersebut dalam bentuk sistem persamaan dengan yang tidak diketahui:<\/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-ea162e98aa70f8d56ffba28438a9de2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 2 \\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} x-2y-3z=3 \\\\[2ex] 5y+6z=-8 \\\\[2ex] 1z=2 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"371\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami memecahkan persamaan yang tidak diketahui dari bawah ke atas. Pertama-tama kita selesaikan persamaan terakhir: <\/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-28e1aa243598bedb00978eb5e0c1dcd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1z= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" 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-4307991ada04e86ea4085fe426ea9f08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita substitusikan nilai z ke dalam persamaan kedua untuk mencari nilai y: <\/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-b5eb143e26fb1f1535d4c2596c889007_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y+6z=-8 \\ \\xrightarrow{z \\ = \\ 2} \\ 5y+6(2)=-8\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"291\" 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-48b6461c0e3832049edb903a568752df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y+12=-8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" 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-4c9094946053033193fa68d290041f3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y=-8-12\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"103\" 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-8492d7042878af6f3863f5e83213a2ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y=-20\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" 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-fe3119924b2e0ee7a98cc5489223e689_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-20}{5} = \\bm{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"121\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita melakukan hal yang sama dengan persamaan pertama: kita mengganti nilai-nilai yang tidak diketahui lainnya dan menyelesaikan x: <\/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-d3e3bbe943253ea68f811850c1b882bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2y-3z=3 \\ \\xrightarrow{y \\ = \\ -4 \\ ; \\ z \\ = \\ 2} \\  x-2(-4)-3(2)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"417\" 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-b5d555ad593794ad6d247dbbc2cd98eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+8-6=3\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" style=\"vertical-align: -2px;\"><\/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-af64e62e2b2b22939ce0f08900f91404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3-8+6\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" style=\"vertical-align: -2px;\"><\/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-df0486e1bf5773e392faebda4843f515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, penyelesaian sistem persamaan tersebut adalah:<\/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-586cec7145ab5b293cadaafd4f7bb738_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-1} \\qquad \\bm{y=-4} \\qquad \\bm{z=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"224\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa itu metode Gauss-Jordan dan cara menyelesaikan sistem persamaan menggunakan metode Gauss. Selain itu, Anda juga akan menemukan contoh dan penyelesaian latihan sistem dengan metode Gauss sehingga Anda dapat mempraktikkan dan memahaminya dengan sempurna. Apa metode Gauss? Metode Gauss-Jordan adalah prosedur yang digunakan untuk menyelesaikan sistem persamaan dengan 3 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/metode-jordan-gauss-dengan-contoh-dan-latihan-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Metode gaussian \u2013 yordania<\/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":[41],"tags":[],"class_list":["post-298","post","type-post","status-publish","format-standard","hentry","category-penjelasan-matematis"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Metode Gaussian \u2013 Yordania -<\/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\/metode-jordan-gauss-dengan-contoh-dan-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Metode Gaussian \u2013 Yordania -\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan mempelajari apa itu metode Gauss-Jordan dan cara menyelesaikan sistem persamaan menggunakan metode Gauss. 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Metode Gauss-Jordan adalah prosedur yang digunakan untuk menyelesaikan sistem persamaan dengan 3 &hellip; Metode gaussian \u2013 yordania Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/metode-jordan-gauss-dengan-contoh-dan-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T16:17:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-088146ef83bbd007e82aca8189434c25_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=\"6 menit\" \/>\n<script type=\"application\/ld+json\" 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