{"id":295,"date":"2023-07-06T17:52:46","date_gmt":"2023-07-06T17:52:46","guid":{"rendered":"https:\/\/mathority.org\/it\/come-risolvere-esempi-di-equazioni-di-matrici-ed-esercizi-risolti-di-matrici-2x2-e-3x3\/"},"modified":"2023-07-06T17:52:46","modified_gmt":"2023-07-06T17:52:46","slug":"come-risolvere-esempi-di-equazioni-di-matrici-ed-esercizi-risolti-di-matrici-2x2-e-3x3","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/come-risolvere-esempi-di-equazioni-di-matrici-ed-esercizi-risolti-di-matrici-2x2-e-3x3\/","title":{"rendered":"Equazioni di matrice"},"content":{"rendered":"<p>In questa pagina imparerai cosa sono <strong>le equazioni di matrice<\/strong> e come risolverle. Inoltre, troverai esempi ed esercizi risolti di equazioni con matrici.<\/p>\n<h2 class=\"wp-block-heading\"> Cosa sono le equazioni di matrice?<\/h2>\n<p> <strong>Le equazioni di matrice<\/strong> sono come le normali equazioni, ma invece di essere composte da numeri, sono costituite da matrici. Per esempio:<\/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> Pertanto anche la soluzione X sar\u00e0 una matrice.<\/p>\n<p> Come gi\u00e0 sai, le matrici non possono essere divise. Pertanto, la matrice X non pu\u00f2 essere cancellata dividendo la matrice che l&#8217;ha moltiplicata dall&#8217;altro lato dell&#8217;equazione:<\/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> Per cancellare invece la matrice X occorre seguire tutta una procedura. Vediamo quindi come risolvere le equazioni di matrice con un esercizio risolto:<\/p>\n<h2 class=\"estil_titol_H2 wp-block-heading\"> Come risolvere le equazioni di matrice. Esempio:<\/h2>\n<ul>\n<li> Risolvi la seguente equazione di matrice:<\/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> La prima cosa che dobbiamo fare \u00e8 risolvere la matrice X. <strong>Quindi sottraiamo la matrice B<\/strong> <strong>dall&#8217;altro lato dell&#8217;equazione:<\/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> Per completare la pulizia, la matrice non pu\u00f2 essere divisa. Ma dobbiamo fare quanto segue:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Dobbiamo moltiplicare entrambi i lati dell&#8217;equazione per l&#8217; <strong>inverso della matrice che moltiplica la matrice X<\/strong> e, inoltre, moltiplicare entrambi i lati <strong>per il lato in cui si trova detta matrice.<\/strong><\/p>\n<p> In questo caso, la matrice che moltiplica X \u00e8 A, e si trova alla sua sinistra. <strong>Moltiplichiamo quindi per sinistra entrambi i membri dell&#8217;equazione per l&#8217;inverso di 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> Una matrice moltiplicata per il suo inverso \u00e8 uguale alla matrice identit\u00e0. Ancora<\/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> Qualsiasi matrice moltiplicata per la matrice identit\u00e0 d\u00e0 la stessa matrice. Ancora:<\/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> E in questo modo <strong>abbiamo gi\u00e0 cancellato X.<\/strong> Adesso basta fare le operazioni con le matrici. Quindi calcoliamo prima la <a href=\"https:\/\/mathority.org\/it\/matrice-inversa\/\">matrice inversa 2 \u00d7 2<\/a> di 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> Calcoliamo l&#8217;aggiunto della matrice 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> E una volta trovata la matrice aggiunta, si procede a calcolare la <a href=\"https:\/\/mathority.org\/it\/esempi-di-matrice-trasposta-o-trasposta-ed-esercizi-risolti\/\">matrice trasposta<\/a> per determinare la matrice inversa:<\/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> Ora sostituiamo tutte le matrici nell&#8217;espressione per calcolare X:<\/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> E procediamo a risolvere le operazioni con le matrici. Per prima cosa calcoliamo le parentesi sottraendo le matrici:<\/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> E, infine, moltiplichiamo le matrici: <\/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\"> Problemi risolti con le equazioni della matrice<\/h2>\n<p> Affinch\u00e9 tu possa esercitarti e quindi comprendere bene il concetto, ti lasciamo di seguito diverse equazioni di matrice risolte. Puoi provare a fare gli esercizi e vedere se hai avuto successo con le soluzioni. Non dimenticare che puoi anche farci tutte le domande che sorgono nei commenti.<\/p>\n<h3 class=\"wp-block-heading\"> Esercizio 1<\/h3>\n<p> Essere<\/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> E<\/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> le seguenti matrici quadrate di dimensione 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> Calcola la matrice<\/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> che soddisfa la seguente equazione di matrice: <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u00c8 necessario prima svuotare la matrice<\/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> dell&#8217;equazione della matrice: <\/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\"> Una volta ottenuta la matrice<\/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> chiaro, basta operare con le matrici. Calcoliamo quindi prima la matrice inversa di 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\"> Ora sostituiamo tutte le matrici nell&#8217;equazione per calcolare la matrice <\/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\"> E, infine, facciamo la moltiplicazione delle matrici: <\/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\">Esercizio 2<\/h3>\n<p> Essere<\/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> E<\/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> le seguenti matrici di ordine 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-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> Calcola la matrice<\/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> che soddisfa la seguente equazione di matrice: <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> La prima cosa che dobbiamo fare \u00e8 svuotare la matrice.<\/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> dell&#8217;equazione della matrice: <\/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\"> Una volta isolata la matrice<\/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> , \u00e8 necessario operare con matrici. Calcoliamo quindi prima la matrice inversa di 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\"> Ora sostituiamo tutte le matrici nell&#8217;equazione per calcolare la matrice <\/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\"> Risolviamo le parentesi sottraendo le matrici:<\/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\"> E, infine, moltiplichiamo le matrici: <\/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\"> Esercizio 3<\/h3>\n<p> Essere<\/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> E<\/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> le seguenti matrici del secondo ordine:<\/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> trova la matrice<\/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> che soddisfa la seguente equazione di matrice: <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Per prima cosa dobbiamo cancellare la matrice<\/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> dell&#8217;equazione della matrice: <\/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\"> Una volta svuotata la matrice<\/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> , \u00e8 necessario operare con matrici. Calcoliamo quindi prima la matrice inversa di 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\"> E invertiamo anche la matrice 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-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\"> Ora sostituiamo tutte le matrici nell&#8217;espressione per calcolare la matrice <\/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\"> Risolviamo prima la moltiplicazione a sinistra <\/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\"> E, infine, eseguiamo la moltiplicazione rimanente: <\/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\">Esercizio 4<\/h3>\n<p> Essere<\/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> E<\/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> le seguenti matrici di dimensione 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> Calcola la matrice<\/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> che soddisfa la seguente equazione di matrice: <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Per prima cosa cancelliamo la matrice<\/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> dell&#8217;equazione della matrice: <\/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\"> Una volta isolata la matrice<\/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> , \u00e8 necessario operare con matrici. Calcoliamo quindi prima la matrice inversa di 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\"> Ora sostituiamo tutte le matrici nell&#8217;espressione per calcolare X: <\/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\"> Trasponiamo la matrice 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\"> Risolviamo le parentesi sottraendo le matrici:<\/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\"> E infine, eseguiamo la moltiplicazione delle matrici:<\/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>In questa pagina imparerai cosa sono le equazioni di matrice e come risolverle. Inoltre, troverai esempi ed esercizi risolti di equazioni con matrici. Cosa sono le equazioni di matrice? Le equazioni di matrice sono come le normali equazioni, ma invece di essere composte da numeri, sono costituite da matrici. Per esempio: Pertanto anche la soluzione &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/come-risolvere-esempi-di-equazioni-di-matrici-ed-esercizi-risolti-di-matrici-2x2-e-3x3\/\"> <span class=\"screen-reader-text\">Equazioni di matrice<\/span> Leggi altro &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":[7],"tags":[],"class_list":["post-295","post","type-post","status-publish","format-standard","hentry","category-determinante-di-una-matrice"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Equazioni della matrice \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\/it\/come-risolvere-esempi-di-equazioni-di-matrici-ed-esercizi-risolti-di-matrici-2x2-e-3x3\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equazioni della matrice \u2013\" \/>\n<meta property=\"og:description\" content=\"In questa pagina imparerai cosa sono le equazioni di matrice e come risolverle. Inoltre, troverai esempi ed esercizi risolti di equazioni con matrici. Cosa sono le equazioni di matrice? Le equazioni di matrice sono come le normali equazioni, ma invece di essere composte da numeri, sono costituite da matrici. Per esempio: Pertanto anche la soluzione &hellip; Equazioni di matrice Leggi altro &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/it\/come-risolvere-esempi-di-equazioni-di-matrici-ed-esercizi-risolti-di-matrici-2x2-e-3x3\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T17:52:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2bc59624603d48ea9b4df50b4c052437_l3.png\" \/>\n<meta name=\"author\" content=\"Squadra di Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Scritto da\" \/>\n\t<meta name=\"twitter:data1\" content=\"Squadra di Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo di lettura stimato\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minuti\" \/>\n<script type=\"application\/ld+json\" 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