{"id":292,"date":"2023-07-06T17:52:46","date_gmt":"2023-07-06T17:52:46","guid":{"rendered":"https:\/\/mathority.org\/id\/cara-menyelesaikan-contoh-persamaan-matriks-dan-latihan-penyelesaian-matriks-2x2-dan-3x3\/"},"modified":"2023-07-06T17:52:46","modified_gmt":"2023-07-06T17:52:46","slug":"cara-menyelesaikan-contoh-persamaan-matriks-dan-latihan-penyelesaian-matriks-2x2-dan-3x3","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/cara-menyelesaikan-contoh-persamaan-matriks-dan-latihan-penyelesaian-matriks-2x2-dan-3x3\/","title":{"rendered":"Persamaan matriks"},"content":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa itu <strong>persamaan matriks<\/strong> dan cara menyelesaikannya. Selain itu, Anda akan menemukan contoh dan latihan persamaan dengan matriks yang diselesaikan.<\/p>\n<h2 class=\"wp-block-heading\"> Apa persamaan matriks?<\/h2>\n<p> <strong>Persamaan matriks<\/strong> sama seperti persamaan biasa, namun tidak terdiri dari bilangan, melainkan terdiri dari matriks. Misalnya:<\/p>\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> Oleh karena itu, solusi X juga akan menjadi matriks.<\/p>\n<p> Seperti yang telah Anda ketahui, matriks tidak dapat dipecah. Oleh karena itu, matriks X tidak dapat diselesaikan dengan membagi matriks yang mengalikannya dengan sisi lain persamaan:<\/p>\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> Sebaliknya, untuk menghapus matriks X, seluruh prosedur harus diikuti. Jadi mari kita lihat cara menyelesaikan persamaan matriks dengan latihan yang terselesaikan:<\/p>\n<h2 class=\"estil_titol_H2 wp-block-heading\"> Cara menyelesaikan persamaan matriks. Contoh:<\/h2>\n<ul>\n<li> Selesaikan persamaan matriks berikut:<\/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> Hal pertama yang perlu kita lakukan adalah menyelesaikan matriks X. <strong>Jadi, kita kurangi matriks B<\/strong> <strong>dari sisi persamaan yang lain:<\/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> Untuk menyelesaikan kliring matriks tidak dapat dibagi. Namun kita harus melakukan hal berikut:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Kita harus mengalikan kedua ruas persamaan dengan <strong>invers matriks yang mengalikan matriks X<\/strong> dan, sebagai tambahan, mengalikan kedua ruas tersebut <strong>dengan sisi letak matriks tersebut.<\/strong><\/p>\n<p> Dalam hal ini, matriks yang mengalikan X adalah A dan terletak di sebelah kirinya. <strong>Oleh karena itu, kita mengalikan kedua ruas kiri persamaan dengan invers dari 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> Suatu matriks dikalikan dengan inversnya sama dengan matriks identitas. Belum<\/p>\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> Setiap matriks dikalikan dengan matriks identitas menghasilkan matriks yang sama. Belum:<\/p>\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> Dan dengan cara ini <strong>kita telah menghapus X.<\/strong> Sekarang tinggal lakukan operasi matriksnya. Jadi kita hitung dulu <a href=\"https:\/\/mathority.org\/id\/matriks-terbalik\/\">matriks invers 2 \u00d7 2<\/a> dari 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> Kami menghitung adjoint dari matriks 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> Dan setelah matriks adjoin ditemukan, kita lanjutkan menghitung <a href=\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\">matriks yang ditransposisikan<\/a> untuk menentukan matriks inversnya:<\/p>\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> Sekarang kita substitusikan semua matriks ke dalam ekspresi untuk menghitung 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> Dan kami melanjutkan untuk menyelesaikan operasi dengan matriks. Pertama-tama kita menghitung tanda kurung dengan mengurangkan matriksnya:<\/p>\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> Dan terakhir, kita mengalikan matriksnya: <\/p>\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\"> Menyelesaikan Masalah Persamaan Matriks<\/h2>\n<p> Agar Anda dapat berlatih dan memahami konsepnya dengan baik, di bawah ini kami tinggalkan beberapa persamaan matriks yang terselesaikan. Anda dapat mencoba melakukan latihan dan melihat apakah Anda berhasil dengan solusinya. Jangan lupa Anda juga dapat menanyakan pertanyaan apa pun yang muncul kepada kami di kolom komentar.<\/p>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Menjadi<\/p>\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> Dan<\/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> matriks persegi berdimensi 2\u00d72 berikut:<\/p>\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> Hitung matriksnya<\/p>\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> yang memenuhi persamaan matriks berikut: <\/p>\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>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Anda harus mengosongkan matriks terlebih dahulu<\/p>\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> persamaan matriks: <\/p>\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\"> Setelah kita memiliki matriksnya<\/p>\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> jelas, operasikan saja dengan matriks. Oleh karena itu, pertama-tama kita menghitung matriks invers dari 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\"> Sekarang kita substitusikan semua matriks ke dalam persamaan untuk menghitung matriks <\/p>\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\"> Dan terakhir, kita melakukan perkalian matriks: <\/p>\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\">Latihan 2<\/h3>\n<p> Menjadi<\/p>\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> Dan<\/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> matriks orde 2 berikut:<\/p>\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> Hitung matriksnya<\/p>\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> yang memenuhi persamaan matriks berikut: <\/p>\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>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Hal pertama yang perlu kita lakukan adalah mengosongkan matriks.<\/p>\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> persamaan matriks: <\/p>\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\"> Setelah kita mengisolasi matriks<\/p>\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> , perlu untuk beroperasi dengan matriks. Oleh karena itu, pertama-tama kita menghitung matriks invers dari 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\"> Sekarang kita substitusikan semua matriks ke dalam persamaan untuk menghitung matriks <\/p>\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\"> Kita menyelesaikan tanda kurung dengan mengurangkan matriks:<\/p>\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\"> Dan terakhir, kita mengalikan matriksnya: <\/p>\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\"> Latihan 3<\/h3>\n<p> Menjadi<\/p>\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> Dan<\/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> matriks orde kedua berikut:<\/p>\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> temukan matriksnya<\/p>\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> yang memenuhi persamaan matriks berikut: <\/p>\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>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama kita perlu menghapus matriks<\/p>\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> persamaan matriks: <\/p>\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\"> Setelah kita mengosongkan matriks<\/p>\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> , perlu untuk beroperasi dengan matriks. Oleh karena itu, pertama-tama kita menghitung matriks invers dari 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\"> Dan kami juga membalikkan matriks 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\"> Sekarang kita substitusikan semua matriks ke dalam ekspresi untuk menghitung matriks <\/p>\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\"> Pertama-tama kita selesaikan perkalian di sebelah kiri <\/p>\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\"> Dan terakhir, kita lakukan perkalian sisanya: <\/p>\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\">Latihan 4<\/h3>\n<p> Menjadi<\/p>\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> Dan<\/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> matriks berdimensi 3\u00d73 berikut:<\/p>\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> Hitung matriksnya<\/p>\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> yang memenuhi persamaan matriks berikut: <\/p>\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>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama kita menghapus matriksnya<\/p>\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> persamaan matriks: <\/p>\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\"> Setelah kita mengisolasi matriks<\/p>\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> , perlu untuk beroperasi dengan matriks. Oleh karena itu, pertama-tama kita menghitung matriks invers dari 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\"> Sekarang kita substitusikan semua matriks ke dalam ekspresi untuk menghitung 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\"> Kami mengubah urutan matriks 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\"> Kita menyelesaikan tanda kurung dengan mengurangkan matriks:<\/p>\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\"> Dan terakhir, kita melakukan perkalian matriks:<\/p>\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>Di halaman ini Anda akan mempelajari apa itu persamaan matriks dan cara menyelesaikannya. Selain itu, Anda akan menemukan contoh dan latihan persamaan dengan matriks yang diselesaikan. Apa persamaan matriks? Persamaan matriks sama seperti persamaan biasa, namun tidak terdiri dari bilangan, melainkan terdiri dari matriks. Misalnya: Oleh karena itu, solusi X juga akan menjadi matriks. Seperti &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/cara-menyelesaikan-contoh-persamaan-matriks-dan-latihan-penyelesaian-matriks-2x2-dan-3x3\/\"> <span class=\"screen-reader-text\">Persamaan matriks<\/span> Selengkapnya &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-292","post","type-post","status-publish","format-standard","hentry","category-penentu-suatu-matriks"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Persamaan Matriks \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\/id\/cara-menyelesaikan-contoh-persamaan-matriks-dan-latihan-penyelesaian-matriks-2x2-dan-3x3\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Persamaan Matriks \u2013\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan mempelajari apa itu persamaan matriks dan cara menyelesaikannya. Selain itu, Anda akan menemukan contoh dan latihan persamaan dengan matriks yang diselesaikan. Apa persamaan matriks? Persamaan matriks sama seperti persamaan biasa, namun tidak terdiri dari bilangan, melainkan terdiri dari matriks. Misalnya: Oleh karena itu, solusi X juga akan menjadi matriks. Seperti &hellip; Persamaan matriks Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/cara-menyelesaikan-contoh-persamaan-matriks-dan-latihan-penyelesaian-matriks-2x2-dan-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=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 menit\" \/>\n<script type=\"application\/ld+json\" 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