{"id":333,"date":"2023-07-06T19:13:46","date_gmt":"2023-07-06T19:13:46","guid":{"rendered":"https:\/\/mathority.org\/nl\/voorbeelden-van-matrix-minor-adjuncten-en-complementaire-adjuncten-en-opgeloste-oefeningen\/"},"modified":"2023-07-06T19:13:46","modified_gmt":"2023-07-06T19:13:46","slug":"voorbeelden-van-matrix-minor-adjuncten-en-complementaire-adjuncten-en-opgeloste-oefeningen","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/voorbeelden-van-matrix-minor-adjuncten-en-complementaire-adjuncten-en-opgeloste-oefeningen\/","title":{"rendered":"Minor, assistent en assistent complementaire matrix"},"content":{"rendered":"<p>In deze sectie zullen we zien wat ze zijn en hoe je een <strong>complementaire minor, een adjunct en de adjunct-matrix<\/strong> kunt berekenen. Daarnaast vind je voorbeelden, zodat je het perfect begrijpt, en oefeningen stap voor stap opgelost, zodat je kunt oefenen.<\/p>\n<h2 class=\"wp-block-heading\"> Wat is de aanvullende minor?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Het wordt <strong>het kleine complement<\/strong> van een element genoemd.<\/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-41d4a89db3722950dc94351832a1bcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> aan de determinant die wordt verkregen door het verwijderen van de lijn<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-695d9d59bd04859c6c99e7feb11daab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> en de kolom<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43c82d5bb00a7568d935a12e3bd969dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"j\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> van een matrix.<\/p>\n<h2 class=\"wp-block-heading\"> Hoe bereken je de complementaire minor van een element?<\/h2>\n<p> Laten we eens kijken hoe de complementaire minor van een element wordt berekend aan de hand van enkele voorbeelden:<\/p>\n<h3 style=\"color:#00B0FF\"> Voorbeeld 1:<\/h3>\n<p> Bereken het <strong>kleine complement van 1<\/strong> van de volgende 3 \u00d7 3 vierkante 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-0a9db280911827ab5d64507cfe71aed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\left( \\begin{array}{ccc} 6 &amp; 1 &amp; 7 \\\\[1.1ex] 3 &amp; 2 &amp; 0 \\\\[1.1ex] 5 &amp; 8 &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> De <strong>complementaire minor van 1<\/strong> is de determinant van de matrix die overblijft bij het elimineren van de rij en kolom waar de 1 zich bevindt. Dat wil zeggen, het verwijderen van de eerste rij en de tweede kolom:<\/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-cb0021e61d4a3779378734771071bdfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{ccc} \\cellcolor[HTML]{F5B7B1}6 &amp; \\cellcolor[HTML]{F5B7B1}1 &amp; \\cellcolor[HTML]{F5B7B1}7 \\\\ &amp; \\cellcolor[HTML]{F5B7B1} &amp; \\\\[-2ex] 3 &amp; \\cellcolor[HTML]{F5B7B1}2 &amp; 0 \\\\ &amp; \\cellcolor[HTML]{F5B7B1} &amp; \\\\[-2ex] 5 &amp;  \\cellcolor[HTML]{F5B7B1}8 &amp; 4                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"486\" 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-7a38c134fa8e592ff15956701ce4521c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 1} =  \\begin{vmatrix} 3 &amp; 0 \\\\[1.1ex] 5 &amp; 4 \\end{vmatrix} = \\bm{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"331\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 style=\"color:#00B0FF\"> Voorbeeld 2:<\/h3>\n<p> Deze keer berekenen we de <strong>complementaire minor van 0<\/strong> van dezelfde matrix als voorheen:<\/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-0a9db280911827ab5d64507cfe71aed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\left( \\begin{array}{ccc} 6 &amp; 1 &amp; 7 \\\\[1.1ex] 3 &amp; 2 &amp; 0 \\\\[1.1ex] 5 &amp; 8 &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> De <strong>complementaire minor van 0<\/strong> is de determinant van de matrix door de rij en kolom te verwijderen waar de 0 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-eeeb42496216ad8689d1a70807b56644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{ccc} 6 &amp; 1 &amp; \\cellcolor[HTML]{F5B7B1}7 \\\\ &amp;  &amp; \\cellcolor[HTML]{F5B7B1} \\\\[-2ex] \\cellcolor[HTML]{F5B7B1} 3 &amp; \\cellcolor[HTML]{F5B7B1}2 &amp; \\cellcolor[HTML]{F5B7B1}0 \\\\ &amp; &amp;\\cellcolor[HTML]{F5B7B1} \\\\[-2ex] 5 &amp;  8 &amp; \\cellcolor[HTML]{F5B7B1}4                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"492\" 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-bd1eff11f2081d56b20c97203fc053c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 0} =  \\begin{vmatrix} 6 &amp; 1 \\\\[1.1ex] 5 &amp; 8 \\end{vmatrix} = \\bm{43}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"332\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Opgeloste oefeningen voor aanvullende minoren<\/h2>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Bereken het kleinste complement van 3 van de volgende 3\u00d73-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-16dac836fa9d63465e46dd35e2f36249_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 5 &amp; 1 &amp; 2 \\\\[1.1ex] 3 &amp; 4 &amp; 7 \\\\[1.1ex] -1 &amp; 6 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\"> De complementaire minor van 3 is de determinant van de matrix die overblijft na het verwijderen van de rij en kolom waar de 3 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-23b957e07aa004db36332997e906169f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 3} = \\begin{vmatrix} 1 &amp; 2 \\\\[1.1ex] 6 &amp; 7 \\end{vmatrix} = \\bm{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"328\" 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> Zoek de complementaire minor van 5 uit de volgende matrix 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-870e864969258f55a07ecd82c68c3132_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -2 &amp; 4 &amp; -2 \\\\[1.1ex] 1 &amp; 3 &amp; 4 \\\\[1.1ex] 5 &amp; 8 &amp; 1 \\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-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\"> De complementaire minor van 5 is de determinant van de matrix die we verkrijgen door de rij en kolom te verwijderen waar de 5 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-f9fc980c8adf2b46e6bcfea0ef69737a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 5} = \\begin{vmatrix} 4 &amp; -2 \\\\[1.1ex] 3 &amp; 4 \\end{vmatrix} = \\bm{22}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"344\" 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> Bereken het kleine complement van 6 van de volgende 4\u00d74-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-c61e20d710e35ab2b27c94ca720e01a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 1 &amp; 3 &amp; 4 \\\\[1.1ex] 2 &amp; 6 &amp; -1 &amp; 8 \\\\[1.1ex] 3 &amp; 9 &amp; -1 &amp; 4 \\\\[1.1ex] 5 &amp; 4 &amp; 1 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"119\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\"> De complementaire minor van 6 is de determinant van de matrix die overblijft na het verwijderen van de rij en kolom waar de 6 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-60150a09c3023b5f1e147bf437df719c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Menor complementario de 6} = \\begin{vmatrix} 1 &amp; 3 &amp; 4 \\\\[1.1ex] 3 &amp; -1 &amp; 4 \\\\[1.1ex] 5&amp; 1 &amp; 3 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"325\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We lossen de determinant op met de Sarrusregel: <\/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-f331c9c3723df34235d8f172f5f41750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; 3 &amp; 4 \\\\[1.1ex] 3 &amp; -1 &amp; 4 \\\\[1.1ex] 5 &amp; 1 &amp; 3 \\end{vmatrix}=-3+60+12+20-4-27 = \\bm{58}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"359\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\">Wat is de adjoint van een array-element? <\/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 align=\"LEFT\"> De <strong>plaatsvervanger<\/strong> van<\/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-41d4a89db3722950dc94351832a1bcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> , dwz regelitem<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-695d9d59bd04859c6c99e7feb11daab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> en de kolom<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43c82d5bb00a7568d935a12e3bd969dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"j\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> , wordt verkregen met de volgende formule: <\/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-dcce4b79a3549da03df7c78b678add31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } a_{ij} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"430\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h2 class=\"wp-block-heading\"> Hoe krijg ik de adjoint van een array-element?<\/h2>\n<p> Laten we eens kijken hoe de adjunct van een element wordt berekend aan de hand van verschillende voorbeelden:<\/p>\n<h3 style=\"color:#00B0FF\"> Voorbeeld 1:<\/h3>\n<p> Bereken de <strong>adjunct van 4<\/strong> van de volgende matrix 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-0acdd22355294e7c19583b1538c9070d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 1 &amp; 2 &amp; 3 \\\\[1.1ex] 4 &amp; 5 &amp; 6 \\\\[1.1ex] 7 &amp; 8 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" 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-32a95816558c4ad5b48cb3e6b06eb8c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } 4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> De 4 staat in <strong>rij 2<\/strong> en <strong>kolom 1<\/strong> , dus in dit geval<\/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-16ec1d81dc1a7d422c1985f813b6603b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" 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-eb4d87f6d5922c8ff5cf03f1ea28faaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"j = 1 :\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\"><\/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-aea771762912a2598233c359dabc88e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 = \\displaystyle (-1)^{2+1} \\bm{\\cdot} \\text{Menor complementario de } 4\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"409\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> En zoals we eerder zagen, is het <strong>kleine complement van 4<\/strong> de determinant van de matrix, waardoor de rij en kolom worden ge\u00eblimineerd waar de 4 zich bevindt. Daarom:<\/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-b1cdd0dac0607a955fcfb19849c05276_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de} 4 = \\displaystyle(-1)^{2+1} \\bm{\\cdot}  \\begin{vmatrix}  2 &amp; 3  \\\\[1.1ex]  8 &amp; 9 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"241\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Nu lossen we de determinant op en <strong>vinden de adjunct van 4:<\/strong> <\/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-d9522581f22ca9b6b750bb9e3e7b0a60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 = (-1)^{3} \\bm{\\cdot}  (-5) = -1 \\cdot (-6) = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"339\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div style=\"background-color:#fffde7;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p align=\"LEFT\"> <strong>Onthoud<\/strong> dat een negatief getal verhoogd tot een even exponent positief is. Als de -1 wordt verhoogd naar een even getal, wordt deze dus positief.<\/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-d5044fab01a117e78360f8982b1d37d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\longrightarrow}(-1)^2=\\bm{+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p align=\"LEFT\"> Aan de andere kant, als een negatief getal wordt verhoogd tot een oneven exponent, is het negatief. Als de -1 wordt verhoogd naar een oneven getal, zal deze dus altijd negatief 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-8b51896f8d21b327891018914418bf6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\longrightarrow}(-1)^3=\\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<h3 style=\"color:#00B0FF\"> Voorbeeld 2:<\/h3>\n<p> We zullen de <strong>plaatsvervanger van 5<\/strong> vinden van dezelfde matrix als voorheen: <\/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-0acdd22355294e7c19583b1538c9070d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 1 &amp; 2 &amp; 3 \\\\[1.1ex] 4 &amp; 5 &amp; 6 \\\\[1.1ex] 7 &amp; 8 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" 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-330e8801d4047cb9970efea37bb1eb8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 5 = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } 5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"405\" style=\"vertical-align: -5px;\"><\/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-f3e47d30b12e053b3f5950033640b662_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de} 5 = \\displaystyle(-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 3  \\\\[1.1ex]  7 &amp; 9 \\end{vmatrix} = 1 \\cdot (-12) = \\bm{-12}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"388\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 style=\"color:#00B0FF\"> Voorbeeld 3:<\/h3>\n<p> Laten we de <strong>plaatsvervanger van 3<\/strong> van dezelfde matrix maken: <\/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-0acdd22355294e7c19583b1538c9070d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 1 &amp; 2 &amp; 3 \\\\[1.1ex] 4 &amp; 5 &amp; 6 \\\\[1.1ex] 7 &amp; 8 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" 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-bb298a5166e562f6a168addd0d1450a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 3 = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } 3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"406\" style=\"vertical-align: -5px;\"><\/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-954d6137c753a58e91682334addc5345_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de} 3 \\displaystyle =  (-1)^{1+3} \\bm{\\cdot} \\begin{vmatrix} 4 &amp; 5  \\\\[1.1ex]  7 &amp; 8 \\end{vmatrix} = 1 \\cdot (-3) = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"370\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> De adjoint van een element wordt gebruikt om determinanten te berekenen, zoals we later zullen zien, en om de adjunct-matrix te berekenen, wat we nu zullen zien.<\/p>\n<h2 class=\"wp-block-heading\"> Opgeloste oefeningen voor assistenten<\/h2>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Bereken de adjunct van 2 van de volgende 3\u00d73 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-340d5ef9265b33c7a6ad4ac7d72633f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 3 &amp; 1 \\\\[1.1ex] -1 &amp; -3 &amp; 5 \\\\[1.1ex] 5 &amp; 3 &amp; 1 \\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-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\"> Om het resultaat van de adjoint van 2 te verkrijgen, past u eenvoudigweg de formule voor de adjoint van een element 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-27e737fcb3ffe43ab7b1ee30a091bfb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de 2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"405\" style=\"vertical-align: -5px;\"><\/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-74e69b36278f7b0518a20be2e02aea4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} \\displaystyle = (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} -3 &amp; 5 \\\\[1.1ex] 3 &amp; 1 \\end{vmatrix} = 1 \\cdot (-18) = \\bm{-18}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"402\" 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> Zoek de adjunct van 4 van de volgende matrix 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-e21733cd834cdbeed5ca8fc433068ccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 3 &amp; 1 &amp; -1 \\\\[1.1ex] 2 &amp; 9 &amp; 4 \\\\[1.1ex] 6 &amp; 5 &amp; -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\"> Om de plaatsvervanger van 4 te verkrijgen, moeten we de formule voor de plaatsvervanger van een element gebruiken: <\/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-58a3653b2ec21f65f85689ffbe978079_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 4} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de 4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"406\" style=\"vertical-align: -5px;\"><\/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-c4a2228588aeef08594e7f3cc93c53ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 4} \\displaystyle = (-1)^{2+3} \\bm{\\cdot} \\begin{vmatrix} 3 &amp; 1 \\\\[1.1ex] 6 &amp; 5 \\end{vmatrix} = -1 \\cdot 9 = \\bm{-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"356\" 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:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\"> Oefening 3<\/h3>\n<p> Zoek de plaatsvervanger van 7 van de volgende 4\u00d74-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-64b3cf6b9f34fce5f66d24502f2434a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 2 &amp; 5 &amp; -2 \\\\[1.1ex] 3 &amp; 1 &amp; -3 &amp; 3 \\\\[1.1ex] 2 &amp; -1 &amp; 4 &amp; 0 \\\\[1.1ex] 2 &amp; 7 &amp; 9 &amp; -4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"147\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\"> Om de adjunct van 7 te maken, passen we de formule voor de adjunct van een element 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-4b62c0cebb18f5b2ae6d01078babc00b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 7}=(-1)^{4+2} \\bm{\\cdot} \\text{Menor complementario de 7}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"409\" style=\"vertical-align: -5px;\"><\/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-54f5200bb9a57df8b0aa73271ec26c7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 7} \\displaystyle = (-1)^{4+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 5 &amp; -2 \\\\[1.1ex] 3 &amp; -3 &amp; 3 \\\\[1.1ex] 2 &amp; 4 &amp; 0\\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"293\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We passen de regel van Sarrus toe om de determinant van de derde orde op te lossen: <\/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-34d456bf805c4a6d8673d00febc983dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = (-1)^{6} \\bm{\\cdot} \\bigl[0+30-24-12-12-0\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"276\" style=\"vertical-align: -7px;\"><\/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-b228f8cd5f96cfdbd7e80138cb109e3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = 1 \\bm{\\cdot} \\bigl[-18 \\bigr] = \\bm{-18}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\">Wat is de bijgevoegde matrix?<\/h2>\n<p> De <strong>bijgevoegde array<\/strong> is een array waarin alle elementen zijn vervangen door hun plaatsvervangers.<\/p>\n<h2 class=\"wp-block-heading\"> Hoe bereken ik de adjunct-matrix?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Om de <strong>plaatsvervangermatrix<\/strong> te berekenen, moeten we alle elementen van de matrix vervangen door hun plaatsvervangers.<\/p>\n<p> Laten we eens kijken hoe de samengevoegde matrix wordt gemaakt aan de hand van een voorbeeld: <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-119\"><\/div>\n<\/div>\n<h3 style=\"color:#00B0FF\"> Voorbeeld:<\/h3>\n<p> Bereken de adjunct-matrix van de volgende vierkante matrix 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-e1d84d025062b24cb6a7ef021cb55de1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A  =  \\begin{pmatrix} 4 &amp; -1 \\\\[1.1ex] 3 &amp; 2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"109\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Om de adjunct-matrix te berekenen, moeten we <strong>de adjunct van elk element van de matrix berekenen<\/strong> . Daarom zullen we eerst de adjuncten van alle elementen oplossen met de formule: <\/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-dcce4b79a3549da03df7c78b678add31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } a_{ij} = (-1)^{i+j} \\bm{\\cdot} \\text{Menor complementario de } a_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"430\" style=\"vertical-align: -6px;\"><\/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-30683bf4304e3072c4fcf46610e06e05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 4 =\\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} 2 \\end{vmatrix} = 1 \\cdot 2 = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"302\" style=\"vertical-align: -7px;\"><\/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-04af89fae8a9060940f892f5d1e0c51d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -1} =\\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix} 3 \\end{vmatrix} = -1 \\cdot 3 = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"336\" style=\"vertical-align: -7px;\"><\/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-042a24b0f0896742500d7455e8f944ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 3 =\\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} -1 \\end{vmatrix} = -1 \\cdot (-1) = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"357\" style=\"vertical-align: -7px;\"><\/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-a0d3e6017c878bc47df1c509936fbcf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de } 2 =\\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 4 \\end{vmatrix} = 1 \\cdot 4 = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"303\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Nu hoeven we alleen maar elk element in de array te vervangen<\/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> door zijn plaatsvervanger om de <strong>plaatsvervangermatrix van<\/strong> te vinden<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1372441aae26d85aebdcbe3baf70cf56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{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-4c4c2583218c84e184a1911972dca72b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{2} &amp; \\bm{-3} \\\\[1.1ex] \\bm{1} &amp; \\bm{4}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> En op deze manier wordt de plaatsvervanger van een matrix gevonden. Maar u vraagt zich waarschijnlijk af waar al deze berekeningen voor dienen? Welnu, een van de voordelen van matrix join is het berekenen van de <a href=\"https:\/\/mathority.org\/nl\/omgekeerde-matrix\/\">inverse van een matrix<\/a> . In feite is de meest gebruikelijke methode voor het vinden van de inverse matrix de adjunct-matrixmethode.<\/p>\n<h2 class=\"wp-block-heading\"> Adjunct-matrixproblemen opgelost<\/h2>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Bereken de adjunct-matrix van de volgende 2\u00d72 vierkante 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-b5fbfc1c22345724f35d7208214f8592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 3  \\\\[1.1ex] -4 &amp; 1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\"> Om de adjunct-matrix te berekenen, moeten we de adjunct-waarde van elk element van de matrix berekenen. Daarom zullen we eerst de adjuncten van alle elementen oplossen met de formule: <\/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-86e59cf1a404062a425e15fde85090cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} =\\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} 1 \\end{vmatrix} = 1 \\cdot 1 = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"302\" style=\"vertical-align: -7px;\"><\/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-74a9e31be5bf93b62a51c1bf23200f48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 3} =\\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix} -4 \\end{vmatrix} = -1 \\cdot (-4) = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"358\" style=\"vertical-align: -7px;\"><\/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-25393a1a057c92d2eea1f57ac2ae914f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -4} =\\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} 3 \\end{vmatrix} = -1 \\cdot 3 = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"336\" style=\"vertical-align: -7px;\"><\/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-f05aa937b693794438cf7c04b75fc924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 1} =\\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 2 \\end{vmatrix} = 1 \\cdot 2 = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"302\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu hoeven we alleen maar elk element in de array te vervangen<\/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> door zijn plaatsvervanger om de plaatsvervangermatrix van te vinden <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed7f99fecb7719c7108eaecc0a21dad2_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-5d3fdee2506136365c141a81596f1d22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{1} &amp; \\bm{4} \\\\[1.1ex] \\bm{-3} &amp; \\bm{2}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"159\" 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> Zoek de adjunct-matrix van de volgende tweede-orde 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-b95133fbf999cb6585b3a32f4b1b906b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 6 &amp; -2  \\\\[1.1ex] 3 &amp; -7  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\"> Om de adjunct-matrix te berekenen, moeten we de adjunct-waarde van elk element van de matrix berekenen. Daarom zullen we eerst de adjuncten van alle elementen oplossen met de formule: <\/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-35b5b261848474e8eb940bee9147c21b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 6} =\\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} -7 \\end{vmatrix} = 1 \\cdot (-7) = \\bm{-7}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"358\" style=\"vertical-align: -7px;\"><\/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-0f1e6a5a5c504b3b6d06e5d3d8e0862e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -2} =\\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix} 3 \\end{vmatrix} = -1 \\cdot 3 = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"336\" style=\"vertical-align: -7px;\"><\/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-05a49201adc9cef4d1e9903157860e4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 3} =\\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} -2 \\end{vmatrix} = -1 \\cdot (-2) = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"357\" style=\"vertical-align: -7px;\"><\/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-9e936a7e026d5fc05b60e032170c85c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -7} =\\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 6 \\end{vmatrix} = 1 \\cdot 6 = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"309\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu hoeven we alleen maar elk element in de array te vervangen<\/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> door zijn plaatsvervanger om de plaatsvervangermatrix van te vinden <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed7f99fecb7719c7108eaecc0a21dad2_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-604112d6e7d95ca76dd5266dc2eceb86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{-7} &amp; \\bm{-3} \\\\[1.1ex] \\bm{2} &amp; \\bm{6}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"173\" 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 3<\/h3>\n<p> Bereken de adjunct-matrix van de volgende 3\u00d73-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-0072b68810f2662ae9f4ec3d11902f97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 3 &amp; -1 \\\\[1.1ex] 2 &amp; 4 &amp; 0 \\\\[1.1ex] 5 &amp; 0 &amp; -2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\"> Om de adjunct-matrix te berekenen, moeten we de adjunct-waarde van elk element van de matrix berekenen. Daarom zullen we eerst de adjuncten van alle elementen oplossen met de formule: <\/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-68e2bee7e07b5749033cdf67d90684a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 1} = \\displaystyle (-1)^{1+1} \\bm{\\cdot} \\begin{vmatrix} 4 &amp; 0 \\\\[1.1ex] 0 &amp; -2\\end{vmatrix} = 1 \\cdot (-8) = \\bm{-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"385\" 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-88120e3a6fa0e6ba43c654ce7884eb41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 3} = \\displaystyle (-1)^{1+2} \\bm{\\cdot} \\begin{vmatrix}  2 &amp; 0 \\\\[1.1ex] 5 &amp; -2\\end{vmatrix} = -1 \\cdot (-4) = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"385\" 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-49c170f202956d9571fcce88cd389889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -1} = \\displaystyle (-1)^{1+3} \\bm{\\cdot} \\begin{vmatrix} 2 &amp; 4 \\\\[1.1ex] 5 &amp; 0\\end{vmatrix} = 1 \\cdot (-20) = \\bm{-20}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"395\" 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-9dd9f81ddb6bd58f2a4e1241c3fbfdb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 2} = \\displaystyle (-1)^{2+1} \\bm{\\cdot} \\begin{vmatrix} 3 &amp; -1 \\\\[1.1ex] 0 &amp; -2\\end{vmatrix} = -1 \\cdot (-6) = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"385\" 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-ee11d10a5ef1719e3eee0d1de8e2fd1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 4} = \\displaystyle (-1)^{2+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; -1 \\\\[1.1ex] 5 &amp; -2\\end{vmatrix} = 1 \\cdot 3 = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"343\" 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-327cba2dd78055703b66b887083d3a50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 0} = \\displaystyle (-1)^{2+3} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 3  \\\\[1.1ex] 5 &amp; 0 \\end{vmatrix} = -1 \\cdot (-15) = \\bm{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"388\" 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-d5df97c790e24f1257c7d1073c4e2af8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 5} = \\displaystyle (-1)^{3+1} \\bm{\\cdot} \\begin{vmatrix} 3 &amp; -1 \\\\[1.1ex] 4 &amp; 0 \\end{vmatrix} = 1 \\cdot 4 = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"343\" 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-0d0cd9b3ea07312942362d52f07c04bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de 0} = \\displaystyle (-1)^{3+2} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; -1 \\\\[1.1ex] 2 &amp; 0\\end{vmatrix} = -1 \\cdot 2 = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"370\" 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-00f3983f64257be282584209b8f2d842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adjunto de -2} = \\displaystyle (-1)^{3+3} \\bm{\\cdot} \\begin{vmatrix} 1 &amp; 3 \\\\[1.1ex] 2 &amp; 4 \\end{vmatrix} = 1 \\cdot (-2) = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"376\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu hoeven we alleen maar elk element in de array te vervangen<\/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> door zijn plaatsvervanger om de plaatsvervangermatrix van te vinden <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed7f99fecb7719c7108eaecc0a21dad2_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-01e49ffda72034d74b18ecdd37d1e3b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Adj} (A)  =  \\begin{pmatrix} \\bm{-8} &amp; \\bm{4} &amp; \\bm{-20} \\\\[1.1ex] \\bm{6} &amp; \\bm{3} &amp; \\bm{15} \\\\[1.1ex] \\bm{4} &amp; \\bm{-2} &amp; \\bm{-2}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"223\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In deze sectie zullen we zien wat ze zijn en hoe je een complementaire minor, een adjunct en de adjunct-matrix kunt berekenen. Daarnaast vind je voorbeelden, zodat je het perfect begrijpt, en oefeningen stap voor stap opgelost, zodat je kunt oefenen. Wat is de aanvullende minor? Het wordt het kleine complement van een element genoemd. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/voorbeelden-van-matrix-minor-adjuncten-en-complementaire-adjuncten-en-opgeloste-oefeningen\/\"> <span class=\"screen-reader-text\">Minor, assistent en assistent complementaire matrix<\/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":[63],"tags":[],"class_list":["post-333","post","type-post","status-publish","format-standard","hentry","category-inverse-matrix"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Minor, assistent en assistent complementaire matrix - 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\/voorbeelden-van-matrix-minor-adjuncten-en-complementaire-adjuncten-en-opgeloste-oefeningen\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Minor, assistent en assistent complementaire matrix - Mathority\" \/>\n<meta property=\"og:description\" content=\"In deze sectie zullen we zien wat ze zijn en hoe je een complementaire minor, een adjunct en de adjunct-matrix kunt berekenen. Daarnaast vind je voorbeelden, zodat je het perfect begrijpt, en oefeningen stap voor stap opgelost, zodat je kunt oefenen. Wat is de aanvullende minor? 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