{"id":310,"date":"2023-07-06T12:10:47","date_gmt":"2023-07-06T12:10:47","guid":{"rendered":"https:\/\/mathority.org\/pt\/matriz-escalar\/"},"modified":"2023-07-06T12:10:47","modified_gmt":"2023-07-06T12:10:47","slug":"matriz-escalar","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/matriz-escalar\/","title":{"rendered":"Matriz escalar"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 o que \u00e9 uma matriz escalar e v\u00e1rios exemplos de matrizes escalares para que seja perfeitamente compreendido. Al\u00e9m disso, voc\u00ea poder\u00e1 ver todas as propriedades das matrizes escalares e as vantagens de fazer opera\u00e7\u00f5es com elas. Por fim, explicamos como calcular o determinante de uma matriz escalar e como inverter este tipo de matriz.<\/p>\n<h2 class=\"wp-block-heading\"> O que \u00e9 uma matriz escalar?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Uma <strong>matriz escalar<\/strong> \u00e9 uma <a href=\"https:\/\/mathority.org\/pt\/matriz-diagonal\/\"><span style=\"text-decoration: underline;\">matriz diagonal<\/span><\/a> na qual todos os valores da diagonal principal s\u00e3o iguais.<\/p>\n<p> Esta \u00e9 a defini\u00e7\u00e3o de matriz escalar, mas tenho certeza que \u00e9 melhor compreendida com exemplos: \ud83d\ude09<\/p>\n<h2 class=\"wp-block-heading\"> Exemplos de matrizes escalares<\/h2>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Exemplo de uma matriz escalar de ordem 2\u00d72<\/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-scalaire-de-dimension-22152-1.webp\" alt=\"exemplo de uma matriz escalar de dimens\u00e3o 2x2\" class=\"wp-image-1910\" width=\"80\" height=\"80\" 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;\">Exemplo de uma matriz escalar 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\/exemple-de-matrice-scalaire-3-dimensionnelle-3-1.webp\" alt=\"exemplo de uma matriz escalar de dimens\u00e3o 3x3\" class=\"wp-image-1911\" width=\"116\" height=\"124\" 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;\">Exemplo de uma matriz escalar de tamanho 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\/exemple-de-matrice-scalaire-de-dimension-42154-1.webp\" alt=\"exemplo de uma matriz escalar de dimens\u00e3o 4x4\" class=\"wp-image-1912\" width=\"218\" height=\"146\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Propriedades de matrizes escalares<\/h2>\n<p> A matriz escalar tamb\u00e9m \u00e9 uma matriz diagonal, ent\u00e3o voc\u00ea ver\u00e1 que ela herda muitas caracter\u00edsticas desta classe de matrizes:<\/p>\n<ul>\n<li> Todas as matrizes escalares tamb\u00e9m s\u00e3o <a href=\"https:\/\/mathority.org\/pt\/exemplos-e-propriedades-de-matrizes-simetricas\/\">matrizes sim\u00e9tricas<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> Uma matriz escalar \u00e9 uma <a href=\"https:\/\/mathority.org\/pt\/matriz-triangular-superior-inferior\/\">matriz triangular superior e uma matriz triangular inferior<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> A <a href=\"https:\/\/mathority.org\/pt\">matriz identidade<\/a> \u00e9 uma matriz escalar.<\/li>\n<\/ul>\n<ul>\n<li> Qualquer matriz escalar pode ser obtida a partir do produto de uma matriz identidade e um n\u00famero escalar.<\/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-b77f7d177c2769b0847de258adfd1386_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4 \\cdot \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix} = \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> A <a href=\"https:\/\/mathority.org\/pt\/matriz-nula-zero\/\">matriz zero<\/a> tamb\u00e9m \u00e9 uma matriz escalar.<\/li>\n<\/ul>\n<ul>\n<li> Os autovalores (ou autovalores) de uma matriz escalar s\u00e3o os elementos de sua diagonal principal. Portanto, seus autovalores ser\u00e3o sempre iguais e se repetir\u00e3o tantas vezes quanto a dimens\u00e3o da matriz.<\/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-2513b8d4aeb6d932d9870934102a1637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 8 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 8 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 8 \\end{pmatrix} \\longrightarrow \\ \\lambda = 8 \\ ; \\ \\lambda = 8 \\ ; \\ \\lambda = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"298\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> O adjunto de uma matriz escalar \u00e9 outra matriz escalar. E mais, os valores da diagonal principal da matriz anexa ser\u00e3o sempre os da matriz original elevada <em>\u00e0 ordem da matriz \u2013 1<\/em> .<\/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-1f7e94cc5a528abace04016dc263c8f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5 \\end{pmatrix} \\longrightarrow \\text{Adj}(A)=\\begin{pmatrix} 5^{3-1} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5^{3-1} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5^{3-1} \\end{pmatrix}= \\begin{pmatrix} 25 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 25 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 25 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"546\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Opera\u00e7\u00f5es com matrizes escalares<\/h2>\n<p> Uma das raz\u00f5es pelas quais as matrizes escalares s\u00e3o t\u00e3o amplamente utilizadas na \u00e1lgebra linear \u00e9 a facilidade com que permitem realizar c\u00e1lculos. \u00c9 por isso que eles s\u00e3o t\u00e3o importantes na matem\u00e1tica.<\/p>\n<p> Ent\u00e3o vamos ver porque \u00e9 t\u00e3o f\u00e1cil fazer c\u00e1lculos com este tipo de matriz quadrada:<\/p>\n<h3 class=\"wp-block-heading\"> Adi\u00e7\u00e3o e subtra\u00e7\u00e3o de matrizes escalares<\/h3>\n<p> Adicionar (e subtrair) duas matrizes escalares \u00e9 muito simples: basta adicionar (ou subtrair) os n\u00fameros nas diagonais principais. Por exemplo:<\/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-761de4b4c9bdbbc835b366b21d8cfc2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix} +\\begin{pmatrix} 3 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 3 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 7&amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"306\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Multiplica\u00e7\u00e3o de matrizes escalares<\/h3>\n<p> Semelhante \u00e0 adi\u00e7\u00e3o e subtra\u00e7\u00e3o, para resolver uma multiplica\u00e7\u00e3o ou produto matricial entre duas matrizes escalares, basta multiplicar os elementos das diagonais entre elas. Por exemplo:<\/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-d30acbf9c6ad31625f8253549e659b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\cdot\\begin{pmatrix} 6 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 6 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 6 \\end{pmatrix} = \\begin{pmatrix} 12 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 12 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 12 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Poder das matrizes escalares<\/h3>\n<p> Calcular a pot\u00eancia de uma matriz escalar tamb\u00e9m \u00e9 muito simples: \u00e9 necess\u00e1rio elevar cada elemento da diagonal ao expoente. Por exemplo:<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle\\left. \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix}\\right.^4=\\begin{pmatrix} 2^ 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2^\n\n*** Error message:\nMissing $ inserted.\nleading text: \\displaystyle\nMissing { inserted.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\right. inserted.\nleading text: \\end{document}\n\n<\/pre>\n<p> &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2^4 \\end{pmatrix}= \\begin{pmatrix} 16 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 16 &amp; 0 \\\\[1.1ex] 0 &amp; 0 e 16 \\end{matriz}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca97d1162704371c21b308778890f436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\n\n<div class=&quot;adsb30&quot; style=&quot; margin:px; text-align:&quot;><\/div>\n<h2 class=&quot;wp-block-heading&quot;> D\u00e9terminant d&#8217;une matrice scalaire<\/h2>\n<p> Calculer le <strong>d\u00e9terminant d&#8217;une matrice scalaire<\/strong> revient \u00e0 r\u00e9soudre le d\u00e9terminant d&#8217;une matrice diagonale : le r\u00e9sultat est le produit des \u00e9l\u00e9ments sur la diagonale principale.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;106&#8243; width=&#8221;582&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> \\displaystyle \\text{det}(A)= \\prod_{i =1}^n a_i<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b3ddf4b77e65a9bd0387f51b7bcaa40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Regardez l'exercice r\u00e9solu suivant dans lequel on trouve le d\u00e9terminant d'une matrice scalaire en multipliant les \u00e9l\u00e9ments de sa diagonale principale :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1099\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 e 0 e 0 \\\\[1.1ex] 0 e 7 e 0 \\\\[1.1ex] 0 e 0 e 7 \\end{vmatrix} = 7 \\cdot 7 \\cdot 7 = \\bm {343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-773692a573846f155d4c92f1e9075001_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" En fait, puisque tous les \u00e9l\u00e9ments de la diagonale principale d'une matrice scalaire sont toujours \u00e9gaux, pour trouver le r\u00e9sultat du d\u00e9terminant, il suffit d'augmenter le num\u00e9ro de la diagonale principale du nombre de fois qu'elle est r\u00e9p\u00e9t\u00e9e. Par cons\u00e9quent, l'exercice pr\u00e9c\u00e9dent peut \u00e9galement \u00eatre r\u00e9solu de la mani\u00e8re suivante :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"2411\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 e 0 e 0 \\\\[1.1ex] 0 e 7 e 0 \\\\[1.1ex] 0 e 0 e 7 \\end{vmatrix} = 7^3= \\bm{343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d24f9aa91fc9fe8ed74f705f83be3b32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D\u00e9montrer ce th\u00e9or\u00e8me est tr\u00e8s simple : il suffit de calculer le d\u00e9terminant d'une matrice scalaire par blocs (ou cofacteurs). Vous trouverez ci-dessous la <strong>d\u00e9monstration<\/strong> de la formule utilisant une matrice scalaire g\u00e9n\u00e9rique :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;62&#8243; width=&#8221;1060&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> \\begin{aligned} \\begin{vmatrix} a &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; a &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; a \\end{vmatrix}&amp; = a \\cdot \\begin{ vmatrix} a &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} \u2013 0 \\cdot \\begin{vmatrix} 0 &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} + 0 \\cdot \\ start{vmatrix} 0 &amp; a \\\\[1.1ex] 0 &amp; 0 \\end{vmatrix} \\\\[2ex] &amp; =a \\cdot (a\\cdot a) \u2013 0 \\cdot 0 + 0 \\cdot 0 \\\\[ 2ex] &amp; = a \\cdot a \\cdot a \\\\[2ex] &amp; = a^3 \\end{aligned}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc127c7827a5f62c565b8ada378986a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Dans ce cas \u00e7a donne\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"149\" style=\"vertical-align: -1px;\"><\/p>\n<p> a ^ 3<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49f5afdd3e1e9918f5323139662a2138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"car la matrice est d'ordre 3, mais il faut toujours l'\u00e9lever \u00e0 l'ordre de la matrice. \n\n<div class=&quot;adsb30&quot; style=&quot; margin:12px; text-align:center&quot;>\n<div id=&quot;ezoic-pub-ad-placeholder-118&quot;><\/div>\n<\/div>\n<h2 class=&quot;wp-block-heading&quot;> Inverser une matrice scalaire<\/h2>\n<p> Une matrice scalaire <strong>est inversible si, et seulement si, tous les \u00e9l\u00e9ments de la diagonale principale sont diff\u00e9rents de 0<\/strong> . Dans ce cas on dit que la matrice scalaire est une matrice r\u00e9guli\u00e8re. De plus, l&#8217;inverse d&#8217;une matrice scalaire sera toujours une autre matrice scalaire avec les <strong>inverses<\/strong> de la diagonale principale :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;174&#8243; width=&#8221;1250&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p> \\displaystyle A= \\begin{pmatrix} 9 e 0 e 0 \\\\[1.1ex] 0 e 9 e 0 \\\\[1.1ex] 0 e 0 e 9 \\end{pmatrix} \\ \\longrightarrow \\ A^{-1 }=\\begin{pmatrix} \\frac{1}{9} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; \\frac{1}{9} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; \\frac{ 1}{9} \\end{matriz}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9eaf19f57b0cbab7f60c5c1dc0ec45eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D'autre part, de la caract\u00e9ristique pr\u00e9c\u00e9dente, on peut d\u00e9duire que le d\u00e9terminant d'une matrice scalaire invers\u00e9e est le r\u00e9sultat de la multiplication des inverses de la diagonale principale : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1373\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle B= \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\displaystyle\\left| B^{-1}\\right|=\\cfrac{1}{2} \\cdot \\cfrac{1}{2} \\cdot \\cfrac{1}{2}=\\cfrac{1}{8} = $ 0,125<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 o que \u00e9 uma matriz escalar e v\u00e1rios exemplos de matrizes escalares para que seja perfeitamente compreendido. Al\u00e9m disso, voc\u00ea poder\u00e1 ver todas as propriedades das matrizes escalares e as vantagens de fazer opera\u00e7\u00f5es com elas. Por fim, explicamos como calcular o determinante de uma matriz escalar e como inverter este &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/matriz-escalar\/\"> <span class=\"screen-reader-text\">Matriz escalar<\/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-310","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 escalar - Matoridade<\/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-escalar\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriz escalar - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 o que \u00e9 uma matriz escalar e v\u00e1rios exemplos de matrizes escalares para que seja perfeitamente compreendido. Al\u00e9m disso, voc\u00ea poder\u00e1 ver todas as propriedades das matrizes escalares e as vantagens de fazer opera\u00e7\u00f5es com elas. Por fim, explicamos como calcular o determinante de uma matriz escalar e como inverter este &hellip; Matriz escalar Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/matriz-escalar\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T12:10:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-22152-1.webp\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/matriz-escalar\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/matriz-escalar\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Matriz escalar\",\"datePublished\":\"2023-07-06T12:10:47+00:00\",\"dateModified\":\"2023-07-06T12:10:47+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/matriz-escalar\/\"},\"wordCount\":602,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Tipos de tabelas\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/matriz-escalar\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/matriz-escalar\/\",\"url\":\"https:\/\/mathority.org\/pt\/matriz-escalar\/\",\"name\":\"Matriz escalar - Matoridade\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-07-06T12:10:47+00:00\",\"dateModified\":\"2023-07-06T12:10:47+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/matriz-escalar\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/matriz-escalar\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/matriz-escalar\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Matriz escalar\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Matriz escalar - Matoridade","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\/pt\/matriz-escalar\/","og_locale":"pt_BR","og_type":"article","og_title":"Matriz escalar - Matoridade","og_description":"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 o que \u00e9 uma matriz escalar e v\u00e1rios exemplos de matrizes escalares para que seja perfeitamente compreendido. Al\u00e9m disso, voc\u00ea poder\u00e1 ver todas as propriedades das matrizes escalares e as vantagens de fazer opera\u00e7\u00f5es com elas. Por fim, explicamos como calcular o determinante de uma matriz escalar e como inverter este &hellip; Matriz escalar Leia mais &raquo;","og_url":"https:\/\/mathority.org\/pt\/matriz-escalar\/","article_published_time":"2023-07-06T12:10:47+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-22152-1.webp"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"4 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/matriz-escalar\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/matriz-escalar\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Matriz escalar","datePublished":"2023-07-06T12:10:47+00:00","dateModified":"2023-07-06T12:10:47+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/matriz-escalar\/"},"wordCount":602,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Tipos de tabelas"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/matriz-escalar\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/matriz-escalar\/","url":"https:\/\/mathority.org\/pt\/matriz-escalar\/","name":"Matriz escalar - Matoridade","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/#website"},"datePublished":"2023-07-06T12:10:47+00:00","dateModified":"2023-07-06T12:10:47+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/pt\/matriz-escalar\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/pt\/matriz-escalar\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/pt\/matriz-escalar\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Matriz escalar"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/pt\/#website","url":"https:\/\/mathority.org\/pt\/","name":"Mathority","description":"Onde a curiosidade encontra o c\u00e1lculo!","publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/pt\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/mathority.org\/pt\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/pt\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00","name":"Equipe Mathoridade","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Equipe Mathoridade"},"sameAs":["http:\/\/mathority.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/310","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/comments?post=310"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/310\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/media?parent=310"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/categories?post=310"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/tags?post=310"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}