{"id":353,"date":"2023-07-06T00:37:26","date_gmt":"2023-07-06T00:37:26","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/"},"modified":"2023-07-06T00:37:26","modified_gmt":"2023-07-06T00:37:26","slug":"contoh-matriks-sifat-nilpoten","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/","title":{"rendered":"Matriks nihil"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan tentang apa itu matriks nilpoten, serta beberapa contohnya agar Anda dapat memahaminya dan tidak ragu lagi. Selain itu, Anda akan dapat melihat struktur matriks nilpoten dan semua properti dari jenis matriks tersebut.<\/p>\n<h2 class=\"wp-block-heading\"> Apa itu matriks nilpoten?<\/h2>\n<p> Pengertian matriks nilpoten adalah sebagai berikut: <\/p>\n<div style=\"background-color:#dff6ff;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p style=\"text-align:left\"> <strong>Matriks nilpoten<\/strong> adalah matriks persegi yang dipangkatkan menjadi bilangan bulat menghasilkan <a href=\"https:\/\/mathority.org\/id\/matriks-nol-nol\/\">matriks nol<\/a> .<\/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-4028c70ed3edfc0f2a8f7458ecce6580_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N^k =0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Emas<\/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-5793832f979c2268e3694c246d53b1bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah matriks nilpoten dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> eksponen pangkat yang menghasilkan matriks nol.<\/p>\n<\/div>\n<p> Kondisi ini bukan berarti pangkat matriks nilpoten selalu bernilai nol berapa pun eksponennya, melainkan jika terdapat paling sedikit satu pangkat matriks yang hasilnya matriks penuh 0, maka matriks tersebut nilpoten.<\/p>\n<p> Sebaliknya, <strong>indeks nilpotensi<\/strong> dari matriks nilpotensi adalah bilangan terkecil yang memenuhi kondisi nilpotensi. Kita juga dapat mengatakan bahwa matriks nilpoten berorde <em>k<\/em> , di mana <em>k<\/em> adalah indeks nilpotensinya.<\/p>\n<h2 class=\"wp-block-heading\"> Contoh matriks nilpoten<\/h2>\n<p> Untuk menyelesaikan pemahaman konsep matriks nilpoten, kita akan melihat beberapa contoh matriks jenis ini:<\/p>\n<h3 class=\"wp-block-heading\"> Contoh matriks nilpoten 2\u00d72<\/h3>\n<p> Matriks persegi berdimensi 2\u00d72 berikut ini nilpoten: <\/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\/exemple-de-matrice-nilpotente-22152-1.webp\" alt=\"contoh matriks nilpoten berdimensi 2x2\" class=\"wp-image-3769\" width=\"133\" height=\"132\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Matriks tersebut nilpoten karena dengan mengkuadratkan matriks A kita memperoleh matriks nol sebagai hasilnya:<\/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-fde370dd31b0e2a533fdf1e9d23cf2c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2=\\begin{pmatrix} 2 &amp;-4 \\\\[1.1ex] 1 &amp; -2 \\end{pmatrix}\\cdot \\begin{pmatrix} 2 &amp;-4 \\\\[1.1ex] 1 &amp; -2 \\end{pmatrix}=\\begin{pmatrix} \\bm{0} &amp;\\bm{0} \\\\[1.1ex] \\bm{0} &amp; \\bm{0} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"291\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, matriks tersebut merupakan matriks nilpoten dan indeks nihilpotensinya adalah 2, karena matriks nol diperoleh pangkat dua.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh matriks nilpoten 3\u00d73<\/h3>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p> <a href=\"https:\/\/mathority.org\/id\/matriks-persegi\/\">Matriks persegi<\/a> berorde 3 berikut ini nilpoten: <\/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\/exemple-de-matrice-nilpotente-32153-1.webp\" alt=\"contoh matriks nilpoten berdimensi 3x3\" class=\"wp-image-3773\" width=\"201\" height=\"112\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Meskipun dengan menaikkan matriks menjadi 2 kita tidak mendapatkan matriks 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-fbad4ccc270e2960ae50cc23eacc7530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^2=\\begin{pmatrix}1&amp;-2&amp;1\\\\[1.1ex] 3&amp;0&amp;3\\\\[1.1ex] -1&amp;2&amp;-1\\end{pmatrix}\\cdot \\begin{pmatrix}1&amp;-2&amp;1\\\\[1.1ex] 3&amp;0&amp;3\\\\[1.1ex] -1&amp;2&amp;-1\\end{pmatrix}= \\begin{pmatrix}-6&amp;0&amp;-6\\\\[1.1ex]0&amp;0&amp;0\\\\[1.1ex] 6&amp;0&amp;6\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"458\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Tetapi ketika menghitung pangkat tiga suatu matriks, kita mendapatkan matriks yang semua elemennya sama dengan 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-da876a04b14d80c156e24c95bd22372e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^3= \\begin{pmatrix}-6&amp;0&amp;-6\\\\[1.1ex]0&amp;0&amp;0\\\\[1.1ex] 6&amp;0&amp;6\\end{pmatrix}\\cdot\\begin{pmatrix}1&amp;-2&amp;1\\\\[1.1ex] 3&amp;0&amp;3\\\\[1.1ex] -1&amp;2&amp;-1\\end{pmatrix}= \\begin{pmatrix}\\bm{0}&amp;\\bm{0}&amp;\\bm{0}\\\\[1.1ex]\\bm{0}&amp;\\bm{0}&amp;\\bm{0}\\\\[1.1ex] \\bm{0}&amp;\\bm{0}&amp;\\bm{0}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"416\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jadi matriks B adalah matriks nilpoten, dan karena matriks nol dipangkatkan 3, maka indeks nilpotensinya adalah 3.<\/p>\n<h2 class=\"wp-block-heading\"> Struktur matriks nilpoten 2 \u00d7 2<\/h2>\n<p> Di bawah ini Anda dapat melihat struktur semua matriks nilpoten. Pembuktiannya agak membosankan, jadi kami langsung memberikan <strong>rumus untuk mendapatkan matriks nilpoten orde 2:<\/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\/formule-de-la-matrice-nilpotente-1.webp\" alt=\"struktur dan rumus matriks nilpoten 2x2\" class=\"wp-image-3789\" width=\"412\" height=\"161\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Jadi matriks apa pun yang memenuhi rumus di atas akan menjadi matriks nilpoten. Untuk ini, nilai-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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> bilangan tersebut dapat berubah-ubah selama bilangan tersebut merupakan bilangan real.<\/p>\n<h2 class=\"wp-block-heading\"> Sifat-sifat matriks nilpoten<\/h2>\n<p> Matriks nilpoten mempunyai ciri-ciri sebagai berikut:<\/p>\n<ul>\n<li> Jejak matriks nilpoten selalu nol.<\/li>\n<\/ul>\n<ul>\n<li> Demikian pula determinan suatu matriks nilpoten selalu sama dengan 0. Namun hal sebaliknya tidak benar, yaitu determinan suatu matriks adalah nol tidak berarti matriks tersebut nilpoten.<\/li>\n<\/ul>\n<ul>\n<li> Satu-satunya matriks nilpoten yang dapat didiagonalisasi adalah matriks nol.<\/li>\n<\/ul>\n<ul>\n<li> Indeks nilpotensi matriks nilpoten berdimensi <em>n\u00d7n<\/em> selalu sama dengan atau kurang dari <em>n<\/em> . Inilah sebabnya mengapa indeks nilpotensi dari matriks nilpoten 2 \u00d7 2 akan selalu sama dengan 2.<\/li>\n<\/ul>\n<ul>\n<li> Matriks nilpoten tidak dapat dibalik.<\/li>\n<\/ul>\n<ul>\n<li> <a href=\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\">Matriks segitiga<\/a> apa pun yang diagonal utamanya nol juga merupakan matriks nilpoten. <\/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<ul>\n<li> Ada teorema yang menyatakan bahwa jika matriks\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5793832f979c2268e3694c246d53b1bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> nilpoten, maka matriksnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-63ce5395b5ca090528c69a062886ee6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N+I\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -2px;\"><\/p>\n<p> dapat dibalik, di mana<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah matriks identitas. Selain itu, matriks inversnya dapat dicari dengan rumus berikut:<\/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-2b1cf043663e9cbfac772bf812359a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle(N+I)^{-1} = \\sum_{m = 0}^\\infty (-N)^m=I-N+N^2-N^3+\\cdots\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"391\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<ul>\n<li> Sama halnya jika\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5793832f979c2268e3694c246d53b1bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah matriks nilpoten, maka invers matriks tersebut dapat dihitung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-af0178ac2726008cea43b8cb2390e1a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N-I\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<p> dengan persamaan berikut:<\/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-a87795d57f3ee25346a24219f59b813c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle(N-I)^{-1} = \\sum_{m = 0}^\\infty (N)^m=I+N+N^2+N^3+\\cdots\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"378\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<ul>\n<li> Matriks tunggal apa pun, artinya tidak dapat dibalik, dapat didekomposisi menjadi hasil kali matriks nilpoten.<\/li>\n<\/ul>\n<ul>\n<li> Semua nilai eigen (atau nilai eigen) dari matriks nilpoten adalah nol.<\/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-44fc8cf9845415c9f1e7a86c1b01f085_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda=0 \\qquad \\forall \\ \\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"104\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Terakhir, yang membuat penasaran, ada juga konsep transformasi nihilpoten, yang mendefinisikan aplikasi linier\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"L\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> dari ruang vektor sedemikian rupa sehingga<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-71cac750ba2e7b5a3b7c1184f6115e4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"L^k=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\"><\/p>\n<p> .<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan tentang apa itu matriks nilpoten, serta beberapa contohnya agar Anda dapat memahaminya dan tidak ragu lagi. Selain itu, Anda akan dapat melihat struktur matriks nilpoten dan semua properti dari jenis matriks tersebut. Apa itu matriks nilpoten? Pengertian matriks nilpoten adalah sebagai berikut: Matriks nilpoten adalah matriks persegi yang &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/\"> <span class=\"screen-reader-text\">Matriks nihil<\/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-353","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 nilpoten - Mathoritas<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriks nilpoten - Mathoritas\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan penjelasan tentang apa itu matriks nilpoten, serta beberapa contohnya agar Anda dapat memahaminya dan tidak ragu lagi. Selain itu, Anda akan dapat melihat struktur matriks nilpoten dan semua properti dari jenis matriks tersebut. Apa itu matriks nilpoten? Pengertian matriks nilpoten adalah sebagai berikut: Matriks nilpoten adalah matriks persegi yang &hellip; Matriks nihil Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T00:37:26+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4028c70ed3edfc0f2a8f7458ecce6580_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=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Matriks nihil\",\"datePublished\":\"2023-07-06T00:37:26+00:00\",\"dateModified\":\"2023-07-06T00:37:26+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/\"},\"wordCount\":469,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Jenis tabel\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/\",\"url\":\"https:\/\/mathority.org\/id\/contoh-matriks-sifat-nilpoten\/\",\"name\":\"Matriks nilpoten - 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