{"id":369,"date":"2023-07-06T08:09:51","date_gmt":"2023-07-06T08:09:51","guid":{"rendered":"https:\/\/mathority.org\/nl\/schakelbare-matrices-voorbeelden-pendelen\/"},"modified":"2023-07-06T08:09:51","modified_gmt":"2023-07-06T08:09:51","slug":"schakelbare-matrices-voorbeelden-pendelen","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/schakelbare-matrices-voorbeelden-pendelen\/","title":{"rendered":"Schakelbare matrices"},"content":{"rendered":"<p>Op deze pagina leggen we uit wat schakelbare matrices zijn. Daarnaast kun je voorbeelden zien om het concept goed te begrijpen en tot slot vind je een stapsgewijze opgeloste oefening waarin we alle matrices leren berekenen die met welke matrix dan ook pendelen.<\/p>\n<h2 class=\"wp-block-heading\"> Wat zijn schakelbare matrices? <\/h2>\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\"> Twee <strong>matrices zijn commuteerbaar<\/strong> als het resultaat van hun product niet afhankelijk is van de volgorde van vermenigvuldiging. Met andere woorden, schakelbare matrices voldoen aan de volgende voorwaarde:<\/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-6eb88f6da7a7fb25d88ae172483b637c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\\cdot B = B \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"104\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<p> Dit is de definitie van commuteerbare matrices. Laten we nu een voorbeeld bekijken:<\/p>\n<h2 class=\"wp-block-heading\"> Voorbeeld van schakelbare matrices<\/h2>\n<p> De volgende twee matrices met afmeting 2\u00d72 zijn schakelbaar tussen de twee:<\/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-d4afa74407be7cf7a0142ce931dbba98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; 0\\\\[1.1ex] 1 &amp; -1 \\end{pmatrix} \\quad B= \\begin{pmatrix} 3&amp; 0\\\\[1.1ex] 1 &amp; 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"229\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> De commutabiliteit van de twee matrices kan worden aangetoond door hun product in beide richtingen te berekenen: <\/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-matrices-commutables-22152-1.webp\" alt=\"voorbeeld van schakelbare matrices met afmeting 2x2\" class=\"wp-image-2759\" width=\"377\" height=\"169\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Zoals u kunt zien, is het resultaat van beide vermenigvuldigingen hetzelfde, ongeacht de volgorde waarin ze worden vermenigvuldigd. Dus de matrixen<\/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-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> En<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> ze zijn schakelbaar.<\/p>\n<h2 class=\"wp-block-heading\"> Opgeloste matrixschakeloefening<\/h2>\n<p> Vervolgens zullen we stap voor stap zien hoe we een commuteerbare matrixoefening kunnen oplossen:<\/p>\n<ul>\n<li> Bepaal alle matrices die pendelen met de volgende vierkante matrix:<\/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-0f69e9df9aa524aeabcc1716a92b5e8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 3 &amp; 1\\\\[1.1ex] 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Om dit probleem op te lossen zullen we een onbekende matrix cre\u00ebren:<\/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-ee9183823ea39248018c37cbac3bf2ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B=\\begin{pmatrix} a &amp; b\\\\[1.1ex] c &amp; d \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"97\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> We moeten daarom deze onbekende matrix vinden.<\/p>\n<p> Om dit te doen, zullen we profiteren van de eigenschap waaraan alle pendelmatrices voldoen:<\/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-6eb88f6da7a7fb25d88ae172483b637c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\\cdot B = B \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"104\" 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-98ac92178351b7dc235918b2bc02ed90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}3 &amp; 1\\\\[1.1ex] 1 &amp; 0\\end{pmatrix}\\cdot \\begin{pmatrix} a &amp; b\\\\[1.1ex] c &amp; d \\end{pmatrix} = \\begin{pmatrix} a &amp; b\\\\[1.1ex] c &amp; d \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 1\\\\[1.1ex] 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"291\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Nu vermenigvuldigen we de matrices aan beide kanten van de vergelijking:<\/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-5bd3e34eadc944aa1aea8f323f9796ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 3a+c &amp;3b+d\\\\[1.1ex] a &amp; b \\end{pmatrix} =  \\begin{pmatrix}3a+b &amp; a\\\\[1.1ex] 3c+d &amp; c \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"256\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Om gelijkheid te laten gelden, moet daarom aan de volgende vergelijkingen worden voldaan:<\/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-d1f3094807b37f4fbc9875b5dddc5f25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} 3a+c=3a+b \\\\[2ex] 3b+d=a \\\\[2ex] a=3c+d\\\\[2ex] b= c \\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"140\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Het enige wat we dus hoeven te doen is het stelsel vergelijkingen op te lossen. Uit de laatste vergelijking kunnen we dat afleiden<\/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-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> moet gelijk zijn aan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> :<\/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-08cf30e231c919c278f8af358e06df4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b=c\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> En als deze twee onbekenden equivalent zijn, wordt de derde vergelijking herhaald met de tweede, we kunnen deze daarom elimineren:<\/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-b3e25af3ab248d099ae0515f9912cdf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} 3a+c=3a+b \\\\[2ex] 3b+d=a \\\\[2ex] \\cancel{a=3c+d}\\\\[2ex] b= c \\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"140\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bovendien kunnen we uit de eerste vergelijking geen conclusies trekken, omdat: <\/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-7608b6e0c6fb91990657aa470c48f5f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3a+c=3a+b \\ \\xrightarrow{b \\ = \\ c} \\ 3a+b=3a+b\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"305\" style=\"vertical-align: -2px;\"><\/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-762f5011b3045c2f20b77035ae8473f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3a=3a\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" 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-378ae3997c3bacdce60cc73eb967fdb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Daarom houden we alleen de tweede en laatste vergelijking over:<\/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-3486d0076e11ddae06ffbfcbb3fab66a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} 3b+d=a \\\\[2ex] b= c \\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"101\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Zodat de matrices pendelen met de matrix<\/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-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> zijn alle vergelijkingen die de twee voorgaande vergelijkingen verifi\u00ebren. Daarom kunnen we, door de gevonden uitdrukkingen vanaf het begin in de onbekende matrix te vervangen, de vorm vinden van matrices die pendelen met<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-944477c7f7578892a57aa3b7c7dd8268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A:\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" 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-ccd60f786e1324e748a7d91e41f86442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} a &amp; b\\\\[1.1ex] c &amp; d \\end{pmatrix} \\ \\longrightarrow \\ \\begin{pmatrix} 3b+d &amp; b \\\\[1.1ex] b &amp; d \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"206\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Goud<\/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-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> En<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4e8716946f6a868f015e0d62f28bc540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> zijn twee re\u00eble getallen.<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p> Dus een voorbeeld van een matrix die met de matrix zou pendelen<\/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-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> zou als volgt zijn:<\/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-0c22c13d155ba46f6a9d0f6891747699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 6 &amp; 1 \\\\[1.1ex] 1 &amp; 3  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Eigenschappen van schakelbare matrices<\/h2>\n<p> Schakelbare matrices hebben de volgende kenmerken:<\/p>\n<ul>\n<li> Schakelbare arrays <strong>hebben niet de transitieve eigenschap<\/strong> . Met andere woorden, zelfs als de matrix\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> pendelen met matrixen<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> En<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> , dit betekent niet dat<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> En<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> zijn hiertussen schakelbaar.<\/li>\n<\/ul>\n<ul>\n<li> <a href=\"https:\/\/mathority.org\/nl\/diagonale-matrix\/\">Diagonale matrices<\/a> pendelen met elkaar, dat wil zeggen dat een diagonale matrix pendelt met elke andere diagonale matrix.<\/li>\n<\/ul>\n<ul>\n<li> Op dezelfde manier pendelt een scalaire matrix in gelijke mate met alle matrices. De <a href=\"https:\/\/mathority.org\/nl\">identiteits- of eenheidsmatrix<\/a> pendelt bijvoorbeeld met alle matrices.<\/li>\n<\/ul>\n<ul>\n<li> Twee <a href=\"https:\/\/mathority.org\/nl\/hermitische-of-hermitische-matrix\/\">Hermitische matrices<\/a> pendelen als hun eigenvectoren (of eigenvectoren) samenvallen.<\/li>\n<\/ul>\n<ul>\n<li> Het is duidelijk dat de <a href=\"https:\/\/mathority.org\/nl\/nulmatrix-nul\/\">nulmatrix<\/a> ook pendelt met alle matrices.<\/li>\n<\/ul>\n<ul>\n<li> Als het product van twee <a href=\"https:\/\/mathority.org\/nl\/symmetrische-matrixvoorbeelden-en-eigenschappen\/\">symmetrische matrices<\/a> een andere symmetrische matrix oplevert, moeten de twee matrices pendelen.<\/li>\n<\/ul>\n<ul>\n<li> Als de diagonalisatie van twee matrices tegelijkertijd kan worden uitgevoerd, moeten ze commuteerbaar zijn. Daarom delen deze twee matrices ook dezelfde orthonormale basis van eigenvectoren of eigenvectoren.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Op deze pagina leggen we uit wat schakelbare matrices zijn. Daarnaast kun je voorbeelden zien om het concept goed te begrijpen en tot slot vind je een stapsgewijze opgeloste oefening waarin we alle matrices leren berekenen die met welke matrix dan ook pendelen. Wat zijn schakelbare matrices? Twee matrices zijn commuteerbaar als het resultaat van &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/schakelbare-matrices-voorbeelden-pendelen\/\"> <span class=\"screen-reader-text\">Schakelbare matrices<\/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-369","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>Schakelbare matrices - 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\/schakelbare-matrices-voorbeelden-pendelen\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Schakelbare matrices - Mathority\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina leggen we uit wat schakelbare matrices zijn. Daarnaast kun je voorbeelden zien om het concept goed te begrijpen en tot slot vind je een stapsgewijze opgeloste oefening waarin we alle matrices leren berekenen die met welke matrix dan ook pendelen. Wat zijn schakelbare matrices? 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Daarnaast kun je voorbeelden zien om het concept goed te begrijpen en tot slot vind je een stapsgewijze opgeloste oefening waarin we alle matrices leren berekenen die met welke matrix dan ook pendelen. Wat zijn schakelbare matrices? 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