{"id":371,"date":"2023-07-06T07:22:50","date_gmt":"2023-07-06T07:22:50","guid":{"rendered":"https:\/\/mathority.org\/nl\/nulmatrix-nul\/"},"modified":"2023-07-06T07:22:50","modified_gmt":"2023-07-06T07:22:50","slug":"nulmatrix-nul","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/nulmatrix-nul\/","title":{"rendered":"Nul- of nulmatrix"},"content":{"rendered":"<p>Op deze pagina vind je de uitleg van nulmatrix, ook wel nulmatrix genoemd. Je zult met voorbeelden ook zien dat de waarden van de elementen onafhankelijk zijn van de dimensie van de matrix, en tot slot zul je alle eigenschappen van dit type matrix vinden.<\/p>\n<h2 class=\"wp-block-heading\"> Wat is de nulmatrix?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> De <strong>nulmatrix<\/strong> (of nulmatrix) is een matrix waarvan de elementen allemaal gelijk zijn aan nul (0).<\/p>\n<p> Daarom kan deze matrix, volgens de definitie van een nulmatrix, alle mogelijke dimensies hebben, zolang alle getallen nul zijn. Kijk naar de volgende voorbeelden:<\/p>\n<h2 class=\"wp-block-heading\"> Voorbeelden van nulmatrices <\/h2>\n<div class=\"wp-block-columns is-layout-flex wp-container-4\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Voorbeeld van 2 \u00d7 2 nulmatrix<\/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\/exemple-de-matrice-nulle-ou-nulle-de-dimension-22152-1.webp\" alt=\"voorbeeld van een nul- of nulmatrix met dimensie 2x2\" class=\"wp-image-2768\" width=\"73\" height=\"73\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Voorbeeld van 3 x 3 nulmatrix<\/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\/exemple-de-matrice-zero-ou-nulle-de-dimension-32153-1.webp\" alt=\"voorbeeld van een nul- of nulmatrix met dimensie 3x3\" class=\"wp-image-2769\" width=\"110\" height=\"117\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Voorbeeld van een 4 \u00d7 4 nulmatrix<\/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\/exemple-de-matrice-nulle-ou-nulle-de-dimension-42154-1.webp\" alt=\"voorbeeld van een nul- of nulmatrix met dimensie 4x4\" class=\"wp-image-2770\" width=\"145\" height=\"148\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> Het lijkt je nu misschien dat deze zeer specifieke matrix er niet toe doet, omdat het eenvoudigweg een matrix vol nullen is. In de wiskunde, meer specifiek op het gebied van lineaire algebra, is het echter een zeer nuttige matrix omdat het berekeningen veel eenvoudiger maakt.<\/p>\n<h2 class=\"wp-block-heading\"> Eigenschappen van nulmatrix<\/h2>\n<p> Nul- (of nul-) matrices hebben de volgende kenmerken:<\/p>\n<ul>\n<li> De nulmatrix is het neutrale element van de matrixoptelling, daarom:<\/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-ac2f2c3b2989e505a4d61bab8759a13d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A + 0 =A\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> Matrixvermenigvuldiging heeft de multiplicatieve eigenschap van nul, dat wil zeggen dat het product van elke matrix vermenigvuldigd met de nulmatrix gelijk is aan 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-3751ce885f4d35454ac076342ecedf61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\\cdot 0 = 0 \\cdot A =0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"126\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Als de matrix vierkant is, is de nulmatrix zowel symmetrisch als <a href=\"https:\/\/mathority.org\/nl\/antisymmetrische-matrixvoorbeelden-en-eigenschappen\/\">antisymmetrisch<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> De nulmatrix is de enige matrix waarvan de rang nul is.<\/li>\n<\/ul>\n<ul>\n<li> De determinant van de nulmatrix evalueert altijd naar 0, dus dit type matrix heeft geen inverse (het is een enkelvoudige matrix).<\/li>\n<\/ul>\n<ul>\n<li> Uiteraard is de nulmatrix een <a href=\"https:\/\/mathority.org\/nl\/matrixvoorbeelden-nilpotente-eigenschappen\/\">voorbeeld van een nilpotente matrix<\/a> .<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Op deze pagina vind je de uitleg van nulmatrix, ook wel nulmatrix genoemd. Je zult met voorbeelden ook zien dat de waarden van de elementen onafhankelijk zijn van de dimensie van de matrix, en tot slot zul je alle eigenschappen van dit type matrix vinden. Wat is de nulmatrix? De nulmatrix (of nulmatrix) is een &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/nulmatrix-nul\/\"> <span class=\"screen-reader-text\">Nul- of nulmatrix<\/span> Lees meer &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-371","post","type-post","status-publish","format-standard","hentry","category-soorten-tafels"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Nul- of nulmatrix - 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\/nl\/nulmatrix-nul\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Nul- of nulmatrix - Mathority\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina vind je de uitleg van nulmatrix, ook wel nulmatrix genoemd. 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