{"id":322,"date":"2023-07-06T22:49:54","date_gmt":"2023-07-06T22:49:54","guid":{"rendered":"https:\/\/mathority.org\/nl\/optellen-aftrekken-van-matrices-2x2-3x3-voorbeelden-opgeloste-oefeningen\/"},"modified":"2023-07-06T22:49:54","modified_gmt":"2023-07-06T22:49:54","slug":"optellen-aftrekken-van-matrices-2x2-3x3-voorbeelden-opgeloste-oefeningen","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/optellen-aftrekken-van-matrices-2x2-3x3-voorbeelden-opgeloste-oefeningen\/","title":{"rendered":"Hoe u het optellen en aftrekken van een matrix kunt berekenen"},"content":{"rendered":"<p>Op deze pagina zullen we zien hoe <strong>je matrices kunt optellen en aftrekken<\/strong> . Je hebt ook voorbeelden waarmee je het perfect kunt begrijpen en opgeloste oefeningen zodat je kunt oefenen. Je vindt er ook alle eigenschappen van matrixoptelling.<\/p>\n<h2 class=\"wp-block-heading\"> Hoe matrices optellen en aftrekken?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Om een <strong>optelling (of aftrekking) van twee matrices te berekenen,<\/strong> moet u de elementen optellen (of aftrekken) die dezelfde positie in de matrices innemen.<\/p>\n<h2 class=\"wp-block-heading\"> Voorbeelden: <\/h2>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/addition-et-soustraction-matricielle.webp\" alt=\"voorbeelden van optellen en aftrekken van 2x2 matrices, bewerkingen met matrices\" class=\"wp-image-1267\" width=\"719\" height=\"373\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Houd er rekening mee dat als u twee matrices wilt optellen of aftrekken, ze <strong>dezelfde dimensie moeten hebben.<\/strong> De volgende matrices kunnen bijvoorbeeld niet worden toegevoegd omdat de eerste een 2&#215;2-matrix is en de tweede een 3&#215;2-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-082c648e15685c4ddeac2cc2da502d96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 3 \\\\[1.1ex] 0 &amp; 2 \\end{pmatrix}  + \\begin{pmatrix} 5 &amp; 6 \\\\[1.1ex] -2 &amp; 4 \\\\[1.1ex] 7 &amp; 1 \\end{pmatrix} \\ \\longleftarrow \\ \\color{red}  \\bm{\\times}}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"247\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Opgeloste oefeningen voor het optellen en aftrekken van matrices<\/h2>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Bereken de volgende som van 2&#215;2 matrices: <\/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\/exercice-resolu-daddition-de-matrices-22.webp\" alt=\"oefening stap voor stap opgelost voor toevoeging van 2x2 matrices\" class=\"wp-image-1271\" width=\"175\" 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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Het is een som van twee vierkante matrices met afmeting 2\u00d72: <\/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-1d9428ad89a6bd149d5e63bc500879ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 3 \\\\[1.1ex] 4 &amp; 1  \\end{pmatrix} + \\begin{pmatrix} 2 &amp; 1 \\\\[1.1ex] 3 &amp; -1  \\end{pmatrix} =  \\begin{pmatrix} 2+2 &amp; 3+1 \\\\[1.1ex] 4+3 &amp; 1+(-1)  \\end{pmatrix} = \\begin{pmatrix} \\bm{4} &amp; \\bm{4} \\\\[1.1ex] \\bm{7} &amp; \\bm{0}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"411\" 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\">Oefening 2<\/h3>\n<p> Voer de volgende matrixaftrekking uit: <\/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\/soustraction-matricielle-resolue-exercice-32.webp\" alt=\"oefening opgelost stap voor stap aftrekken van matrices, bewerkingen met matrices\" width=\"193\" height=\"99\" 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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Het is een aftrekking van twee matrices met afmeting 3\u00d72: <\/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-c371e1f01df59f4b8abb018e476e66d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 5 &amp; 2  \\\\[1.1ex] 1 &amp; 6 \\\\[1.1ex] -3 &amp; 0  \\end{pmatrix} - \\begin{pmatrix} 4 &amp; 6 \\\\[1.1ex] -3 &amp; 1 \\\\[1.1ex]-2 &amp; 5 \\end{pmatrix} =  \\begin{pmatrix} 5-4 &amp; 2-6  \\\\[1.1ex] 1-(-3) &amp; 6-1 \\\\[1.1ex] -3-(-2) &amp; 0-5  \\end{pmatrix}  = \\begin{pmatrix} \\bm{1}&amp;  \\bm{-4} \\\\[1.1ex] \\bm{4} &amp; \\bm{5} \\\\[1.1ex] \\bm{-1} &amp; \\bm{-5} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"477\" 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\">Oefening 3<\/h3>\n<p> Zoek het resultaat van de volgende matrixsom van dimensie 3\u00d73: <\/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\/exercice-resolu-daddition-de-matrices-33.webp\" alt=\"oefening stap voor stap opgelost door optelling van 3x3 matrices, bewerkingen met matrices\" width=\"255\" height=\"102\" 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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Het is een som van twee vierkante matrices van de orde 3\u00d73: <\/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-280299cb0b37e1a585466c4570439ec4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 4 &amp; 1 &amp; -2 \\\\[1.1ex] 0 &amp; 3 &amp; 2 \\\\[1.1ex] 5 &amp; 1 &amp; 6 \\end{pmatrix} + \\begin{pmatrix} 2 &amp; 0 &amp; 5 \\\\[1.1ex] -3 &amp; 4 &amp; 1 \\\\[1.1ex] 1 &amp; 7 &amp; 8 \\end{pmatrix} =  \\begin{pmatrix} 4+2 &amp; 1+0 &amp; -2+5 \\\\[1.1ex] 0+(-3) &amp; 3+4 &amp; 2+1 \\\\[1.1ex] 5+1 &amp; 1+7 &amp; 6+8 \\end{pmatrix} = \\begin{pmatrix} \\bm{6}&amp;  \\bm{1} &amp; \\bm{3} \\\\[1.1ex] \\bm{-3} &amp; \\bm{7} &amp; \\bm{3} \\\\[1.1ex] \\bm{6} &amp; \\bm{8} &amp; \\bm{14} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"595\" 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\"> Oefening 4<\/h3>\n<p> Bereken de volgende optelling en aftrekking van vierkante matrices van orde 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\/exercice-combine-daddition-et-de-soustraction-de-matrices-22152.webp\" alt=\"oefening opgelost stap voor stap optellen en aftrekken van 2x2 matrices, bewerkingen met matrices\" width=\"323\" 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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Het is een bewerking gecombineerd met optellen en aftrekken van vierkante matrices van orde 2:<\/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-c9fa4dba7699c0035ce5081756b4f62e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 5 &amp; 1 \\\\[1.1ex] -2 &amp; 4  \\end{pmatrix} +  \\begin{pmatrix} 6 &amp; -2 \\\\[1.1ex] 3 &amp; -5  \\end{pmatrix} -\\begin{pmatrix} -3 &amp; 4 \\\\[1.1ex] 1 &amp; -2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"276\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dus voegen we eerst de matrices aan de linkerkant toe:<\/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-e1544e4da9d5ad2ea3ec2e4ad0326023_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 11 &amp; -1 \\\\[1.1ex] 1 &amp; -1  \\end{pmatrix}  -\\begin{pmatrix} -3 &amp; 4 \\\\[1.1ex] 1 &amp; -2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"188\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En dan berekenen we het aftrekken van matrices: <\/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-bd7f32fc7c9429fdfc3b5b745e85975c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} \\bm{14} &amp; \\bm{-5} \\\\[1.1ex] \\bm{0} &amp; \\bm{1}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"77\" 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\">Oefening 5<\/h3>\n<p> Los de volgende optelling en aftrekking van de matrix op: <\/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\/exercice-combine-daddition-et-de-soustraction-de-matrices-33.webp\" alt=\"oefening opgelost stap voor stap optellen en aftrekken van 3x3 matrices, bewerkingen met matrices\" width=\"437\" height=\"106\" 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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Het is een gecombineerde bewerking van aftrekken en optellen van vierkante matrices van orde 3:<\/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-ae66268adcd61258654056815542cf58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}5 &amp; 3 &amp; -1 \\\\[1.1ex] 6 &amp; -4 &amp; -2 \\\\[1.1ex] 2 &amp; 3 &amp; 2 \\end{pmatrix}-\\begin{pmatrix} 3 &amp; 2 &amp; 6 \\\\[1.1ex]-1 &amp; 5 &amp; 0 \\\\[1.1ex] 2 &amp; 4 &amp; 1 \\end{pmatrix} + \\begin{pmatrix}2 &amp; -1 &amp; 5 \\\\[1.1ex] -3 &amp; 1 &amp; 4 \\\\[1.1ex] 6 &amp; 0 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"373\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Eerst lossen we de matrixaftrekking op:<\/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-4401b28babce2beaaa6f840c4ed8c959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}2 &amp; 1 &amp; -7 \\\\[1.1ex] 7 &amp; -9 &amp; -2 \\\\[1.1ex] 0 &amp; -1 &amp; 1 \\end{pmatrix}+\\begin{pmatrix}2 &amp; -1 &amp; 5 \\\\[1.1ex] -3 &amp; 1 &amp; 4 \\\\[1.1ex] 6 &amp; 0 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"247\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En tenslotte voegen we de matrices toe: <\/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-ffba1ade3d98c434960b54fc0c7ffe1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} \\bm{4} &amp; \\bm{0} &amp; \\bm{-2} \\\\[1.1ex] \\bm{4} &amp; \\bm{-8} &amp; \\bm{2}  \\\\[1.1ex] \\bm{6} &amp; \\bm{-1} &amp; \\bm{4} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"108\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Nu je weet hoe je matrices moet optellen en aftrekken, is het een goed moment om te zien hoe <a href=\"https:\/\/mathority.org\/nl\/vermenigvuldiging-van-2x2-en-3x3-matrices-voorbeelden-en-oefeningen-stap-voor-stap-opgelost\/\">je matrices kunt vermenigvuldigen<\/a> , ongetwijfeld de belangrijkste matrixbewerking. Je vindt er ook opgeloste stap-voor-stap matrixvermenigvuldigingsoefeningen zodat je kunt oefenen, zoals op alle pagina&#8217;s van deze site. \ud83d\ude09<\/p>\n<h2 class=\"wp-block-heading\"> Voeg matrixeigenschappen toe<\/h2>\n<p> Matrixoptelling heeft de volgende kenmerken:<\/p>\n<ul>\n<li> Matrixoptelling heeft de <strong><span style=\"color:#1976d2;\">commutatieve eigenschap<\/span><\/strong> :<\/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-82f98b26399adb4b532b48c18bbbae16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A +B = B + A\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"122\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Daarom is de volgorde waarin we de matrices toevoegen hetzelfde. Om dit te demonstreren, zullen we twee matrices toevoegen door hun volgorde te veranderen en je zult zien hoe het resultaat hetzelfde is.<\/p>\n<p> We gaan daarom verder met het toevoegen van twee matrices in een bepaalde volgorde:<\/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-a7eb454436dc3268ae8d6d2b62f395a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 3 \\\\[1.1ex] 2 &amp; -1 \\end{pmatrix}  +  \\begin{pmatrix} 4 &amp; 1 \\\\[1.1ex] 5 &amp; 2  \\end{pmatrix}= \\begin{pmatrix} \\bm{5} &amp; \\bm{4} \\\\[1.1ex] \\bm{7} &amp; \\bm{1}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"237\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Merk op dat als we de volgorde van optelling van de matrices omkeren, het resultaat hetzelfde blijft: <\/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-c1e9cd77bc490913ed30ff63815da355_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{pmatrix} 4 &amp; 1 \\\\[1.1ex] 5 &amp; 2  \\end{pmatrix}  +  \\begin{pmatrix} 1 &amp; 3 \\\\[1.1ex] 2 &amp; -1 \\end{pmatrix}=  \\begin{pmatrix} \\bm{5} &amp; \\bm{4} \\\\[1.1ex] \\bm{7} &amp; \\bm{1}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"237\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<ul>\n<li> Een andere eigenschap van matrixoptelling is die van het <strong style=\"color: rgb(25, 118, 210);\">tegenovergestelde element:<\/strong><\/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-5195a54259faa7e6f78b82f517a58e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A + (-A) =0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Met andere woorden, als we een matrix plus dezelfde matrix toevoegen, maar waarvan alle elementen van teken veranderen, zal het resultaat een nulmatrix 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-add832e83fe554143cbd4c710315c1c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{pmatrix} 4 &amp; 1 &amp; -3 \\\\[1.1ex] 2 &amp; 0 &amp; 9 \\end{pmatrix} + \\begin{pmatrix} -4 &amp; -1 &amp; 3 \\\\[1.1ex] -2 &amp; 0 &amp; -9 \\end{pmatrix} =  \\begin{pmatrix} \\bm{0} &amp; \\bm{0} &amp; \\bm{0} \\\\[1.1ex] \\bm{0} &amp; \\bm{0} &amp; \\bm{0}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"353\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Matrixoptelling heeft ook de <strong><span style=\"color:#1976d2;\">neutrale elementeigenschap:<\/span><\/strong><\/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<p> Deze eigenschap is het meest voor de hand liggend. Het verwijst naar het feit dat elke matrix plus een matrix vol nullen equivalent is aan dezelfde 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-ac7b0ba246075c196188798be2c6a034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 1 &amp; 5 \\\\[1.1ex] -3 &amp; 4 &amp; 9 \\\\[1.1ex] 1 &amp; 12 &amp; 6 \\end{pmatrix} + \\begin{pmatrix} 0 &amp; 0  &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 0  \\end{pmatrix} =  \\begin{pmatrix} \\bm{2} &amp; \\bm{1} &amp; \\bm{5} \\\\[1.1ex] \\bm{-3} &amp; \\bm{4} &amp; \\bm{9} \\\\[1.1ex] \\bm{1} &amp; \\bm{12} &amp; \\bm{6} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"351\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Matrixoptelling heeft de <strong><span style=\"color:#1976d2;\">associatieve eigenschap:<\/span><\/strong><\/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-9b1aee88fd57af78c40429c93c7a2136_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\left( A + B \\right) + C  =A +  \\left(  B + C \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Daarom is de volgorde waarin we de matrices toevoegen hetzelfde. Kijk naar het volgende voorbeeld, waar we 3 matrices met verschillende volgorde toevoegen en het resultaat hetzelfde is: <\/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-bae8e10bca43351f3a84f83bfe50ab55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =  \\begin{pmatrix} 2  \\\\[1.1ex] 1 \\end{pmatrix}  \\qquad B = \\begin{pmatrix} 4  \\\\[1.1ex] -1  \\end{pmatrix} \\qquad C = \\begin{pmatrix} 3  \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"310\" 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-2cc2b7a14cacc7e403cd729cd863d309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\left( A + B \\right) + C &amp; =\\left(  \\begin{pmatrix} 2  \\\\[1.1ex] 1  \\end{pmatrix}   +  \\begin{pmatrix} 4  \\\\[1.1ex] -1  \\end{pmatrix} \\right) + \\begin{pmatrix} 3  \\\\[1.1ex] 0  \\end{pmatrix}  \\\\[2ex] &amp; =   \\begin{pmatrix} 6  \\\\[1.1ex] 0  \\end{pmatrix} + \\begin{pmatrix} 3  \\\\[1.1ex] 0 \\end{pmatrix} \\\\[2ex] &amp; =\\begin{pmatrix} \\bm{9}  \\\\[1.1ex] \\bm{0} \\end{pmatrix} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"204\" width=\"313\" 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-7ab1f88e74b139451eccb0471988c3db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} A +  \\left(  B + C \\right) &amp; = \\begin{pmatrix} 2  \\\\[1.1ex] 1  \\end{pmatrix}  + \\left( \\begin{pmatrix} 4  \\\\[1.1ex] -1  \\end{pmatrix}  +\\begin{pmatrix} 3  \\\\[1.1ex] 0  \\end{pmatrix} \\right) \\\\[2ex] &amp; =  \\begin{pmatrix} 2  \\\\[1.1ex] 1  \\end{pmatrix} + \\begin{pmatrix} 7  \\\\[1.1ex] -1  \\end{pmatrix} \\\\[2ex] &amp; = \\begin{pmatrix}  \\bm{9}  \\\\[1.1ex] \\bm{0}\\end{pmatrix} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"204\" width=\"314\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Op deze pagina zullen we zien hoe je matrices kunt optellen en aftrekken . Je hebt ook voorbeelden waarmee je het perfect kunt begrijpen en opgeloste oefeningen zodat je kunt oefenen. Je vindt er ook alle eigenschappen van matrixoptelling. Hoe matrices optellen en aftrekken? Om een optelling (of aftrekking) van twee matrices te berekenen, moet &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/optellen-aftrekken-van-matrices-2x2-3x3-voorbeelden-opgeloste-oefeningen\/\"> <span class=\"screen-reader-text\">Hoe u het optellen en aftrekken van een matrix kunt berekenen<\/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":[52],"tags":[],"class_list":["post-322","post","type-post","status-publish","format-standard","hentry","category-schilderijen"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Hoe matrix optellen en aftrekken te berekenen - 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\/optellen-aftrekken-van-matrices-2x2-3x3-voorbeelden-opgeloste-oefeningen\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hoe matrix optellen en aftrekken te berekenen - Mathority\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina zullen we zien hoe je matrices kunt optellen en aftrekken . 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