{"id":307,"date":"2023-07-06T13:14:29","date_gmt":"2023-07-06T13:14:29","guid":{"rendered":"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/"},"modified":"2023-07-06T13:14:29","modified_gmt":"2023-07-06T13:14:29","slug":"matriks-segitiga-atas-bawah","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/","title":{"rendered":"Matriks segitiga atas dan bawah"},"content":{"rendered":"<p>Pada halaman ini Anda akan melihat apa itu matriks segitiga dan macam-macam matriks segitiga beserta contohnya. Selain itu, Anda akan mengetahui cara menghitung determinan matriks segitiga dan apa saja sifat-sifat matriks yang sangat menarik ini. Terakhir, kami juga akan menjelaskan apa itu matriks Hessenberg, karena merupakan matriks yang berkaitan dengan matriks segitiga.<\/p>\n<h2 class=\"wp-block-heading\"> Apa itu matriks segitiga?<\/h2>\n<p> Definisi matriks segitiga:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>Matriks segitiga<\/strong> adalah matriks persegi yang semua elemen di atas atau di bawah diagonal utamanya bernilai nol (0).<\/p>\n<p> Matriks segitiga banyak digunakan dalam perhitungan aljabar linier, karena membalikkan matriks segitiga, menghitung determinannya, atau bahkan menyelesaikan sistem persamaan linier dengan matriks jenis ini jauh lebih mudah dibandingkan dengan matriks yang memiliki elemen selain 0 di semua posisi. .<\/p>\n<h2 class=\"wp-block-heading\"> matriks segitiga atas<\/h2>\n<p> <strong>Matriks segitiga atas<\/strong> adalah matriks persegi yang elemen-elemen di bawah diagonal utamanya bernilai nol (0).<\/p>\n<p> Contoh matriks segitiga atas: <\/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\/matrice-triangulaire-superieure.webp\" alt=\"contoh matriks segitiga atas\" class=\"wp-image-1648\" width=\"130\" height=\"114\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> matriks segitiga bawah<\/h2>\n<p> <strong>Matriks segitiga bawah<\/strong> adalah matriks persegi yang mempunyai angka nol (0) pada setiap elemennya yang berada di atas diagonal utama.<\/p>\n<p> Contoh matriks segitiga bawah: <\/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\/matrice-triangulaire-inferieure.webp\" alt=\"contoh matriks segitiga bawah\" class=\"wp-image-1649\" width=\"143\" height=\"113\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Kadang-kadang matriks ini disebut juga dengan huruf U, untuk matriks segitiga atas, dan dengan huruf L, untuk matriks segitiga bawah. Meskipun tata nama ini terutama digunakan dalam bahasa Inggris, sebenarnya U adalah singkatan dari <em>matriks segitiga atas<\/em> dan L adalah <em>matriks segitiga bawah<\/em> .<\/p>\n<h2 class=\"wp-block-heading\"> Contoh matriks segitiga<\/h2>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Matriks segitiga 2\u00d72 dimensi<\/span> <\/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\/matrice-triangulaire-superieure-22152-1.webp\" alt=\"Contoh matriks segitiga atas 2x2\" class=\"wp-image-1658\" width=\"75\" height=\"72\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Matriks segitiga berorde 3\u00d73<\/span> <\/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\/matrice-triangulaire-inferieur-32153-1.webp\" alt=\"Contoh matriks segitiga bawah 3x3\" class=\"wp-image-1659\" width=\"131\" height=\"117\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">matriks segitiga berukuran 4\u00d74<\/span> <\/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\/matrice-triangulaire-superieure-42154-1.webp\" alt=\"Contoh matriks segitiga atas 4x4\" class=\"wp-image-1660\" width=\"197\" height=\"144\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Penentu matriks segitiga<\/h2>\n<p> <strong>Penentu matriks segitiga<\/strong> , baik segitiga atas maupun bawah, adalah hasil kali elemen-elemen pada diagonal utama.<\/p>\n<p> Perhatikan latihan berikut untuk menyelesaikan cara menghitung perkalian elemen-elemen diagonal utama matriks segitiga dengan cukup untuk mencari determinannya:<\/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-7503e88c4eaabd74347a4f79461a3ebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2 &amp; 5 &amp; -6 \\\\[1.1ex] 0 &amp; 4 &amp; 9 \\\\[1.1ex] 0 &amp; 0 &amp; 3 \\end{vmatrix} = 2 \\cdot 4 \\cdot 3 = \\bm{24}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"200\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Teorema ini mudah ditunjukkan: cukup hitung determinan matriks segitiga dengan blok (atau kofaktor). <strong>Demonstrasi<\/strong> ini dirinci di bawah ini menggunakan matriks segitiga umum:<\/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-91281c322af35f07cfbfd6fe61fc3c58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\begin{vmatrix} a &amp; b &amp; c \\\\[1.1ex] 0 &amp; d &amp; e \\\\[1.1ex] 0 &amp; 0 &amp; f \\end{vmatrix}&amp;  = a \\cdot \\begin{vmatrix} d &amp; e \\\\[1.1ex] 0 &amp; f \\end{vmatrix} - b \\cdot \\begin{vmatrix} 0 &amp;  e \\\\[1.1ex] 0 &amp;  f \\end{vmatrix} + c \\cdot \\begin{vmatrix} 0 &amp; d \\\\[1.1ex] 0 &amp; 0 \\end{vmatrix} \\\\[2ex] &amp; =a \\cdot (d\\cdot f) - b \\cdot 0 + c \\cdot 0 \\\\[2ex] &amp; = a \\cdot d \\cdot f \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"170\" width=\"341\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sebaliknya, kita mengetahui bahwa suatu matriks dapat dibalik jika determinannya berbeda dengan 0. Jadi, jika tidak ada elemen pada diagonal utama yang bernilai 0, maka matriks segitiga tersebut juga dapat dibalik dan akibatnya menjadi matriks beraturan. matriks.<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h2 class=\"wp-block-heading\"> Sifat-sifat matriks segitiga<\/h2>\n<p> Sekarang mari kita lihat apa saja sifat-sifat matriks segitiga:<\/p>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Hasil kali dua matriks segitiga atas<\/strong><\/span> sama dengan satu matriks segitiga atas. Dan sebaliknya: mengalikan dua matriks segitiga bawah menghasilkan matriks segitiga bawah lainnya.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dfd46e0ab8070d1c4c544d384fcf0f84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 3 &amp; 1 &amp; 4 \\\\[1.1ex] 0 &amp; -1 &amp; 2 \\\\[1.1ex] 0 &amp; 0 &amp; 5 \\end{pmatrix} \\cdot \\begin{pmatrix} 6 &amp; 2 &amp; 1 \\\\[1.1ex] 0 &amp; 3 &amp; 5 \\\\[1.1ex] 0 &amp; 0 &amp; 9 \\end{pmatrix} = \\begin{pmatrix}18&amp;9&amp;44\\\\[1.1ex] 0&amp;-3&amp;13\\\\[1.1ex]0&amp;0&amp;45\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"343\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Transpos matriks segitiga atas<\/strong><\/span> adalah matriks segitiga bawah, dan sebaliknya: transpos matriks segitiga bawah adalah matriks segitiga atas.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca1b4a07e3136aa75d1a8026e5e7c1ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{pmatrix} 1 &amp; 2 &amp; 6 &amp; 3 \\\\[1.1ex] 0 &amp; 9 &amp; 4 &amp; 1  \\\\[1.1ex] 0 &amp; 0 &amp; -2 &amp; 8 \\\\[1.1ex] 0 &amp; 0 &amp; 0 &amp; 7 \\end{pmatrix}\\right.^{\\bm{t}} =  \\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex] 2 &amp; 9 &amp; 0 &amp; 0 \\\\[1.1ex] 6 &amp; 4 &amp; -2 &amp; 0 \\\\[1.1ex] 3 &amp; 1 &amp; 8 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"279\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Suatu <span style=\"color:#1976d2;\"><strong>matriks segitiga dapat dibalik<\/strong><\/span> jika semua elemennya pada diagonal utama bukan nol, yaitu jika berbeda dari nol. Dalam hal ini, invers matriks segitiga atas (bawah) juga merupakan matriks segitiga atas (bawah).<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-adafaa535a161d29c9bcb8a31a572dc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{pmatrix}1&amp;0&amp;0\\\\[1.1ex] -3&amp;2&amp;0\\\\[1.1ex] 2&amp;4&amp;3\\end{pmatrix} \\right.^{-1} =\\begin{pmatrix}1&amp;0&amp;0\\\\[1.1ex] \\frac{3}{2}&amp;\\frac{1}{2}&amp;0\\\\[1.1ex] -\\frac{8}{3}&amp;-\\frac{2}{3}&amp;\\frac{1}{3}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"89\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Selain itu, diagonal utama matriks terbalik akan selalu memuat invers elemen diagonal utama matriks segitiga asal.<\/p>\n<ul>\n<li> Setiap matriks diagonal merupakan matriks segitiga atas dan matriks segitiga bawah, misalnya:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-497726e030cc2af2c07b16fdf3544024_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 3 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 8 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; -2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Jadi <a href=\"https:\/\/mathority.org\/id\/matriks-skalar\/\">matriks skalar<\/a> juga merupakan matriks segitiga atas dan bawah. Misalnya matriks identitas:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4e4e9931fb7ae104414006cee93978a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"80\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Jelasnya <a href=\"https:\/\/mathority.org\/id\/matriks-nol-nol\/\">matriks nol<\/a> juga merupakan matriks segitiga atas dan bawah, karena elemen-elemen di atas dan di bawah diagonal utama adalah 0:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-edb061dcbc869eba51ece12af43f796f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 0 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"80\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Nilai eigen (atau nilai eigen) suatu matriks segitiga<\/strong><\/span> adalah elemen diagonal utama.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-272d0e156e1f27c20348b171c984e390_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 1 &amp; 3 &amp; 0 \\\\[1.1ex] 2 &amp; 6 &amp; -2 \\end{pmatrix} \\longrightarrow \\ \\lambda = -2 \\ ; \\ \\lambda = 3 \\ ; \\ \\lambda = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"325\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Matriks segitiga atas atau bawah selalu mampu melakukan diagonalisasi<\/strong><\/span> berdasarkan vektor eigen (atau vektor eigen).<\/li>\n<\/ul>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Matriks apa pun dapat difaktorkan menjadi hasil kali matriks segitiga bawah dan matriks segitiga atas<\/strong><\/span> . Artinya, matriks apa pun dapat diubah menjadi perkalian matriks segitiga. Selain itu, jika matriksnya dapat dibalik, transformasi ini bersifat unik. Untuk memfaktorkan suatu matriks, metode dekomposisi LU sering digunakan. <\/li>\n<\/ul>\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\"> Melakukan segitiga pada suatu matriks<\/h2>\n<p> Ada beberapa teorema tentang matriks yang dapat ditriangularkan dengan mengubah alasnya. Namun, di sini kita akan melihat cara melakukan triangulasi suatu matriks dengan menerapkan <strong>transformasi elementer pada garis<\/strong> , seperti pada metode Gauss.<\/p>\n<p> Misalnya:<\/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-f66a4f370b37168439de204c1b0b401c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 1 &amp; 2 &amp; 4 \\\\[1.1ex] 2 &amp; -3 &amp; 5 \\\\[1.1ex]1 &amp; -1 &amp; 6 \\end{pmatrix} \\begin{array}{c} \\\\[1.1ex] \\xrightarrow{f_2 -2f_1}\\\\[1.1ex] \\xrightarrow{f_3 -f_1} \\end{array}  \\begin{pmatrix} 1 &amp; 2 &amp; 4 \\\\[1.1ex] 0 &amp; -7 &amp; -3 \\\\[1.1ex] 0 &amp; -3 &amp; 2 \\end{pmatrix}\\begin{array}{c} \\\\[1.1ex]\\\\[1.1ex] \\xrightarrow{7f_3 -3f_2} \\end{array}  \\begin{pmatrix} 1 &amp; 2 &amp; 4 \\\\[1.1ex] 0 &amp; -7 &amp; -3 \\\\[1.1ex] 0 &amp; 0 &amp; 23 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"496\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan dengan cara ini, kita telah membuat segitiga matriks aslinya.<\/p>\n<p> Ingatlah bahwa transformasi dasar yang diotorisasi antar garis dalam metode Gaussian adalah:<\/p>\n<ul>\n<li> Gantikan sebuah garis dengan kombinasi linier dari garis-garis lainnya.<\/li>\n<li> Kalikan atau bagi semua suku dalam satu baris dengan angka selain 0.<\/li>\n<li> Edit baris pesanan.<\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"> Matriks Hessenberg<\/h2>\n<p> Pengertian matriks Hessenberg adalah sebagai berikut:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>Matriks Hessenberg<\/strong> merupakan matriks yang \u201champir\u201d berbentuk segitiga, artinya semua elemennya bernilai nol mulai dari subdiagonal pertama (matriks Hessenberg atas) atau superdiagonal pertama (matriks Hessenberg bawah).<\/p>\n<p> Saya yakin ini paling baik dipahami dengan contoh matriks Hessenberg atas dan contoh matriks Hessenberg bawah lainnya: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-28\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <strong>Matriks Hessenberg Atas<\/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-e76ad0fae8a28b5e5f31535683e63df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{pmatrix} 3 &amp; 5 &amp; 1 &amp; 4 \\\\[1.1ex] 8 &amp; 2 &amp; 7 &amp; 1 \\\\[1.1ex] 0 &amp; 6 &amp; 3 &amp; 5 \\\\[1.1ex] 0 &amp; 0 &amp; 1 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"105\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <strong>Matriks Hessenberg Bawah<\/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-a9b13730483eaf930193baeb953d1d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{pmatrix} 2 &amp; 4 &amp; 0 &amp; 0 \\\\[1.1ex] 1 &amp; 9 &amp; 6 &amp; 0 \\\\[1.1ex] 3 &amp; 5 &amp; 1 &amp; 2 \\\\[1.1ex] 8 &amp; 2 &amp; 3 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"105\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Matriks yang merupakan matriks Hessenberg atas dan bawah merupakan <a href=\"https:\/\/mathority.org\/id\/matriks-diagonal\/\">matriks tridiagonal<\/a> .<\/p>\n<p> Nama matriks ini diambil dari nama Karl Hessenberg, seorang insinyur dan matematikawan terkemuka Jerman abad ke-20.<\/p>\n<p> Terakhir, matriks jenis ini memiliki kekhasan yaitu jika dikalikan dengan matriks segitiga maka hasilnya selalu berupa matriks Hessenberg.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada halaman ini Anda akan melihat apa itu matriks segitiga dan macam-macam matriks segitiga beserta contohnya. Selain itu, Anda akan mengetahui cara menghitung determinan matriks segitiga dan apa saja sifat-sifat matriks yang sangat menarik ini. Terakhir, kami juga akan menjelaskan apa itu matriks Hessenberg, karena merupakan matriks yang berkaitan dengan matriks segitiga. Apa itu matriks &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\"> <span class=\"screen-reader-text\">Matriks segitiga atas dan bawah<\/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":[64],"tags":[],"class_list":["post-307","post","type-post","status-publish","format-standard","hentry","category-jenis-tabel"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matriks segitiga atas dan bawah - 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\/matriks-segitiga-atas-bawah\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriks segitiga atas dan bawah - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada halaman ini Anda akan melihat apa itu matriks segitiga dan macam-macam matriks segitiga beserta contohnya. Selain itu, Anda akan mengetahui cara menghitung determinan matriks segitiga dan apa saja sifat-sifat matriks yang sangat menarik ini. Terakhir, kami juga akan menjelaskan apa itu matriks Hessenberg, karena merupakan matriks yang berkaitan dengan matriks segitiga. Apa itu matriks &hellip; Matriks segitiga atas dan bawah Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T13:14:29+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/matrice-triangulaire-superieure.webp\" \/>\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\/matriks-segitiga-atas-bawah\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Matriks segitiga atas dan bawah\",\"datePublished\":\"2023-07-06T13:14:29+00:00\",\"dateModified\":\"2023-07-06T13:14:29+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\"},\"wordCount\":717,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Jenis tabel\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\",\"url\":\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\",\"name\":\"Matriks segitiga atas dan bawah - 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