{"id":336,"date":"2023-07-06T17:52:46","date_gmt":"2023-07-06T17:52:46","guid":{"rendered":"https:\/\/mathority.org\/nl\/voorbeelden-van-matrixvergelijkingen-en-opgeloste-oefeningen-van-2x2-en-3x3-matrices\/"},"modified":"2023-07-06T17:52:46","modified_gmt":"2023-07-06T17:52:46","slug":"voorbeelden-van-matrixvergelijkingen-en-opgeloste-oefeningen-van-2x2-en-3x3-matrices","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/voorbeelden-van-matrixvergelijkingen-en-opgeloste-oefeningen-van-2x2-en-3x3-matrices\/","title":{"rendered":"Matrixvergelijkingen"},"content":{"rendered":"<p>Op deze pagina leert u wat <strong>matrixvergelijkingen<\/strong> zijn en hoe u ze kunt oplossen. Daarnaast vind je voorbeelden en opgeloste oefeningen van vergelijkingen met matrices.<\/p>\n<h2 class=\"wp-block-heading\"> Wat zijn matrixvergelijkingen?<\/h2>\n<p> <strong>Matrixvergelijkingen<\/strong> lijken op normale vergelijkingen, maar in plaats van uit getallen te bestaan, bestaan ze uit matrices. Bijvoorbeeld:<\/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-2bc59624603d48ea9b4df50b4c052437_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  AX=B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Daarom zal oplossing X ook een matrix zijn.<\/p>\n<p> Zoals je al weet, kunnen matrices niet worden gesplitst. Daarom kan de matrix X niet worden gewist door de matrix die deze vermenigvuldigde te delen aan de andere kant 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-13f935eb2129110be40aa176554bb557_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\renewcommand{\\CancelColor}{\\color{red}}  \\xcancel{X =\\cfrac{B}{A}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"57\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Integendeel, om de X-matrix leeg te maken moet een hele procedure worden gevolgd. Laten we dus eens kijken hoe we matrixvergelijkingen kunnen oplossen met een opgeloste oefening:<\/p>\n<h2 class=\"estil_titol_H2 wp-block-heading\"> Hoe matrixvergelijkingen op te lossen. Voorbeeld:<\/h2>\n<ul>\n<li> Los de volgende matrixvergelijking op:<\/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-c9274aedf7d1f424b7e21547f7968321_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  AX+B = C\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" 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-9727c78818a9661573310f22ec2fb3cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A =\\begin{pmatrix}2 &amp; 1 \\\\[1.1ex] 4 &amp; 3 \\end{pmatrix} \\qquad B = \\begin{pmatrix} 3 &amp; -1 \\\\[1.1ex] 0 &amp; 5 \\end{pmatrix} \\qquad C =\\begin{pmatrix} 2 &amp; 1 \\\\[1.1ex] 6 &amp; -3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Het eerste dat we moeten doen is matrix X oplossen <strong>. Dus trekken we matrix B af<\/strong> <strong>van de andere kant van de vergelijking:<\/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-c9274aedf7d1f424b7e21547f7968321_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  AX+B = C\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" 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-9e74a9aaf9e3c11fb261374224402346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  AX = C-B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"103\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Om het wissen te voltooien, kan de matrix niet worden verdeeld. Maar we moeten het volgende doen:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> We moeten beide zijden van de vergelijking vermenigvuldigen met de <strong>inverse van de matrix die de matrix X vermenigvuldigt<\/strong> en bovendien beide zijden vermenigvuldigen <strong>met de zijde waar de matrix zich bevindt.<\/strong><\/p>\n<p> In dit geval is de matrix die X vermenigvuldigt A, en deze bevindt zich links ervan. <strong>We vermenigvuldigen daarom links en rechts van de vergelijking met de inverse van A<\/strong> (A <sup>-1<\/sup> ):<\/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-9e74a9aaf9e3c11fb261374224402346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  AX = C-B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"103\" 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-d233c41796c59c73995600f80e74f323_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\definecolor{vermell}{HTML}{F44336} \\color{vermell}\\bm{A^{-1}} \\color{black} \\cdot AX =  \\color{vermell}\\bm{A^{-1}} \\color{black}  \\cdot (C-B)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"587\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Een matrix vermenigvuldigd met zijn inverse is gelijk aan de identiteitsmatrix. Nog<\/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-7ecd5173741978b59218941381221723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{A^{-1} \\cdot A = I }:\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" 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-58279bb023cd9b14c2019eccfc240afa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  IX = A^{-1} \\cdot (C-B)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Elke matrix vermenigvuldigd met de identiteitsmatrix geeft dezelfde matrix. Nog:<\/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-de90329d45b7fa427640506649c111e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  X = A^{-1} \\cdot (C-B)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> En op deze manier <strong>hebben we X al gewist.<\/strong> Voer nu gewoon de matrixbewerkingen uit. We berekenen dus eerst de <a href=\"https:\/\/mathority.org\/nl\/omgekeerde-matrix\/\">2 \u00d7 2 inverse matrix<\/a> van A:<\/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-b79c0ae6349ac5ac0267e179e641b66e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A =\\begin{pmatrix}2 &amp; 1 \\\\[1.1ex] 4 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" 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-1fe85ec6c4385daba7d2488b0d60ee2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1} = \\cfrac{1}{\\vert A \\vert } \\cdot \\Bigl( \\text{Adj}(A)\\Bigr)^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"175\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> We berekenen de adjunct van de matrix A:<\/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-1eb7c7a828453c5310d59386f0303b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{2} \\cdot \\begin{pmatrix}3 &amp; -4 \\\\[1.1ex] -1 &amp; 2 \\end{pmatrix}^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"173\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p> En zodra de aangrenzende matrix is gevonden, gaan we verder met het berekenen van de <a href=\"https:\/\/mathority.org\/nl\/voorbeelden-van-getransponeerde-of-getransponeerde-matrix-en-opgeloste-oefeningen\/\">getransponeerde matrix<\/a> om de inverse matrix te bepalen:<\/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-aa12c355319a6894e76343c9cb9185d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{2} \\cdot \\begin{pmatrix}3 &amp; -1 \\\\[1.1ex] -4 &amp; 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"164\" 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-a2fd06e0ad4a2a18560f644b718dadf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\begin{pmatrix} \\frac{3}{2} &amp; -\\frac{1}{2} \\\\[1.3ex] -2 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"143\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Nu vervangen we alle matrices in de uitdrukking om X te berekenen:<\/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-de90329d45b7fa427640506649c111e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  X = A^{-1} \\cdot (C-B)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"147\" 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-99716e9accb7ee578fb1119d4e800e4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  X = \\begin{pmatrix} \\frac{3}{2} &amp; -\\frac{1}{2} \\\\[1.3ex] -2 &amp; 1\\end{pmatrix} \\cdot \\left(\\begin{pmatrix} \\vphantom{\\frac{3}{2}} 2 &amp; 1 \\\\[1.3ex] 6 &amp; -3\\end{pmatrix}-\\begin{pmatrix} \\vphantom{\\frac{3}{2}}3 &amp; -1 \\\\[1.3ex] 0 &amp; 5 \\end{pmatrix}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"341\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> En we gaan verder met het oplossen van de bewerkingen met matrices. We berekenen eerst de haakjes door de matrices af te trekken:<\/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-d07c28ad6104e391605836ecdd297251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  X = \\begin{pmatrix} \\frac{3}{2} &amp; -\\frac{1}{2} \\\\[1.3ex] -2 &amp; 1\\end{pmatrix}\\begin{pmatrix} -1 &amp; 2 \\\\[1.1ex] 6 &amp; -8 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"220\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> En ten slotte vermenigvuldigen we de 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-b28076f6ab18dc77a0083388046c5cd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  X = \\begin{pmatrix} \\frac{3}{2}\\cdot (-1) + \\left(-\\frac{1}{2} \\right) \\cdot 6 &amp; \\frac{3}{2}\\cdot 2 + \\left(-\\frac{1}{2} \\right)\\cdot (-8) \\\\[1.3ex] -2\\cdot (-1)+1\\cdot 6 &amp; -2\\cdot 2 +1\\cdot (-8) \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"368\" 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-7d20e85150a382ba9f11bf328b866834_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  X = \\begin{pmatrix} -\\frac{3}{2} -\\frac{6}{2} &amp; 3 + 4 \\\\[1.3ex] 2+6 &amp; -4-8 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"190\" 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-5d3e7ebae094a92690d97b614b0487a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{X =} \\begin{pmatrix} \\bm{-} \\frac{\\bm{9}}{\\bm{2}} &amp; \\bm{7} \\\\[1.3ex] \\bm{8} &amp; \\bm{-12} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"134\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Problemen met matrixvergelijkingen opgelost<\/h2>\n<p> Om ervoor te zorgen dat u kunt oefenen en het concept goed kunt begrijpen, laten we u hieronder enkele opgeloste matrixvergelijkingen zien. Je kunt proberen de oefeningen te doen en kijken of het je gelukt is met de oplossingen. Vergeet niet dat u ons ook eventuele vragen kunt stellen in de opmerkingen.<\/p>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> 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-36386dbc4f20fb573357a406ce713887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 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-a08b2dd56803fba7d8e5a0dcb0430601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> de volgende 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-0f40b96fc0f1047fb0c39a7d41be04ea_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} \\qquad B = \\begin{pmatrix} 4 &amp; 2 \\\\[1.1ex] -1 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bereken 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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> die voldoet aan de volgende matrixvergelijking: <\/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-ec1e9c04147230526534e694fb54f316_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle AX=B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" 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\"> U moet eerst de matrix leegmaken<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> van de matrixvergelijking: <\/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-ec1e9c04147230526534e694fb54f316_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle AX=B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" 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-e79aa1830295bd486a911b5f5c279c9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1} \\cdot AX=A^{-1} \\cdot B\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"156\" 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-d76831ec8e157e150f59ce0900114b77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle IX=A^{-1} \\cdot B\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"107\" 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-dc068e1794d487229ee0be3976454154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=A^{-1} \\cdot B\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Zodra we de matrix hebben<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> duidelijk, werk gewoon met de matrices. We berekenen daarom eerst de inverse matrix van A: <\/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-2fb5c4785b78010fcac56e1189338b99_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=\"109\" 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-1fe85ec6c4385daba7d2488b0d60ee2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1} = \\cfrac{1}{\\vert A \\vert } \\cdot \\Bigl( \\text{Adj}(A)\\Bigr)^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"175\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c4d4a6bfca6d2eedde52937c8ee0917_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{1} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 3 \\end{pmatrix}^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"160\" 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-695a05e4176ced4a4beaec27ce201b4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{1} \\cdot \\begin{pmatrix}0 &amp; 1 \\\\[1.1ex] -1 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"151\" 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-a12ae8d0ae9ce16f04540ecd1a0ac907_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\begin{pmatrix} 0 &amp; 1 \\\\[1.1ex] -1 &amp; 3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu vervangen we alle matrices in de vergelijking om de matrix te berekenen <\/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-f31b6ad36b8ba2d917f13bb377de636f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"25\" 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-dc068e1794d487229ee0be3976454154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=A^{-1} \\cdot B\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" 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-92d5f580fddfc830181cde2e67013987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X= \\begin{pmatrix} 0 &amp; 1 \\\\[1.1ex] -1 &amp; 3\\end{pmatrix}\\cdot \\begin{pmatrix} 4 &amp; 2 \\\\[1.1ex] -1 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"200\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En ten slotte doen we de vermenigvuldiging van de 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-787643b41cb362e276b8f80c9211fb52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{X=} \\begin{pmatrix}\\bm{ -1} &amp; \\bm{3} \\\\[1.1ex] \\bm{-7} &amp; \\bm{7}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"109\" 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> 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-36386dbc4f20fb573357a406ce713887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a08b2dd56803fba7d8e5a0dcb0430601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 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-cbff3f75ba97791e8db3213060854130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> de volgende volgorde 2 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-4f4f1f244d15039c64282a9fe347cee4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =\\begin{pmatrix} 3 &amp; 6 \\\\[1.1ex] 2 &amp; -1 \\end{pmatrix} \\qquad B = \\begin{pmatrix} -2 &amp; 1 \\\\[1.1ex] 3 &amp; -3 \\end{pmatrix}\\qquad C = \\begin{pmatrix} 6 &amp; 4 \\\\[1.1ex] 3 &amp; -2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"426\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bereken 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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> die voldoet aan de volgende matrixvergelijking: <\/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-2779ee661e4a42242acbed40277bf774_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A+ XB=C\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" style=\"vertical-align: -2px;\"><\/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\"> Het eerste wat we moeten doen is de matrix leegmaken.<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> van de matrixvergelijking: <\/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-2779ee661e4a42242acbed40277bf774_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A+ XB=C\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" 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-0d8aea6239fb382563c5f5135145a77b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  XB=C-A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"103\" 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-4f7f75794139db4c21b8c91bb459a7a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle XB \\cdot B^{-1}=\\left(C-A\\right)\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"206\" 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-8766c612738778657de57a198fb0cd29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle XI=\\left(C-A\\right)\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"156\" 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-7bd40901bc80289bb49d0fd47f6236c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X = \\left(C-A\\right)\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Zodra we de matrix hebben ge\u00efsoleerd<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> , is het noodzakelijk om met matrices te werken. We berekenen daarom eerst de inverse matrix van B: <\/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-33c4a446ecdc391935728843e6a34964_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B =\\begin{pmatrix} -2 &amp; 1 \\\\[1.1ex] 3 &amp; -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"123\" 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-da88dade6c0344edc4f87207bc9b915c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^{-1} = \\cfrac{1}{\\vert B \\vert } \\cdot \\Bigl( \\text{Adj}(B)\\Bigr)^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"178\" style=\"vertical-align: -17px;\"><\/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-4850852b0e29a3d530b32dc1cd635499_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B^{-1} = \\cfrac{1}{3} \\cdot \\begin{pmatrix} -3 &amp; -3 \\\\[1.1ex] -1 &amp; -2 \\end{pmatrix}^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"174\" 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-b8817da5e89bc39e89bd17390cfd61c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B^{-1} = \\cfrac{1}{3} \\cdot \\begin{pmatrix} -3 &amp; -1 \\\\[1.1ex] -3 &amp; -2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"165\" 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-a5fc342354f6410cb87fa6b0ddf833a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B^{-1} = \\begin{pmatrix} -1 &amp; -\\frac{1}{3} \\\\[1.3ex] -1 &amp; -\\frac{2}{3} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"144\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu vervangen we alle matrices in de vergelijking om de matrix te berekenen <\/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-f31b6ad36b8ba2d917f13bb377de636f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"25\" 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-d2bda3fe0c2275283c3ce9dcd7cdfce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\left(C-A\\right)\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"147\" 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-79abf2abf8a29e6357f65a1b62c9a80f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  X=\\left(\\begin{pmatrix} 6 &amp; 4 \\\\[1.3ex] 3 &amp; -2 \\end{pmatrix}-\\begin{pmatrix} 3 &amp; 6 \\\\[1.3ex] 2 &amp; -1 \\end{pmatrix}\\right)\\cdot \\begin{pmatrix} -1 &amp; -\\frac{1}{3} \\\\[1.3ex] -1 &amp; -\\frac{2}{3} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"341\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We lossen de haakjes op door de matrices af te trekken:<\/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-f5141a4cb61be8db15676e185b10767f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 3 &amp; -2 \\\\[1.3ex] 1 &amp; -1 \\end{pmatrix}\\cdot \\begin{pmatrix} -1 &amp; -\\frac{1}{3} \\\\[1.3ex] -1 &amp; -\\frac{2}{3} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"216\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En ten slotte vermenigvuldigen we de 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-1d5482b1eb8fd6af1d6c61547b05c0bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} -3+2 &amp; -1+\\frac{4}{3} \\\\[1.3ex] -1+1 &amp; -\\frac{1}{3}+\\frac{2}{3} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"190\" 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-779a021183e139f0e138fbc288d4adea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{X=} \\begin{pmatrix}\\bm{ -1} &amp; \\frac{\\bm{1}}{\\bm{3}} \\\\[1.3ex] \\bm{0} &amp; \\frac{\\bm{1}}{\\bm{3}} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"111\" 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> 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-36386dbc4f20fb573357a406ce713887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a08b2dd56803fba7d8e5a0dcb0430601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 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-cbff3f75ba97791e8db3213060854130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> de volgende tweede orde 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-6292882d305055e4e8fb287a4bc93b71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =\\begin{pmatrix} -1 &amp; 1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} \\qquad B = \\begin{pmatrix} 4 &amp; -2 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix}\\qquad C = \\begin{pmatrix} 6 &amp; 4 \\\\[1.1ex] 22 &amp; 14 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"416\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> zoek 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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> die voldoet aan de volgende matrixvergelijking: <\/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-3241bccca1a61191660195f8076bb990_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle AXB=C\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"81\" 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\"> Eerst moeten we de matrix leegmaken<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> van de matrixvergelijking: <\/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-3241bccca1a61191660195f8076bb990_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle AXB=C\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"81\" 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-1e90337c58e38fc6ec3c2b2c884d7fed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1}\\cdot AXB\\cdot B^{-1}=A^{-1}\\cdot C\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"260\" 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-b4b610cde38418d268b1f5c5d01463d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displastyle IXI=A^{-1}\\cdot C\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"161\" 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-e9076f1a9803ae41329636d95a8c8182_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displastyle X=A^{-1}\\cdot C\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"142\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Zodra we de matrix hebben geleegd<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> , is het noodzakelijk om met matrices te werken. We berekenen daarom eerst de inverse matrix van A: <\/p>\n<p class=\"has-text-align-center\">\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b09ce42998b548267e70e47b135b6508_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A =\\begin{pmatrix} -1 &amp; 1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"109\" 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-1fe85ec6c4385daba7d2488b0d60ee2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1} = \\cfrac{1}{\\vert A \\vert } \\cdot \\Bigl( \\text{Adj}(A)\\Bigr)^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"175\" style=\"vertical-align: -17px;\"><\/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-2a29b310de613bc1ec42a6e1452db147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{-1} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] -1 &amp; -1 \\end{pmatrix}^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"187\" 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-c0e0b895fed20ba908417f6ee3482ce0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{-1} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] -1 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"178\" 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-c19685457cd40098cadf6eeff41405d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\begin{pmatrix} 0 &amp; 1 \\\\[1.1ex] 1 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"113\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En we keren ook matrix B om: <\/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-d3f5048394796b2378c8197c9c9c1cb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B =\\begin{pmatrix} 4 &amp; -2 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"110\" 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-da88dade6c0344edc4f87207bc9b915c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^{-1} = \\cfrac{1}{\\vert B \\vert } \\cdot \\Bigl( \\text{Adj}(B)\\Bigr)^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"178\" style=\"vertical-align: -17px;\"><\/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-261eb432e305f5df596fc1dff9f183d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B^{-1} = \\cfrac{1}{2} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 2 &amp; 4 \\end{pmatrix}^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"161\" 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-96d40ae8aa7c350c8a63d57d06b6fa6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B^{-1} = \\cfrac{1}{2} \\cdot \\begin{pmatrix} 0 &amp; 2 \\\\[1.1ex] -1 &amp; 4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"152\" 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-80ee47f61b0671b42f9df06e7f384847_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  B^{-1} = \\begin{pmatrix} 0 &amp; 1 \\\\[1.3ex] -\\frac{1}{2} &amp; 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"130\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu vervangen we alle matrices in de uitdrukking om de matrix te berekenen <\/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-f31b6ad36b8ba2d917f13bb377de636f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"25\" 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-f765275df3d12633f97c500c3d7ca336_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=A^{-1}\\cdot C\\cdot B^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"142\" 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-de94e47503b17f761f7fcb764f4def59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 0 &amp; 1 \\\\[1.3ex] 1 &amp; 1 \\end{pmatrix}\\cdot\\begin{pmatrix} 6 &amp; 4 \\\\[1.3ex] 22 &amp; 14 \\end{pmatrix}\\cdot \\begin{pmatrix} 0 &amp; 1 \\\\[1.3ex] -\\frac{1}{2} &amp; 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"281\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We lossen eerst de vermenigvuldiging aan de linkerkant 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-ca95f4870d5be13a3f7e241e5a40934b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 0+22 &amp; 0+14 \\\\[1.3ex] 6+22 &amp; 4+14 \\end{pmatrix}\\cdot \\begin{pmatrix} 0 &amp; 1 \\\\[1.3ex] -\\frac{1}{2} &amp; 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"267\" 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-3df7709b9d5c5f5194744d4c88d2cb66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 22 &amp; 14 \\\\[1.3ex] 28 &amp; 18 \\end{pmatrix}\\cdot \\begin{pmatrix} 0 &amp; 1 \\\\[1.3ex] -\\frac{1}{2} &amp; 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"206\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En ten slotte doen we de resterende vermenigvuldiging: <\/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-62d83b02b8768a7e95ee71b7782d7759_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 0-7 &amp; 22+28 \\\\[1.3ex] 0-9 &amp; 28+36 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"176\" 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-4b3a393915b3c49bdf9dd9ee6ada5020_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{X=} \\begin{pmatrix}\\bm{-7} &amp; \\bm{50} \\\\[1.3ex] \\bm{-9} &amp; \\bm{64} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"118\" 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 4<\/h3>\n<p> 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-36386dbc4f20fb573357a406ce713887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 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-a08b2dd56803fba7d8e5a0dcb0430601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> de volgende matrices met afmeting 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-da8b3d05ecc85eea72fd7d14c282f58c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =\\begin{pmatrix}1 &amp; 0 &amp; 1\\\\[1.1ex] 0 &amp; -1 &amp; 0 \\\\[1.1ex] 1 &amp; 2 &amp; 2 \\end{pmatrix} \\qquad B = \\begin{pmatrix} 1 &amp; -1 &amp; 0 \\\\[1.1ex] 2 &amp; 3 &amp; -2 \\\\[1.1ex] -3 &amp; 1 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"344\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bereken 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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> die voldoet aan de volgende matrixvergelijking: <\/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-380b29380ba0a0dab3c183ea8b29e098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^{t}- AX=B\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" 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\"> Eerst maken we de matrix leeg<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> van de matrixvergelijking: <\/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-3a038bf0cecb3080614f71975c72a41c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^t- AX=B\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" 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-ea7312ca34bee43be5f7727bdcf3ad3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^t- B=AX\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" 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-9531df9bff4bb2e5a0015f0aa4c91d6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1}\\cdot \\left(B^t- B \\right)=A^{-1}\\cdot AX\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"214\" 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-ea87eb7eca24cc40f458bb082b5bd0ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1}\\cdot \\left(B^t- B \\right)=IX\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"166\" 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-32d5781c515b740e3b7c20b62215d5bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1}\\cdot \\left(B^t- B \\right)=X\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"156\" 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-f6081c855462d0193b955600b1d5db48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=A^{-1}\\cdot \\left(B^t- B \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"154\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Zodra we de matrix hebben ge\u00efsoleerd<\/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-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> , is het noodzakelijk om met matrices te werken. We berekenen daarom eerst de inverse matrix van A: <\/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-1a92fa898838b531bf1b51356dbbb2de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A =\\begin{pmatrix} 1 &amp; 0 &amp; 1\\\\[1.1ex] 0 &amp; -1 &amp; 0 \\\\[1.1ex] 1 &amp; 2 &amp; 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"136\" 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-1fe85ec6c4385daba7d2488b0d60ee2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{-1} = \\cfrac{1}{\\vert A \\vert } \\cdot \\Bigl( \\text{Adj}(A)\\Bigr)^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"175\" style=\"vertical-align: -17px;\"><\/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-9cc1a5bb552d5eadacef8677265cba0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{-1} \\cdot \\begin{pmatrix} \\begin{vmatrix} -1 &amp; 0 \\\\ 2 &amp; 2 \\end{vmatrix} &amp; -\\begin{vmatrix} 0 &amp; 0 \\\\  1 &amp; 2 \\end{vmatrix} &amp; \\begin{vmatrix}  0 &amp; -1  \\\\ 1 &amp; 2 \\end{vmatrix}\\\\[4ex] -\\begin{vmatrix}  0 &amp; 1 \\\\ 2 &amp; 2 \\end{vmatrix} &amp; \\begin{vmatrix} 1  &amp; 1\\\\ 1 &amp; 2 \\end{vmatrix} &amp; -\\begin{vmatrix} 1 &amp; 0 \\\\ 1 &amp; 2  \\end{vmatrix} \\\\[4ex] \\begin{vmatrix} 0 &amp; 1\\\\  -1 &amp; 0 \\end{vmatrix} &amp; -\\begin{vmatrix} 1  &amp; 1\\\\ 0 &amp; 0  \\end{vmatrix} &amp; \\begin{vmatrix} 1 &amp; 0 \\\\ 0 &amp; -1 \\end{vmatrix} \\end{pmatrix}^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"175\" width=\"349\" 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-e668ed3a6e233bed8245f99e80638633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\cfrac{1}{-1} \\cdot \\begin{pmatrix} -2 &amp; 0 &amp; 1 \\\\[1.1ex] 2 &amp; 1 &amp; -2 \\\\[1.1ex] 1  &amp; 0 &amp; -1 \\end{pmatrix}^{\\bm{t}}\" title=\"Rendered by QuickLaTeX.com\" height=\"89\" width=\"215\" 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-eeb999734b9ba4b6e9a01e788bee6649_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = -1 \\cdot \\begin{pmatrix} -2 &amp; 2 &amp; 1 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 1  &amp; -2 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"218\" 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-f8f2379d6d616b29b78005aaafe39f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A^{-1} = \\begin{pmatrix} 2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; -1 &amp; 0 \\\\[1.1ex] -1  &amp; 2 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"182\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu vervangen we alle matrices in de uitdrukking om X te berekenen: <\/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-f6081c855462d0193b955600b1d5db48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=A^{-1}\\cdot \\left(B^t- B \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"154\" 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-c91b944756316c7cde33eb90743d54d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; -1 &amp; 0 \\\\[1.1ex] -1  &amp; 2 &amp; 1 \\end{pmatrix}\\cdot \\left(\\begin{pmatrix} 1 &amp; -1 &amp; 0 \\\\[1.1ex] 2 &amp; 3 &amp; -2 \\\\[1.1ex] -3 &amp; 1 &amp; -1 \\end{pmatrix}^t- \\begin{pmatrix} 1 &amp; -1 &amp; 0 \\\\[1.1ex] 2 &amp; 3 &amp; -2 \\\\[1.1ex] -3 &amp; 1 &amp; -1 \\end{pmatrix} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"89\" width=\"501\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We transponeren matrix B:<\/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-3a81f0c3d7367d756d53221e9c56d1e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; -1 &amp; 0 \\\\[1.1ex] -1  &amp; 2 &amp; 1 \\end{pmatrix}\\cdot \\left(\\begin{pmatrix} 1 &amp; 2 &amp; -3 \\\\[1.1ex] -1 &amp; 3 &amp; 1 \\\\[1.1ex] 0 &amp; -2 &amp; -1 \\end{pmatrix}- \\begin{pmatrix} 1 &amp; -1 &amp; 0 \\\\[1.1ex] 2 &amp; 3 &amp; -2 \\\\[1.1ex] -3 &amp; 1 &amp; -1 \\end{pmatrix} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"495\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We lossen de haakjes op door matrices af te trekken:<\/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-5f822e84288230368a5c0918c79398bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X=\\begin{pmatrix} 2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; -1 &amp; 0 \\\\[1.1ex] -1  &amp; 2 &amp; 1 \\end{pmatrix}\\cdot \\begin{pmatrix} 0 &amp; 3 &amp; -3 \\\\[1.1ex] -3 &amp; 0 &amp; 3 \\\\[1.1ex] 3 &amp; -3 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"311\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En tenslotte doen we de matrixvermenigvuldiging:<\/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-552e3809229102041ddf02a78badfea0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{X=}\\begin{pmatrix} \\bm{3} &amp; \\bm{9} &amp; \\bm{-12} \\\\[1.1ex] \\bm{3} &amp; \\bm{0} &amp; \\bm{-3} \\\\[1.1ex] \\bm{-3}  &amp; \\bm{-6} &amp; \\bm{9} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"173\" 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>Op deze pagina leert u wat matrixvergelijkingen zijn en hoe u ze kunt oplossen. Daarnaast vind je voorbeelden en opgeloste oefeningen van vergelijkingen met matrices. Wat zijn matrixvergelijkingen? Matrixvergelijkingen lijken op normale vergelijkingen, maar in plaats van uit getallen te bestaan, bestaan ze uit matrices. Bijvoorbeeld: Daarom zal oplossing X ook een matrix zijn. Zoals &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/voorbeelden-van-matrixvergelijkingen-en-opgeloste-oefeningen-van-2x2-en-3x3-matrices\/\"> <span class=\"screen-reader-text\">Matrixvergelijkingen<\/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":[39],"tags":[],"class_list":["post-336","post","type-post","status-publish","format-standard","hentry","category-determinant-van-een-matrix"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matrixvergelijkingen \u2013<\/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-matrixvergelijkingen-en-opgeloste-oefeningen-van-2x2-en-3x3-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matrixvergelijkingen \u2013\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina leert u wat matrixvergelijkingen zijn en hoe u ze kunt oplossen. Daarnaast vind je voorbeelden en opgeloste oefeningen van vergelijkingen met matrices. Wat zijn matrixvergelijkingen? Matrixvergelijkingen lijken op normale vergelijkingen, maar in plaats van uit getallen te bestaan, bestaan ze uit matrices. Bijvoorbeeld: Daarom zal oplossing X ook een matrix zijn. 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Daarnaast vind je voorbeelden en opgeloste oefeningen van vergelijkingen met matrices. Wat zijn matrixvergelijkingen? Matrixvergelijkingen lijken op normale vergelijkingen, maar in plaats van uit getallen te bestaan, bestaan ze uit matrices. Bijvoorbeeld: Daarom zal oplossing X ook een matrix zijn. 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