{"id":348,"date":"2023-07-06T01:36:03","date_gmt":"2023-07-06T01:36:03","guid":{"rendered":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/"},"modified":"2023-07-06T01:36:03","modified_gmt":"2023-07-06T01:36:03","slug":"kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/","title":{"rendered":"Matriks emas yang dapat dibalik"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan tentang matriks beraturan atau matriks yang dapat dibalik dan cara mengetahui kapan inversi suatu matriks dapat dilakukan dan kapan tidak. Selain itu, Anda juga akan melihat beberapa contoh matriks beraturan untuk memahami konsepnya sepenuhnya dan, terakhir, kami akan menunjukkan kepada Anda semua properti dari jenis matriks ini.<\/p>\n<h2 class=\"wp-block-heading\"> Apa itu matriks beraturan?<\/h2>\n<p> Pengertian matriks beraturan adalah sebagai berikut:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>Matriks beraturan<\/strong> adalah matriks persegi yang dapat diinversi, yaitu invers dari matriks tersebut dapat dihitung. Oleh karena itu, determinannya bukan nol (0).<\/p>\n<p> Matriks beraturan disebut juga <strong>matriks invertible, non-singular, atau non-degenerate<\/strong> .<\/p>\n<p> Matriks yang berlawanan dengan matriks beraturan adalah matriks singular atau matriks degenerasi.<\/p>\n<p> Jadi, untuk mengetahui suatu matriks beraturan atau tunggal, yaitu suatu matriks dapat dibalik atau tidak, cukup dengan menyelesaikan determinan matriks tersebut:<\/p>\n<ul>\n<li> Jika determinan suatu matriks bukan nol, maka matriks tersebut beraturan atau dapat dibalik.<\/li>\n<\/ul>\n<ul>\n<li> Jika determinan matriks sama dengan nol, maka matriks tersebut berbentuk tunggal atau tidak dapat dibalik.<\/li>\n<\/ul>\n<p> Kesimpulannya, menghitung determinan suatu matriks adalah cara paling sederhana untuk mengetahui apakah suatu matriks mempunyai invers atau tidak, jadi inilah yang kami rekomendasikan untuk menentukan invertibilitas suatu matriks.<\/p>\n<p> Jika Anda ingin mengetahui cara membalikkan matriks, Anda dapat melihat <a href=\"https:\/\/mathority.org\/id\/matriks-terbalik\/\">rumus invers matriks<\/a> , yang menjelaskan langkah demi langkah cara membalikkan matriks, dan Anda juga akan menemukan beberapa contoh dan latihan penyelesaian untuk dipraktikkan.<\/p>\n<h2 class=\"wp-block-heading\"> Contoh matriks beraturan atau matriks inversi<\/h2>\n<p> Setelah kita mengetahui pengertian matriks beraturan atau matriks inversi, mari kita lihat beberapa contoh matriks beraturan yang dimensinya berbeda:<\/p>\n<h3 class=\"wp-block-heading\"> Contoh matriks 2\u00d72 beraturan atau dapat dibalik <\/h3>\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\/exemple-de-matrice-reguliere-ou-inversible-22152-1.webp\" alt=\"contoh matriks beraturan atau matriks inversi berdimensi 2x2\" class=\"wp-image-3654\" width=\"67\" height=\"64\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Kita dapat memverifikasi bahwa ini adalah matriks reguler dengan menghitung 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-9e4a833393b2e66b49eb3b434136b755_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} 3&amp;5 \\\\[1.1ex] 1 &amp; 2\\end{vmatrix}=1\\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"104\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Penentu matriks orde 2 berbeda dengan 0, sehingga merupakan matriks beraturan.<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\"> Contoh matriks 3\u00d73 beraturan atau dapat dibalik <\/h3>\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\/exemple-de-matrice-reguliere-ou-inversible-32153-1.webp\" alt=\"contoh matriks beraturan atau matriks inversi berdimensi 3x3\" class=\"wp-image-3655\" width=\"101\" height=\"105\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Kita harus menentukan determinan matriks tersebut untuk membuktikan bahwa matriks tersebut merupakan matriks yang dapat dibalik:<\/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-c0389d86d007f9ee667b14c0071b6395_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} 2&amp;1&amp;4\\\\[1.1ex] 3&amp;1&amp;0\\\\[1.1ex] 1&amp;0&amp;3\\end{vmatrix}=-7\\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"143\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Penentu matriks orde 3 memberikan hasil selain 0, sehingga merupakan matriks beraturan.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh matriks 4\u00d74 beraturan atau dapat dibalik <\/h3>\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\/exemple-de-matrice-reguliere-ou-inversible-42154-1.webp\" alt=\"contoh matriks beraturan atau matriks inversi berdimensi 4x4\" class=\"wp-image-3656\" width=\"156\" height=\"129\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Pengambilan determinan matriks menunjukkan bahwa matriks tersebut merupakan matriks beraturan:<\/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-2a07b3fa1ed83267c0bc723dd027d724_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} 1&amp;3&amp;-2&amp;0\\\\[1.1ex] 2&amp;-1&amp;0&amp;5\\\\[1.1ex] 1&amp;3&amp;1&amp;2\\\\[1.1ex] 0&amp;-1&amp;2&amp;4\\end{vmatrix}=-49\\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"204\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Penentu matriks berorde 4 tidak nol, sehingga merupakan matriks yang dapat dibalik.<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7\"> <strong>Peringatan:<\/strong> Jika Anda ragu dengan perhitungan determinan, Anda dapat membaca halaman <a href=\"https:\/\/mathority.org\/id\" rel=\"nofollow\">cara menghitung determinan<\/a> .<\/p>\n<h2 class=\"wp-block-heading\"> Sifat-sifat matriks beraturan atau matriks yang dapat dibalik<\/h2>\n<p> Matriks beraturan atau matriks inversi sangat penting untuk aljabar linier, dan hal ini disebabkan oleh ciri-ciri berikut:<\/p>\n<ul>\n<li> Jika A adalah matriks yang dapat dibalik, maka matriksnya juga dapat ditransposisikan atau ditransposisikan. Selain itu, matriks invers transpos sama dengan transpos invers.<\/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-599aaadb6e9a0ed681ae1ed37cbe75f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(A^t\\right)^{-1}=\\left(A^{-1}\\right)^t\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"128\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li> Jangkauan suatu matriks beraturan selalu sebesar mungkin, atau dengan kata lain jangkauan tersebut ekuivalen dengan dimensi matriks.<\/li>\n<\/ul>\n<ul>\n<li> Hasil kali matriks antara dua matriks yang dapat dibalik menghasilkan matriks beraturan lainnya. Kondisi ini dapat dengan mudah ditunjukkan dengan sifat-sifat determinan:<\/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-88d940d46390d4f5f0d6e694ac5a18d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l}\\text{det}(A\\cdot B)=\\text{det}(A)\\cdot\\text{det}(B) \\\\[2ex] \\text{det}(A)\\neq 0 \\quad ; \\quad \\text{det}(B) \\neq 0 \\end{array}\\right\\} \\longrightarrow \\ \\text{det}(A\\cdot B) \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Setiap <a href=\"https:\/\/mathority.org\/id\/contoh-matriks-ortogonal-sifat-2x2-3x3\/\">matriks ortogonal<\/a> sekaligus merupakan matriks beraturan.<\/li>\n<\/ul>\n<ul>\n<li> Misalkan A adalah matriks yang menyatakan sistem persamaan linier\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d22ca4e8614c8321dd6cc5a4fe4737ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(Ax=b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"><\/p>\n<p> , jika A adalah matriks beraturan, sistem mempunyai solusi unik, oleh karena itu sistem tersebut merupakan sistem determinan yang kompatibel (SCD).<\/li>\n<\/ul>\n<ul>\n<li> Apalagi jika sistem tersebut merupakan sistem yang homogen\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-838426cb27867bef9fede0552233b03e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(Ax=0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan A dapat dibalik, penyelesaian sistemnya sepele:<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d6889ee3f02f0af137641306363d2da7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li> Kolom dan baris matriks beraturan tidak bergantung linier satu sama lain.<\/li>\n<\/ul>\n<ul>\n<li> Semua nilai eigen (atau nilai eigen) dari matriks beraturan atau matriks yang dapat dibalik adalah bukan nol.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan tentang matriks beraturan atau matriks yang dapat dibalik dan cara mengetahui kapan inversi suatu matriks dapat dilakukan dan kapan tidak. Selain itu, Anda juga akan melihat beberapa contoh matriks beraturan untuk memahami konsepnya sepenuhnya dan, terakhir, kami akan menunjukkan kepada Anda semua properti dari jenis matriks ini. Apa &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\"> <span class=\"screen-reader-text\">Matriks emas yang dapat dibalik<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[63],"tags":[],"class_list":["post-348","post","type-post","status-publish","format-standard","hentry","category-matriks-terbalik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matriks beraturan atau dapat dibalik - 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\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriks beraturan atau dapat dibalik - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan penjelasan tentang matriks beraturan atau matriks yang dapat dibalik dan cara mengetahui kapan inversi suatu matriks dapat dilakukan dan kapan tidak. Selain itu, Anda juga akan melihat beberapa contoh matriks beraturan untuk memahami konsepnya sepenuhnya dan, terakhir, kami akan menunjukkan kepada Anda semua properti dari jenis matriks ini. Apa &hellip; Matriks emas yang dapat dibalik Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T01:36:03+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-reguliere-ou-inversible-22152-1.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=\"3 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Matriks emas yang dapat dibalik\",\"datePublished\":\"2023-07-06T01:36:03+00:00\",\"dateModified\":\"2023-07-06T01:36:03+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\"},\"wordCount\":511,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Matriks terbalik\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\",\"url\":\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\",\"name\":\"Matriks beraturan atau dapat dibalik - 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Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/","og_locale":"id_ID","og_type":"article","og_title":"Matriks beraturan atau dapat dibalik - Mathority","og_description":"Di halaman ini Anda akan menemukan penjelasan tentang matriks beraturan atau matriks yang dapat dibalik dan cara mengetahui kapan inversi suatu matriks dapat dilakukan dan kapan tidak. Selain itu, Anda juga akan melihat beberapa contoh matriks beraturan untuk memahami konsepnya sepenuhnya dan, terakhir, kami akan menunjukkan kepada Anda semua properti dari jenis matriks ini. Apa &hellip; Matriks emas yang dapat dibalik Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/","article_published_time":"2023-07-06T01:36:03+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-reguliere-ou-inversible-22152-1.webp"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"3 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Matriks emas yang dapat dibalik","datePublished":"2023-07-06T01:36:03+00:00","dateModified":"2023-07-06T01:36:03+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/"},"wordCount":511,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Matriks terbalik"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/","url":"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/","name":"Matriks beraturan atau dapat dibalik - 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