{"id":282,"date":"2023-07-06T21:48:53","date_gmt":"2023-07-06T21:48:53","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/"},"modified":"2023-07-06T21:48:53","modified_gmt":"2023-07-06T21:48:53","slug":"contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/","title":{"rendered":"Perkalian matriks"},"content":{"rendered":"<p>Pada halaman ini kita akan melihat cara <strong>mengalikan matriks<\/strong> berdimensi 2\u00d72, 3\u00d73, 4\u00d74, dst. Kami menjelaskan prosedur perkalian matriks langkah demi langkah melalui sebuah contoh, kemudian Anda akan menemukan latihan yang terselesaikan sehingga Anda juga dapat berlatih. Terakhir, Anda akan mengetahui kapan dua matriks tidak dapat dikalikan dan semua properti operasi matriks tersebut.<\/p>\n<h2 class=\"wp-block-heading\"> Bagaimana cara mengalikan dua matriks?<\/h2>\n<p> Mari kita lihat tata cara melakukan perkalian dua matriks dengan contoh: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-multiplication-matricielle-22152.webp\" alt=\"contoh cara mengalikan dua matriks berdimensi 2x2, operasi dengan matriks\" width=\"228\" height=\"60\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Untuk menghitung <strong>perkalian matriks,<\/strong> <strong>baris<\/strong> matriks kiri harus dikalikan dengan <strong>kolom<\/strong> matriks kanan.<\/p>\n<p> Jadi pertama-tama kita perlu mengalikan <strong>baris pertama dengan kolom pertama.<\/strong> Caranya, kita mengalikan setiap elemen pada baris pertama dengan setiap elemen pada kolom pertama satu per satu, dan menjumlahkan hasilnya. Jadi semua ini akan menjadi elemen pertama dari baris pertama array yang dihasilkan. Lihatlah prosedurnya: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-multiplier-des-matrices-22152.webp\" alt=\"cara menyelesaikan perkalian matriks 2x2, operasi dengan matriks\" width=\"504\" height=\"87\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> 1 <strong>\u22c5<\/strong> 3 + 2 <strong>\u22c5<\/strong> 4 = 3 + 8 = 11. Jadi: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p class=\"has-text-align-justify\"> Sekarang kita perlu mengalikan <strong>baris pertama dengan kolom kedua<\/strong> . Oleh karena itu, kami mengulangi prosedurnya: kami mengalikan setiap elemen pada baris pertama satu per satu dengan setiap elemen pada kolom kedua, dan kami menjumlahkan hasilnya. Dan semua ini akan menjadi elemen kedua dari baris pertama array yang dihasilkan:<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p>1 <strong>\u22c5<\/strong> 5 + 2 <strong>\u22c5<\/strong> 1 = 5 + 2 = 7. Jadi: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p> Setelah kita mengisi baris pertama dari matriks yang dihasilkan, kita berpindah ke baris kedua. Oleh karena itu, kita mengalikan <strong>baris kedua dengan kolom pertama<\/strong> dengan mengulangi prosedur ini: kita mengalikan satu per satu setiap elemen baris kedua dengan setiap elemen kolom pertama, dan menjumlahkan hasilnya:<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p>-3 <strong>\u22c5<\/strong> 3 + 0 <strong>\u22c5<\/strong> 4 = -9 + 0 = -9. Belum: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p class=\"has-text-align-justify\"> Terakhir, kita kalikan <strong>baris kedua dengan kolom kedua<\/strong> . Selalu dengan prosedur yang sama: kita mengalikan setiap elemen baris kedua satu per satu dengan setiap elemen kolom kedua, dan kita menjumlahkan hasilnya:<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p>-3 <strong>\u22c5<\/strong> 5 + 0 <strong>\u22c5<\/strong> 1 = -15 + 0 = -15. Belum:<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p>Dan disinilah perkalian kedua matriks tersebut berakhir. Seperti yang Anda lihat, Anda perlu mengalikan baris dengan kolom, selalu mengulangi prosedur yang sama: kalikan setiap elemen baris dengan setiap elemen kolom satu per satu, dan tambahkan hasilnya.<\/p>\n<h2 class=\"wp-block-heading\"> Latihan perkalian matriks terpecahkan<\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Selesaikan perkalian matriks berikut: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-de-produit-de-matrices-22.webp\" alt=\"latihan menyelesaikan perkalian langkah demi langkah matriks 2x2, operasi dengan matriks\" width=\"172\" height=\"68\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini adalah produk dari matriks orde 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-747926b92c1d388c1150613b0f471d7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] 3 &amp; 4  \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; -2 \\\\[1.1ex] 1 &amp; 5  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"142\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Untuk menyelesaikan perkalian matriks, Anda harus mengalikan baris matriks kiri dengan kolom matriks kanan.<\/p>\n<p class=\"has-text-align-left has-text-align-justify\"> Jadi kita kalikan dulu <strong>baris pertama dengan kolom pertama.<\/strong> Caranya, kita mengalikan setiap elemen pada baris pertama dengan setiap elemen pada kolom pertama satu per satu, dan menjumlahkan hasilnya. Dan semua ini akan menjadi elemen pertama dari baris pertama array yang dihasilkan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eff23eaf91738d6ffb383949e4b70856_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] 3 &amp; 4  \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; -2 \\\\[1.1ex] 1 &amp; 5  \\end{pmatrix}  = \\begin{pmatrix} 1\\cdot 3 +2 \\cdot 1 &amp; \\\\[1.1ex] &amp; \\end{pmatrix} = \\begin{pmatrix} 5 &amp; \\\\[1.1ex] &amp; \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"370\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kalikan <strong>baris pertama dengan kolom kedua,<\/strong> untuk mendapatkan elemen kedua dari baris pertama matriks yang dihasilkan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-558838bcc38efc1aeeaf298d3e7151dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] 3 &amp; 4  \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; -2 \\\\[1.1ex] 1 &amp; 5  \\end{pmatrix}  = \\begin{pmatrix} -1 &amp; 1\\cdot (-2) +2 \\cdot 5 \\\\[1.1ex] &amp; \\end{pmatrix} = \\begin{pmatrix}5 &amp; 8 \\\\[1.1ex] &amp; \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"429\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kita menuju ke baris kedua, jadi kita mengalikan <strong>baris kedua dengan kolom pertama:<\/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-daab54a49cc53c320bb2965f691fd7ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] 3 &amp; 4  \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; -2 \\\\[1.1ex] 1 &amp; 5  \\end{pmatrix} = \\begin{pmatrix} -1 &amp; 8 \\\\[1.1ex] 3\\cdot 3 +4 \\cdot 1 &amp; \\end{pmatrix}= \\begin{pmatrix}5 &amp; 8 \\\\[1.1ex] 13 &amp; \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Terakhir, kita mengalikan <strong>baris kedua dengan kolom kedua<\/strong> , untuk menghitung elemen terakhir tabel:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a85e0d62a0db18c7712fd1b354f92bd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] 3 &amp; 4  \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; -2 \\\\[1.1ex] 1 &amp; 5  \\end{pmatrix}= \\begin{pmatrix} -1 &amp; 8 \\\\[1.1ex]1 &amp; 3\\cdot (-2) +4 \\cdot 5 \\end{pmatrix}=\\begin{pmatrix} 5 &amp; 8 \\\\[1.1ex] 13 &amp; 14 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"447\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi hasil perkalian matriksnya adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76f1283db0175bc1a95b0a10c8961761_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} \\bm{5} &amp; \\bm{8} \\\\[1.1ex]\\bm{13} &amp; \\bm{14} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"72\" 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> Carilah hasil perkalian matriks persegi 2&#215;2 berikut: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-de-multiplication-matricielle-22.webp\" alt=\"Latihan diselesaikan selangkah demi selangkah dalam perkalian matriks 2x2, operasi matriks\" width=\"230\" height=\"70\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini adalah hasil kali matriks berdimensi 2\u00d72.<\/p>\n<p class=\"has-text-align-left\"> Untuk menyelesaikan perkalian, Anda harus mengalikan baris matriks kiri dengan kolom matriks kanan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc7217dab49f67df2a9d2abc561baf9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{pmatrix} 4 &amp; -1  \\\\[1.1ex] -2 &amp; 3  \\end{pmatrix} \\cdot \\begin{pmatrix} -2 &amp; 5 \\\\[1.1ex] 6 &amp; -3  \\end{pmatrix}  &amp; = \\begin{pmatrix} 4\\cdot (-2)+(-1) \\cdot 6 &amp;  4\\cdot 5+(-1) \\cdot (-3)  \\\\[1.1ex](-2)\\cdot (-2)+3 \\cdot 6 &amp; (-2)\\cdot 5+3 \\cdot (-3)\\end{pmatrix} \\\\[2ex] &amp; =\\begin{pmatrix} \\bm{-14} &amp; \\bm{23} \\\\[1.1ex]\\bm{22} &amp; \\bm{-19} \\end{pmatrix} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"528\" 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> Hitung perkalian matriks 3&#215;3 berikut: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-de-multiplication-matricielle-33.webp\" alt=\"latihan menyelesaikan perkalian matriks 3x3 langkah demi langkah, operasi matriks\" width=\"277\" height=\"109\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk melakukan perkalian matriks 3\u00d73, Anda harus mengalikan baris matriks kiri dengan kolom matriks kanan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef6ee7bb6e4ac095a9fd51a545b163b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{array}{l} \\begin{pmatrix} 1 &amp; 2 &amp; 0 \\\\[1.1ex] 3 &amp; 2 &amp; -1 \\\\[1.1ex] 5 &amp; 1 &amp; -2  \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 &amp; 0 \\\\[1.1ex] 1 &amp; 0 &amp; -2 \\\\[1.1ex] -1 &amp; 2 &amp; 1 \\end{pmatrix} = \\\\[7.5ex] =\\begin{pmatrix} 1 \\cdot 3+2 \\cdot 1+ 0 \\cdot (-1) &amp; 1 \\cdot 4+2 \\cdot 0+ 0 \\cdot 2 &amp; 1 \\cdot 0+2 \\cdot (-2)+ 0 \\cdot 1 \\\\[1.1ex] 3 \\cdot 3+2 \\cdot 1+ (-1) \\cdot (-1) &amp; 3 \\cdot 4+2 \\cdot 0+ (-1) \\cdot 2 &amp; 3 \\cdot 0+2 \\cdot (-2)+ (-1) \\cdot 1 \\\\[1.1ex] 5 \\cdot 3+1 \\cdot 1+ (-2) \\cdot (-1) &amp; 5 \\cdot 4+1 \\cdot 0+ (-2) \\cdot 2 &amp; 5 \\cdot 0+1 \\cdot (-2)+ (-2) \\cdot 1 \\end{pmatrix} = \\\\[7.5ex]  =\\begin{pmatrix} \\bm{5} &amp; \\bm{4} &amp; \\bm{-4} \\\\[1.1ex] \\bm{12} &amp; \\bm{10} &amp; \\bm{-5} \\\\[1.1ex] \\bm{18} &amp; \\bm{16} &amp; \\bm{-4} \\end{pmatrix}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"306\" width=\"643\" 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> diberikan 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-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27365f9993caf4fcdb747352e4ae539d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} 3 &amp; 1 &amp; -2 \\\\[1.1ex] 4 &amp; 2 &amp; -1   \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"134\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Menghitung: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-307d37497055a6891b797bdb89b456e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2A\\cdot A^t\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" 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-tama kita akan menghitung matriks transpos dari<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> untuk melakukan perkalian. Dan untuk membuat matriks transpose, kita perlu mengubah baris menjadi kolom. Artinya, baris pertama matriks menjadi kolom pertama matriks dan baris kedua matriks menjadi kolom kedua matriks. 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-ac4785c47f2e48e15b3d98ba426848b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^t= \\begin{pmatrix} 3 &amp; 4 \\\\[1.1ex] 1 &amp; 2  \\\\[1.1ex] -2 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"131\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, operasi matriksnya tetap:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9513fa8cc6996e18e3cf287f0210817a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2A\\cdot A^t = 2 \\begin{pmatrix} 3 &amp; 1 &amp; -2 \\\\[1.1ex] 4 &amp; 2 &amp; -1   \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 \\\\[1.1ex] 1 &amp; 2  \\\\[1.1ex] -2 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"291\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita bisa melakukan perhitungan. Kita hitung dulu<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4e94385e2fa1b091190a9ce266a8c43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<p> (walaupun kita juga bisa menghitungnya terlebih dahulu<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae92cabff7a388b31fe67b559dfead7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A \\cdot A^t\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<p> ): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae5e95f09aedac8f0861bf13fb9c78a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{pmatrix} 2 \\cdot 3 &amp; 2 \\cdot 1 &amp; 2 \\cdot (-2) \\\\[1.1ex] 2 \\cdot 4 &amp; 2 \\cdot 2 &amp; 2 \\cdot (-1) \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 \\\\[1.1ex] 1 &amp; 2  \\\\[1.1ex] -2 &amp; -1 \\end{pmatrix} =\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"299\" 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-24c003b8da1081d6ca494adc3356b06b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  =\\begin{pmatrix} 6 &amp; 2 &amp; -4 \\\\[1.1ex] 8 &amp; 4 &amp; -2 \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 \\\\[1.1ex] 1 &amp; 2  \\\\[1.1ex] -2 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"220\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita menyelesaikan 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-0eb8f1817f0163a82ae39cc6c81d478e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{pmatrix} 6 \\cdot 3 +2 \\cdot 1 + (-4) \\cdot (-2) &amp; 6 \\cdot 4 +2 \\cdot 2 + (-4) \\cdot (-1) \\\\[1.1ex] 8 \\cdot 3 +4 \\cdot 1 + (-2) \\cdot (-2) &amp; 8 \\cdot 4 +4 \\cdot 2 + (-2) \\cdot (-1) \\end{pmatrix} =\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"438\" 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-33533be747b72497915048e486d16541_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = \\begin{pmatrix} \\bm{28} &amp; \\bm{32} \\\\[1.1ex]\\bm{32} &amp; \\bm{42} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"94\" 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 5<\/h3>\n<p> Perhatikan 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-6e26aec2eee6bcae0e344682d20038f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; 4  \\\\[1.1ex] -3 &amp; 5 \\end{pmatrix} \\qquad B=\\begin{pmatrix} -1 &amp; -2  \\\\[1.1ex] 3 &amp; -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"275\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Menghitung: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78d69cf0ef5ec44cd0aacf00f4f2d613_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\\cdot B - B \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"102\" 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\"> Ini adalah operasi yang menggabungkan pengurangan dengan perkalian matriks orde 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43f79f2d970bb02caaeddec34d5ad2a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\\cdot B - B \\cdot A= \\begin{pmatrix} 2 &amp; 4  \\\\[1.1ex] -3 &amp; 5 \\end{pmatrix}\\cdot \\begin{pmatrix} -1 &amp; -2  \\\\[1.1ex] 3 &amp; -3 \\end{pmatrix} - \\begin{pmatrix} -1 &amp; -2  \\\\[1.1ex] 3 &amp; -3 \\end{pmatrix}  \\cdot \\begin{pmatrix} 2 &amp; 4  \\\\[1.1ex] -3 &amp; 5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"500\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Pertama-tama kita hitung perkaliannya 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-05ff586671fb0af274884169c54e5817_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2\\cdot (-1) + 4 \\cdot 3 &amp; 2\\cdot (-2) + 4 \\cdot (-3) \\\\[1.1ex] (-3)\\cdot (-1) + 5 \\cdot 3 &amp; (-3)\\cdot (-2) + 5 \\cdot (-3)  \\end{pmatrix} - \\begin{pmatrix} -1 &amp; -2  \\\\[1.1ex] 3 &amp; -3 \\end{pmatrix}  \\cdot \\begin{pmatrix} 2 &amp; 4  \\\\[1.1ex] -3 &amp; 5 \\end{pmatrix} =\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"550\" 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-43c234a2d7aa4f9dcaf3140f617480f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle= \\begin{pmatrix} 10 &amp; -16  \\\\[1.1ex] 18 &amp; -9 \\end{pmatrix} - \\begin{pmatrix} -1 &amp; -2  \\\\[1.1ex] 3 &amp; -3 \\end{pmatrix}  \\cdot \\begin{pmatrix} 2 &amp; 4  \\\\[1.1ex] -3 &amp; 5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"308\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita selesaikan perkalian di sebelah kanan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-552309dd1be2f69bb72633539809283b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 10 &amp; -16  \\\\[1.1ex] 18 &amp; -9 \\end{pmatrix} - \\begin{pmatrix} -1 \\cdot 2 +(-2) \\cdot (-3) &amp;  -1 \\cdot 4 +(-2) \\cdot 5  \\\\[1.1ex]3 \\cdot 2 +(-3) \\cdot (-3) &amp;  3 \\cdot 4 +(-3) \\cdot 5  \\end{pmatrix} =\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"449\" 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-eeac84965cc522402e869234a841ba67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =\\begin{pmatrix} 10 &amp; -16  \\\\[1.1ex] 18 &amp; -9 \\end{pmatrix} - \\begin{pmatrix} 4 &amp;-14  \\\\[1.1ex]15 &amp; -3  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"223\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir kita kurangi 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-faefbc14fc49439616b3d131243eba79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 10-4 &amp; -16 -(-14) \\\\[1.1ex] 18-15 &amp; -9-(-3) \\end{pmatrix} =\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"214\" 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-50bac6ac99e1cf6e4b77a1a8718f9fe4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =\\begin{pmatrix} \\bm{6} &amp; \\bm{-2} \\\\[1.1ex] \\bm{3} &amp; \\bm{-6} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"90\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\">Kapan dua matriks tidak bisa dikalikan?<\/h2>\n<p> <strong>Tidak semua matriks dapat dikalikan.<\/strong> Untuk mengalikan dua matriks, jumlah kolom pada matriks pertama harus sama dengan jumlah baris pada matriks kedua.<\/p>\n<p> Misalnya perkalian berikut tidak dapat dilakukan karena matriks pertama mempunyai 3 kolom dan matriks kedua mempunyai 2 baris:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8314f9238afb3676bee5c9000c02752_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{pmatrix} 1 &amp; 3 &amp; -2 \\\\[1.1ex] 4 &amp; 0 &amp; 5 \\end{pmatrix} \\cdot  \\begin{pmatrix} 2 &amp; 1  \\\\[1.1ex] 3 &amp; -1  \\end{pmatrix}  \\ \\longleftarrow \\ \\color{red} \\bm{\\times}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"274\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Tapi kalau kita membalik urutannya, jumlahnya bisa berlipat ganda. Karena matriks pertama mempunyai dua kolom dan matriks kedua mempunyai dua baris:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37d01cc99b578d3756312c3e6ff12cae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{pmatrix} 2 &amp; 1  \\\\[1.1ex] 3 &amp; -1  \\end{pmatrix} \\cdot \\begin{pmatrix} 1 &amp; 3 &amp; -2 \\\\[1.1ex] 4 &amp; 0 &amp; 5  \\end{pmatrix}  &amp; = \\begin{pmatrix} 2\\cdot 1 + 1 \\cdot 4 &amp; 2\\cdot 3 + 1 \\cdot 0 &amp; 2\\cdot (-2) + 1 \\cdot 5  \\\\[1.1ex] 3\\cdot 1 + (-1) \\cdot 4 &amp; 3\\cdot 3 + (-1) \\cdot 0 &amp; 3\\cdot (-2) + (-1) \\cdot 5   \\end{pmatrix} \\\\[2ex] &amp; = \\begin{pmatrix} \\bm{6} &amp; \\bm{6} &amp; \\bm{1}  \\\\[1.1ex]\\bm{-1} &amp; \\bm{9} &amp; \\bm{-11}   \\end{pmatrix}   \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"624\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Sifat Perkalian Matriks<\/h2>\n<p> Jenis operasi matriks ini memiliki ciri-ciri sebagai berikut:<\/p>\n<ul>\n<li> Perkalian matriks bersifat <strong><span style=\"color:#1976d2;\">asosiatif:<\/span><\/strong><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-38541ff37ecadb79ac36ffb1e19cc187_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( A \\cdot B \\right) \\cdot C = A \\cdot \\left( B \\cdot C \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Perkalian matriks juga mempunyai <strong><span style=\"color:#1976d2;\">sifat distributif:<\/span><\/strong> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f8ca2784a9dd93cf71cd34d4d0303eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\\cdot \\left(B+C\\right) = A\\cdot B + A \\cdot C\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"216\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-119\"><\/div>\n<\/div>\n<ul>\n<li> Hasil kali matriks <strong><span style=\"color:#1976d2;\">tidak bersifat komutatif:<\/span><\/strong><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67f2cce38b1aab5659a5f888daf1ff84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A \\cdot B \\neq B \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Misalnya perkalian matriks berikut memberikan hasil:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e780b321b160ad4a612e608199a374b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{pmatrix} 1 &amp; -1  \\\\[1.1ex] 2 &amp; 3  \\end{pmatrix} \\cdot \\begin{pmatrix} -2 &amp; 5  \\\\[1.1ex] 0 &amp; 1   \\end{pmatrix}  &amp; = \\begin{pmatrix} 1\\cdot (-2) + (-1) \\cdot 0 &amp; 1\\cdot 5 + (-1) \\cdot 1   \\\\[1.1ex] 2\\cdot (-2) + 3 \\cdot 0 &amp;  2\\cdot 5 + 3 \\cdot 1    \\end{pmatrix} \\\\[2ex] &amp; = \\begin{pmatrix} \\bm{-2} &amp; \\bm{4} \\\\[1.1ex] \\bm{-4} &amp;  \\bm{13} \\end{pmatrix}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"472\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Namun hasil perkaliannya akan berbeda jika kita membalik urutan perkalian 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-177d78a209e5d9e18828617e4913176d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned}\\begin{pmatrix} -2 &amp; 5  \\\\[1.1ex] 0 &amp; 1   \\end{pmatrix} \\cdot  \\begin{pmatrix} 1 &amp; -1  \\\\[1.1ex] 2 &amp; 3  \\end{pmatrix} &amp; = \\begin{pmatrix} -2 \\cdot 1 + 5\\cdot 2 &amp;  -2 \\cdot (-1) + 5\\cdot 3  \\\\[1.1ex] 0 \\cdot 1 + 1\\cdot 2 &amp;  0 \\cdot (-1) + 1\\cdot 3   \\end{pmatrix} \\\\[2ex] &amp; = \\begin{pmatrix} \\bm{8} &amp;  \\bm{17}  \\\\[1.1ex] \\bm{2} &amp;  \\bm{3} \\end{pmatrix}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"445\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Selain itu, matriks apa pun dikalikan dengan matriks identitas akan menghasilkan matriks yang sama. Ini disebut <strong><span style=\"color:#1976d2;\">sifat identitas perkalian:<\/span><\/strong><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ab05972282922f1e10f75a50e636887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A \\cdot I=A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" 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-2c32986a7c34108a47500a4f0ec2967b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle I \\cdot A=A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> 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-9c1e72173419eb76554256cf6ccd0d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{pmatrix} 2 &amp; 7  \\\\[1.1ex] -6 &amp; 5  \\end{pmatrix} \\cdot \\begin{pmatrix} 1 &amp; 0  \\\\[1.1ex] 0 &amp; 1 \\end{pmatrix} = \\begin{pmatrix} \\bm{2} &amp; \\bm{7}  \\\\[1.1ex] \\bm{-6} &amp; \\bm{5}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"242\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Terakhir, seperti yang sudah Anda duga, matriks apa pun dikalikan dengan matriks nol sama dengan matriks nol. Ini disebut <strong><span style=\"color:#1976d2;\">sifat perkalian dari nol:<\/span><\/strong><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf700c38f25e0c3bdf1c46851341a815_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A \\cdot 0=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" 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-ac3340bc96ba3df60f6ddeb6bbd3b4b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0\\cdot A=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> 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-3152d82054a80d61d548e969290aea4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{pmatrix} 6 &amp; -4  \\\\[1.1ex] 3 &amp; 8  \\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; 0  \\\\[1.1ex] 0 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} \\bm{0} &amp; \\bm{0}  \\\\[1.1ex] \\bm{0} &amp; \\bm{0}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"228\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada halaman ini kita akan melihat cara mengalikan matriks berdimensi 2\u00d72, 3\u00d73, 4\u00d74, dst. Kami menjelaskan prosedur perkalian matriks langkah demi langkah melalui sebuah contoh, kemudian Anda akan menemukan latihan yang terselesaikan sehingga Anda juga dapat berlatih. Terakhir, Anda akan mengetahui kapan dua matriks tidak dapat dikalikan dan semua properti operasi matriks tersebut. Bagaimana cara &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\"> <span class=\"screen-reader-text\">Perkalian 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":[52],"tags":[],"class_list":["post-282","post","type-post","status-publish","format-standard","hentry","category-lukisan"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Perkalian matriks - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Perkalian matriks - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada halaman ini kita akan melihat cara mengalikan matriks berdimensi 2\u00d72, 3\u00d73, 4\u00d74, dst. Kami menjelaskan prosedur perkalian matriks langkah demi langkah melalui sebuah contoh, kemudian Anda akan menemukan latihan yang terselesaikan sehingga Anda juga dapat berlatih. Terakhir, Anda akan mengetahui kapan dua matriks tidak dapat dikalikan dan semua properti operasi matriks tersebut. Bagaimana cara &hellip; Perkalian matriks Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T21:48:53+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-multiplication-matricielle-22152.webp\" \/>\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=\"4 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Perkalian matriks\",\"datePublished\":\"2023-07-06T21:48:53+00:00\",\"dateModified\":\"2023-07-06T21:48:53+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\"},\"wordCount\":729,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Lukisan\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\",\"url\":\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\",\"name\":\"Perkalian matriks - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-07-06T21:48:53+00:00\",\"dateModified\":\"2023-07-06T21:48:53+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Perkalian matriks\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/id\/#website\",\"url\":\"https:\/\/mathority.org\/id\/\",\"name\":\"Mathority\",\"description\":\"Di mana rasa ingin tahu bertemu dengan perhitungan!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/id\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/id\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\",\"name\":\"Tim Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Tim Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Perkalian matriks - Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/","og_locale":"id_ID","og_type":"article","og_title":"Perkalian matriks - Mathority","og_description":"Pada halaman ini kita akan melihat cara mengalikan matriks berdimensi 2\u00d72, 3\u00d73, 4\u00d74, dst. Kami menjelaskan prosedur perkalian matriks langkah demi langkah melalui sebuah contoh, kemudian Anda akan menemukan latihan yang terselesaikan sehingga Anda juga dapat berlatih. Terakhir, Anda akan mengetahui kapan dua matriks tidak dapat dikalikan dan semua properti operasi matriks tersebut. Bagaimana cara &hellip; Perkalian matriks Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/","article_published_time":"2023-07-06T21:48:53+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-multiplication-matricielle-22152.webp"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"4 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Perkalian matriks","datePublished":"2023-07-06T21:48:53+00:00","dateModified":"2023-07-06T21:48:53+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/"},"wordCount":729,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Lukisan"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/","url":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/","name":"Perkalian matriks - Mathority","isPartOf":{"@id":"https:\/\/mathority.org\/id\/#website"},"datePublished":"2023-07-06T21:48:53+00:00","dateModified":"2023-07-06T21:48:53+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/id\/"},{"@type":"ListItem","position":2,"name":"Perkalian matriks"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/id\/#website","url":"https:\/\/mathority.org\/id\/","name":"Mathority","description":"Di mana rasa ingin tahu bertemu dengan perhitungan!","publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/id\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"id"},{"@type":"Organization","@id":"https:\/\/mathority.org\/id\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/id\/","logo":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38","name":"Tim Mathority","image":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Tim Mathority"},"sameAs":["http:\/\/mathority.org\/id"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/comments?post=282"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/282\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/media?parent=282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/categories?post=282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/tags?post=282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}