{"id":326,"date":"2023-07-06T07:22:50","date_gmt":"2023-07-06T07:22:50","guid":{"rendered":"https:\/\/mathority.org\/pt\/matriz-nula-zero\/"},"modified":"2023-07-06T07:22:50","modified_gmt":"2023-07-06T07:22:50","slug":"matriz-nula-zero","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/matriz-nula-zero\/","title":{"rendered":"Matriz nula ou nula"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o da matriz zero, tamb\u00e9m chamada de matriz nula. Voc\u00ea tamb\u00e9m ver\u00e1 com exemplos que os valores de seus elementos s\u00e3o independentes da dimens\u00e3o da matriz e, por fim, encontrar\u00e1 todas as propriedades deste tipo de matriz.<\/p>\n<h2 class=\"wp-block-heading\"> Qual \u00e9 a matriz nula?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> A <strong>matriz nula<\/strong> (ou matriz nula) \u00e9 uma matriz cujos elementos s\u00e3o todos iguais a zero (0).<\/p>\n<p> Portanto, pela defini\u00e7\u00e3o de matriz zero, esta matriz pode ter todas as dimens\u00f5es poss\u00edveis, desde que todos os seus n\u00fameros sejam zero. Veja os seguintes exemplos:<\/p>\n<h2 class=\"wp-block-heading\"> Exemplos de matrizes nulas <\/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;\">Exemplo de matriz nula 2 \u00d7 2<\/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=\"exemplo de matriz zero ou nula de dimens\u00e3o 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;\">Exemplo de matriz nula 3 \u00d7 3<\/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=\"exemplo de matriz zero ou nula de dimens\u00e3o 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;\">Exemplo de matriz nula 4 \u00d7 4<\/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=\"exemplo de matriz zero ou nula de dimens\u00e3o 4x4\" class=\"wp-image-2770\" width=\"145\" height=\"148\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> Pode agora parecer-lhe que esta matriz muito particular n\u00e3o importa, uma vez que \u00e9 simplesmente uma matriz cheia de zeros. Por\u00e9m, em matem\u00e1tica, mais especificamente na \u00e1rea de \u00e1lgebra linear, \u00e9 uma matriz muito \u00fatil porque facilita muito os c\u00e1lculos.<\/p>\n<h2 class=\"wp-block-heading\"> Propriedades da matriz nula<\/h2>\n<p> Matrizes nulas (ou nulas) possuem as seguintes caracter\u00edsticas:<\/p>\n<ul>\n<li> A matriz zero \u00e9 o elemento neutro da opera\u00e7\u00e3o de adi\u00e7\u00e3o de matrizes, portanto:<\/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> A multiplica\u00e7\u00e3o de matrizes tem a propriedade multiplicativa de zero, ou seja, o produto de qualquer matriz multiplicado pela matriz zero \u00e9 igual a 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> Se a matriz for quadrada, a matriz zero \u00e9 sim\u00e9trica e <a href=\"https:\/\/mathority.org\/pt\/exemplos-e-propriedades-de-matrizes-antissimetricas\/\">antissim\u00e9trica<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> A matriz zero \u00e9 a \u00fanica matriz cuja classifica\u00e7\u00e3o \u00e9 zero.<\/li>\n<\/ul>\n<ul>\n<li> O determinante da matriz zero sempre avalia 0, portanto este tipo de matriz n\u00e3o possui inversa (\u00e9 uma matriz singular).<\/li>\n<\/ul>\n<ul>\n<li> Obviamente, a matriz zero \u00e9 um <a href=\"https:\/\/mathority.org\/pt\/exemplos-de-matrizes-propriedades-nilpotentes\/\">exemplo de matriz nilpotente<\/a> .<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o da matriz zero, tamb\u00e9m chamada de matriz nula. Voc\u00ea tamb\u00e9m ver\u00e1 com exemplos que os valores de seus elementos s\u00e3o independentes da dimens\u00e3o da matriz e, por fim, encontrar\u00e1 todas as propriedades deste tipo de matriz. Qual \u00e9 a matriz nula? A matriz nula (ou matriz nula) \u00e9 uma &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/matriz-nula-zero\/\"> <span class=\"screen-reader-text\">Matriz nula ou nula<\/span> Leia mais &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":[37],"tags":[],"class_list":["post-326","post","type-post","status-publish","format-standard","hentry","category-tipos-de-tabelas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matriz nula ou nula - 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\/pt\/matriz-nula-zero\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriz nula ou nula - Mathority\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o da matriz zero, tamb\u00e9m chamada de matriz nula. Voc\u00ea tamb\u00e9m ver\u00e1 com exemplos que os valores de seus elementos s\u00e3o independentes da dimens\u00e3o da matriz e, por fim, encontrar\u00e1 todas as propriedades deste tipo de matriz. Qual \u00e9 a matriz nula? 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