{"id":284,"date":"2023-07-06T20:35:33","date_gmt":"2023-07-06T20:35:33","guid":{"rendered":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/"},"modified":"2023-07-06T20:35:33","modified_gmt":"2023-07-06T20:35:33","slug":"determinantes-2x2-exemplos-e-exercicios-resolvidos","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/","title":{"rendered":"Como calcular o determinante de uma matriz 2&#215;2"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea aprender\u00e1 o que \u00e9 o determinante de uma matriz 2\u00d72. Al\u00e9m disso, voc\u00ea encontrar\u00e1 exemplos resolvidos passo a passo e exerc\u00edcios sobre como resolver determinantes de ordem 2, para que possa praticar e entender perfeitamente.<\/p>\n<h2 class=\"wp-block-heading\"> O que \u00e9 um determinante 2\u00d72?<\/h2>\n<p> Um <strong>determinante de ordem 2<\/strong> \u00e9 uma matriz de dimens\u00e3o 2 \u00d7 2 <strong>representada por uma barra vertical em cada lado da matriz.<\/strong> Por exemplo, se tivermos a seguinte matriz:<\/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-50ff006696d04e4eee005e245ba217e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A = \\begin{pmatrix} 3 &amp; 1 \\\\[1.1ex] 5 &amp; 2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> O <strong>determinante da matriz A<\/strong> \u00e9 representado da seguinte forma:<\/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-3dc95ca8f173419691852fd137d67154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert A \\rvert = \\begin{vmatrix} 3 &amp; 1 \\\\[1.1ex] 5 &amp; 2 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"89\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Como voc\u00ea viu, escrever o determinante de uma matriz quadrada 2\u00d72 \u00e9 f\u00e1cil. Agora vamos ver como \u00e9 calculado:<\/p>\n<h2 class=\"wp-block-heading\"> Como resolver um determinante de ordem 2?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Para <strong>calcular o determinante de uma matriz 2&#215;2,<\/strong> precisamos multiplicar os elementos da diagonal principal e subtrair o produto da diagonal secund\u00e1ria. <\/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\/calculer-le-determinant-dune-matrice-22152.webp\" alt=\"exemplo de c\u00e1lculo do determinante de uma matriz 2x2\" class=\"wp-image-1531\" width=\"491\" height=\"168\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Exemplos de c\u00e1lculo de determinantes 2\u00d72:<\/h2>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-228cbdabc4e6d330b56fae20f5163e64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} 3 &amp; 4 \\\\[1.1ex] 2 &amp; 1 \\end{vmatrix} = 3 \\cdot 1 - 2 \\cdot 4 = 3 - 8 = \\bm{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"259\" style=\"vertical-align: 0px;\"><\/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-5e9aed81d00e74873a5e797746861a51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} 2 &amp; -3 \\\\[1.1ex] 1 &amp; 5 \\end{vmatrix} = 2 \\cdot 5 - 1 \\cdot (-3) =10-(-3) = 10+3= \\bm{13}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\">Problemas resolvidos de determinantes de matrizes 2 \u00d7 2<\/h2>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Calcule o seguinte determinante 2&#215;2: <\/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\/determinant-dexercice-resolu-22152.webp\" alt=\"exerc\u00edcio resolvido passo a passo do determinante 2x2\" class=\"wp-image-1534\" width=\"57\" height=\"68\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para fazer um determinante 2\u00d72, voc\u00ea deve multiplicar os elementos da diagonal principal e subtrair o produto da diagonal secund\u00e1ria: <\/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-8d03764083647c0b05f9a5d7266c8915_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; 2 \\\\[1.1ex] 3 &amp; 5 \\end{vmatrix} = 1 \\cdot 5 - 3 \\cdot 2 = 5 - 6 = \\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"259\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 2<\/h3>\n<p> Resolva o seguinte determinante de dimens\u00e3o 2\u00d72: <\/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\/determinants-resolus-de-lexercice-22152.webp\" alt=\"exerc\u00edcios resolvidos passo a passo de determinantes 2x2\" class=\"wp-image-1536\" width=\"72\" height=\"69\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para encontrar a solu\u00e7\u00e3o de um determinante de ordem 2, deve-se multiplicar os elementos da diagonal principal e subtrair o produto da diagonal secund\u00e1ria: <\/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-56c917d70b8c6ec3697612d44f84e522_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} -3 &amp; 5 \\\\[1.1ex] 2 &amp; 4 \\end{vmatrix} = -3 \\cdot 4 - 2 \\cdot 5 = -12 - 10 = \\bm{-22}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"327\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 3<\/h3>\n<p> Encontre a solu\u00e7\u00e3o para o seguinte determinante de ordem 2: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/determinant-dexercice-resolu-dune-matrice-22152.webp\" alt=\"exerc\u00edcio resolvido passo a passo de um determinante de uma matriz 2x2\" width=\"72\" height=\"71\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para encontrar a solu\u00e7\u00e3o para um determinante de dimens\u00e3o 2, deve-se multiplicar os elementos da diagonal principal e subtrair o produto da diagonal secund\u00e1ria: <\/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-cbd06fd83283d3e82105c24eaf95af9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 4 &amp; -2 \\\\[1.1ex] 7 &amp; -3\\end{vmatrix} = 4 \\cdot (-3) - 7 \\cdot (-2) = -12 - (-14) =-12+14= \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"467\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 4<\/h3>\n<p> Calcule o seguinte determinante 2&#215;2: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-resoudre-le-determinant-dune-matrice-22152.webp\" alt=\"como resolver o determinante de uma matriz 2x2, exerc\u00edcio resolvido passo a passo\" width=\"91\" height=\"70\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para calcular os determinantes de matrizes 2&#215;2, precisamos multiplicar os elementos da diagonal principal e subtrair o produto da diagonal secund\u00e1ria: <\/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-34915d9aff298587a13346c6fc30bfcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 5 &amp; -3 \\\\[1.1ex] -2 &amp; 4\\end{vmatrix} = 5 \\cdot 4 - (-2) \\cdot (-3) = 20 - (+6) = \\bm{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"374\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 5<\/h3>\n<p> Determine o resultado do seguinte determinante 2&#215;2: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-resoudre-pas-a-pas-le-determinant-dune-matrice-dordre-2.webp\" alt=\"Exerc\u00edcio resolvido sobre a resolu\u00e7\u00e3o passo a passo do determinante de uma matriz de ordem 2\" width=\"70\" height=\"69\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para encontrar a solu\u00e7\u00e3o para um determinante 2&#215;2, precisamos multiplicar os elementos da diagonal principal e subtrair o produto da diagonal secund\u00e1ria: <\/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-4c6e4a7fdc04f0458d95c1d62b12d7ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 3 &amp; 4 \\\\[1.1ex] -2 &amp; 7\\end{vmatrix} = 3 \\cdot 7 - (-2) \\cdot 4 = 21 - (-8)=21+8 = \\bm{29}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Brilhante! Agora voc\u00ea sabe criar determinantes de dimens\u00e3o 2\u00d72! Agora com certeza voc\u00ea j\u00e1 consegue entender como o <a href=\"https:\/\/mathority.org\/pt\/determinantes-3x3-exemplos-de-regras-sarrus-e-exercicios-resolvidos\/\">determinante 3\u00d73<\/a> \u00e9 calculado e tamb\u00e9m como \u00e9 resolvido o <a href=\"https:\/\/mathority.org\/pt\/determinantes-4x4-por-exemplos-complementares-e-exercicios-resolvidos\/\">determinante de uma matriz 4\u00d74<\/a> .<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea aprender\u00e1 o que \u00e9 o determinante de uma matriz 2\u00d72. Al\u00e9m disso, voc\u00ea encontrar\u00e1 exemplos resolvidos passo a passo e exerc\u00edcios sobre como resolver determinantes de ordem 2, para que possa praticar e entender perfeitamente. O que \u00e9 um determinante 2\u00d72? Um determinante de ordem 2 \u00e9 uma matriz de dimens\u00e3o 2 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/\"> <span class=\"screen-reader-text\">Como calcular o determinante de uma matriz 2&#215;2<\/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":[12],"tags":[],"class_list":["post-284","post","type-post","status-publish","format-standard","hentry","category-determinante-de-uma-matriz"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como calcular o determinante de uma matriz 2\u00d72 - 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\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como calcular o determinante de uma matriz 2\u00d72 - Mathority\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea aprender\u00e1 o que \u00e9 o determinante de uma matriz 2\u00d72. Al\u00e9m disso, voc\u00ea encontrar\u00e1 exemplos resolvidos passo a passo e exerc\u00edcios sobre como resolver determinantes de ordem 2, para que possa praticar e entender perfeitamente. O que \u00e9 um determinante 2\u00d72? 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Al\u00e9m disso, voc\u00ea encontrar\u00e1 exemplos resolvidos passo a passo e exerc\u00edcios sobre como resolver determinantes de ordem 2, para que possa praticar e entender perfeitamente. O que \u00e9 um determinante 2\u00d72? Um determinante de ordem 2 \u00e9 uma matriz de dimens\u00e3o 2 &hellip; Como calcular o determinante de uma matriz 2&#215;2 Leia mais &raquo;","og_url":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/","article_published_time":"2023-07-06T20:35:33+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50ff006696d04e4eee005e245ba217e4_l3.png"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"2 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Como calcular o determinante de uma matriz 2&#215;2","datePublished":"2023-07-06T20:35:33+00:00","dateModified":"2023-07-06T20:35:33+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/"},"wordCount":349,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Determinante de uma matriz"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/","url":"https:\/\/mathority.org\/pt\/determinantes-2x2-exemplos-e-exercicios-resolvidos\/","name":"Como calcular o determinante de uma matriz 2\u00d72 - 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