{"id":280,"date":"2023-07-06T22:09:09","date_gmt":"2023-07-06T22:09:09","guid":{"rendered":"https:\/\/mathority.org\/id\/perkalian-suatu-bilangan-dengan-matriks-2x2-dan-3x3-contoh-dan-latihan-soalnya\/"},"modified":"2023-07-06T22:09:09","modified_gmt":"2023-07-06T22:09:09","slug":"perkalian-suatu-bilangan-dengan-matriks-2x2-dan-3x3-contoh-dan-latihan-soalnya","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/perkalian-suatu-bilangan-dengan-matriks-2x2-dan-3x3-contoh-dan-latihan-soalnya\/","title":{"rendered":"Mengalikan suatu bilangan dengan matriks"},"content":{"rendered":"<p>Pada halaman ini kita akan melihat cara <strong>mengalikan suatu bilangan dengan matriks.<\/strong> Anda juga memiliki contoh yang akan membantu Anda memahaminya dengan sempurna dan menyelesaikan latihan sehingga Anda dapat berlatih. Anda juga akan menemukan semua properti hasil kali skalar dan matriks.<\/p>\n<h2 class=\"wp-block-heading\"> Bagaimana cara mengalikan suatu bilangan dengan matriks?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Untuk <strong>mengalikan suatu bilangan dengan matriks<\/strong> , kalikan setiap elemen matriks dengan bilangan tersebut.<\/p>\n<h2 class=\"wp-block-heading\"> Contoh: <\/h2>\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-dun-nombre-par-une-matrice.webp\" alt=\"contoh perkalian atau hasil kali suatu bilangan dengan matriks\" width=\"514\" height=\"122\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Menyelesaikan masalah perkalian suatu bilangan dengan matriks<\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1: <\/h3>\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-scalaire-entre-un-nombre-et-une-matrice-22.webp\" alt=\"Menyelesaikan latihan perkalian suatu bilangan dengan matriks 2x2, operasi dengan matriks\" width=\"107\" 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 perkalian skalar dengan matriks persegi berorde 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-590b79c0fea524b963397181b6f2bea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 3 \\begin{pmatrix} 1 &amp; 3 \\\\[1.1ex] 2 &amp; -4  \\end{pmatrix} = \\begin{pmatrix} 3\\cdot 1 &amp; 3\\cdot 3 \\\\[1.1ex] 3\\cdot 2 &amp; 3\\cdot (-4)  \\end{pmatrix} = \\begin{pmatrix} \\bm{3} &amp; \\bm{9} \\\\[1.1ex] \\bm{6} &amp; \\bm{-12} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"348\" 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<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-dun-nombre-par-une-matrice-33.webp\" alt=\"latihan diselesaikan langkah demi langkah perkalian suatu bilangan dengan matriks 3x3, operasi dengan matriks\" width=\"184\" height=\"106\" 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 suatu bilangan dengan matriks persegi berorde 3: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5042f0f8cd9b7a4d0e28974f793b145b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -4 \\begin{pmatrix} 2 &amp; 1 &amp; 5 \\\\[1.1ex] -1 &amp; 0 &amp; 3 \\\\[1.1ex] 6 &amp; -2 &amp; -3  \\end{pmatrix} = \\begin{pmatrix} -4 \\cdot 2 &amp; -4 \\cdot 1 &amp; -4 \\cdot 5 \\\\[1.1ex] -4 \\cdot (-1) &amp; -4 \\cdot 0 &amp; -4 \\cdot 3 \\\\[1.1ex] -4 \\cdot 6 &amp; -4 \\cdot (-2) &amp; -4 \\cdot (-3)  \\end{pmatrix}= \\begin{pmatrix} \\bm{-8} &amp; \\bm{-4} &amp; \\bm{-20} \\\\[1.1ex] \\bm{4} &amp; \\bm{0} &amp; \\bm {-12}  \\\\[1.1ex] \\bm{-24} &amp; \\bm{8} &amp; \\bm {12} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"627\" 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 3: <\/h3>\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\/operations-combinees-avec-des-matrices-22152.webp\" alt=\"Soal latihan perkalian suatu bilangan dengan matriks 2x2, operasi gabungan matriks\" width=\"233\" 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 operasi yang menggabungkan hasil kali bilangan dengan matriks dan jumlah matriks berdimensi 2\u00d72:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56d2a40f021be13a5d92d0c10d353684_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2 \\begin{pmatrix} 5 &amp; 1 \\\\[1.1ex] -2 &amp; 3  \\end{pmatrix}+5\\begin{pmatrix} 5 &amp; 1 \\\\[1.1ex] -2 &amp; 3  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"193\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, pertama-tama kita perlu menyelesaikan produk:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-068901abef987767025bb01b24579226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 10 &amp; 2 \\\\[1.1ex] -4 &amp; 6  \\end{pmatrix}+\\begin{pmatrix} 25 &amp; 5 \\\\[1.1ex] -10 &amp; 15  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"183\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir kita menjumlahkan 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-d15ea16036f522af0f23fee0bb796757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} \\bm{35} &amp; \\bm{7} \\\\[1.1ex] \\bm{-14} &amp; \\bm{21}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"85\" 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 class=\"has-text-align-left\"> 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-5374cb55dbbfa80c91a478b4cbdb2ee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; -3 &amp; 5 \\\\ 1 &amp; 4 &amp; 0 \\\\ -3 &amp; 2 &amp; -5 \\end{pmatrix}  \\qquad B=\\begin{pmatrix} 6 &amp; 0 &amp; 2 \\\\ -3 &amp; 4 &amp; 1 \\\\ 3 &amp; 2 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"344\" style=\"vertical-align: -27px;\"><\/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-d5f0b93a77e7bb1b7b99d63546652e8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2A+5I-3B\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"119\" 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\"> Merupakan operasi yang menggabungkan perkalian skalar dengan penjumlahan dan pengurangan matriks berdimensi 3\u00d73. Selanjutnya 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-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah matriks identitas, yang terdiri dari 1 pada diagonal utama dan 0 pada elemen lainnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dce934040dc05714321dbbeac4e20c73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2\\begin{pmatrix} 2 &amp; -3 &amp; 5 \\\\[1.1ex] 1 &amp; 4 &amp; 0 \\\\[1.1ex] -3 &amp; 2 &amp; -5 \\end{pmatrix}+5\\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex]  0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix} -3 \\begin{pmatrix} 6 &amp; 0 &amp; 2 \\\\[1.1ex] -3 &amp; 4 &amp; 1 \\\\[1.1ex] 3 &amp; 2 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"412\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kita lakukan perkalian 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-dc26f29384abcfb6f08a36b601e4ff61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -4 &amp; 6 &amp; -10 \\\\[1.1ex] -2 &amp; -8 &amp; 0 \\\\[1.1ex] 6 &amp; -4 &amp; 10 \\end{pmatrix}+\\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5 \\end{pmatrix} - \\begin{pmatrix} 18 &amp; 0 &amp; 6 \\\\[1.1ex] -9 &amp; 12 &amp; 3 \\\\[1.1ex] 9 &amp; 6 &amp; 21 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"385\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menambahkan dua matriks pertama:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-897ec02d46bc09bdec58d9b3246c6f4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{pmatrix} 1 &amp; 6 &amp; -10 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\\\[1.1ex] 6 &amp; -4 &amp; 15 \\end{pmatrix}-\\begin{pmatrix} 18 &amp; 0 &amp; 6 \\\\[1.1ex] -9 &amp; 12 &amp; 3 \\\\[1.1ex] 9 &amp; 6 &amp; 21 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"274\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Terakhir, kami melakukan pengurangan 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-9ddd808a46a137f4c7742545c4f76f46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} \\bm{-17} &amp; \\bm{6} &amp; \\bm{-16} \\\\[1.1ex] \\bm{7} &amp; \\bm{-15} &amp; \\bm{-3} \\\\[1.1ex] \\bm{-3} &amp; \\bm{-10} &amp; \\bm{-6} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"148\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Jika latihan tentang perkalian skalar matriks ini bermanfaat bagi Anda, jangan ragu untuk berlatih dengan latihan yang diselesaikan langkah demi langkah tentang <a href=\"https:\/\/mathority.org\/id\/penjumlahan-pengurangan-matriks-2x2-3x3-contoh-soal-latihan-yang-diselesaikan\/\">penjumlahan matriks<\/a> dan <a href=\"https:\/\/mathority.org\/id\/contoh-perkalian-matriks-2x2-dan-3x3-serta-latihannya-diselesaikan-langkah-demi-langkah\/\">hasil kali matriks<\/a> , dua jenis operasi matriks yang akan diulangi lebih lanjut.<\/p>\n<h2 class=\"wp-block-heading\"> Sifat-sifat hasil kali suatu bilangan dengan matriks<\/h2>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p> Seperti yang telah anda ketahui, ada banyak <a href=\"https:\/\/mathority.org\/id\/jenis-matriks\/\">jenis matriks<\/a> : matriks persegi, matriks segitiga, matriks identitas, dll. Namun untungnya, semua sifat hasil kali bilangan dengan matriks berlaku untuk semua kelas matriks.<\/p>\n<p> Berikut sifat-sifat perkalian antara skalar dan matriks:<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Properti 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-bff3550cd8d240f651354e6646e6bf15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a \\cdot (b \\cdot A) = (a \\cdot b) \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Perhatikan dua operasi berikut karena keduanya memberikan hasil yang sama tidak peduli bagaimana kita mengalikan 2 dan 3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e9fd568edd5833238d8d21fdf4d1a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2 \\cdot \\left(3 \\cdot \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 2 &amp; -1 \\end{pmatrix} \\right) =2 \\cdot \\begin{pmatrix} 3 &amp; 0 \\\\[1.1ex] 6 &amp; -3 \\end{pmatrix} = \\begin{pmatrix} \\bm{6} &amp; \\bm{0} \\\\[1.1ex] \\bm{12} &amp; \\bm{-6} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"372\" 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-9f8ee596b3e2ca16ff1c507717982ee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (2 \\cdot 3) \\cdot \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 2 &amp; -1 \\end{pmatrix}  =6 \\cdot \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 2 &amp; -1 \\end{pmatrix}   = \\begin{pmatrix} \\bm{6} &amp; \\bm{0} \\\\[1.1ex] \\bm{12} &amp; \\bm{-6}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"357\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Sifat distributif<\/span><\/strong> terhadap penjumlahan skalar:<\/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-5829e6e40633068cc4f35b43184a41e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b) \\cdot A = a \\cdot A+ b \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"192\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Seperti terlihat pada contoh di bawah, sama saja jika kita menjumlahkan 1+2 terlebih dahulu kemudian mengalikannya dengan matriks, atau jika kita mengalikan matriks secara terpisah dengan 1 dan 2 kemudian dijumlahkan hasilnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-025ac9b0851ed93fd0c3870328d6144b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (1 + 2) \\cdot  \\begin{pmatrix} 2 &amp; -1 \\\\[1.1ex] 3 &amp; 5 \\\\[1.1ex] -2 &amp; -4 \\end{pmatrix} =3 \\cdot  \\begin{pmatrix} 2 &amp; -1 \\\\[1.1ex] 3 &amp; 5 \\\\[1.1ex] -2 &amp; -4 \\end{pmatrix}=  \\begin{pmatrix} \\bm{6} &amp; \\bm{-3} \\\\[1.1ex] \\bm{9} &amp; \\bm{15} \\\\[1.1ex] \\bm{-6} &amp; \\bm{-12} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"416\" 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-2f54f4d5ae113e2462b752c150b3f43b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1  \\cdot  \\begin{pmatrix} 2 &amp; -1 \\\\[1.1ex] 3 &amp; 5 \\\\[1.1ex] -2 &amp; -4 \\end{pmatrix} + 2  \\cdot  \\begin{pmatrix} 2 &amp; -1 \\\\[1.1ex] 3 &amp; 5 \\\\[1.1ex] -2 &amp; -4\\end{pmatrix} = \\begin{pmatrix} 2 &amp; -1 \\\\[1.1ex] 3 &amp; 5\\\\[1.1ex] -2 &amp; -4 \\end{pmatrix} +  \\begin{pmatrix} 4 &amp; -2 \\\\[1.1ex] 6 &amp; 10 \\\\[1.1ex] -4 &amp; -8\\end{pmatrix}=  \\begin{pmatrix} \\bm{6} &amp; \\bm{-3} \\\\[1.1ex] \\bm{9} &amp; \\bm{15} \\\\[1.1ex] \\bm{-6} &amp; \\bm{-12}  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"568\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Sifat distributif<\/span><\/strong> terhadap penjumlahan matriks:<\/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-fac6ec8cbb2d4ead773b75d0180bca20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a \\cdot \\left(A + B \\right) = a \\cdot A + a \\cdot B\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"202\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dengan kata lain, menjumlahkan dua matriks matematika lalu mengalikannya dengan suatu bilangan sama dengan mengalikan kedua matriks tersebut secara terpisah dengan bilangan yang sama lalu menjumlahkan hasilnya. Pada contoh di bawah ini Anda dapat memeriksa:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdb35d5c66ee525c3d52fe7576e75758_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 4 \\cdot  \\left( \\begin{pmatrix} 3 &amp; -2 \\\\[1.1ex] 6 &amp; -1 \\end{pmatrix}+\\begin{pmatrix} -1 &amp; 3 \\\\[1.1ex] 0 &amp; 4 \\end{pmatrix} \\right) =4 \\cdot   \\begin{pmatrix} 2 &amp; 1 \\\\[1.1ex] 6 &amp; 3 \\end{pmatrix}= \\begin{pmatrix} \\bm{8} &amp; \\bm{4} \\\\[1.1ex] \\bm{24} &amp; \\bm{12} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"430\" 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-0ef9d3f8f503371fa5f3d2478f728d88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 4 \\cdot  \\begin{pmatrix} 3 &amp; -2 \\\\[1.1ex] 6 &amp; -1 \\end{pmatrix}+ 4 \\cdot \\begin{pmatrix} -1 &amp; 3 \\\\[1.1ex] 0 &amp; 4 \\end{pmatrix} = \\begin{pmatrix} 12 &amp; -8 \\\\[1.1ex] 24 &amp; -4 \\end{pmatrix}+\\begin{pmatrix} -4 &amp; 12 \\\\[1.1ex] 0 &amp; 16 \\end{pmatrix} = \\begin{pmatrix} \\bm{8} &amp; \\bm{4} \\\\[1.1ex] \\bm{24} &amp; \\bm{12} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"530\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Properti elemen netral:<\/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-244c951ff1cce8dc60f6d66a781c0580_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1 \\cdot A = A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, ketika mengalikan suatu matriks dengan 1, kita tidak mengubah matriks tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ee2c0afd1bf2904722701caca883125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 \\cdot   \\begin{pmatrix} 5 &amp; -4 &amp; 0 \\\\[1.1ex] 1 &amp; 3 &amp; -3 \\\\[1.1ex] 2 &amp; 9 &amp; 4 \\end{pmatrix}=\\begin{pmatrix} \\bm{5} &amp; \\bm{-4} &amp; \\bm{0} \\\\[1.1ex] \\bm{1} &amp; \\bm{3} &amp; \\bm{-3} \\\\[1.1ex] \\bm{2} &amp; \\bm{9} &amp; \\bm{4} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"275\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ini semua adalah sifat-sifat hasil kali skalar dan matriks, jadi itulah akhir artikel ini. Kami harap Anda menyukainya dan, yang terpenting, Anda mempelajari cara menyelesaikan perkalian bilangan dengan matriks.<\/p>\n<p> Di sisi lain, operasi matriks lain yang terkait dengan perkalian, dan yang sangat berguna, adalah pangkat. Di sini kami meninggalkan Anda halaman di mana Anda akan mempelajari apa itu dan bagaimana menyelesaikan <a href=\"https:\/\/mathority.org\/id\/contoh-pangkat-matriks-2x2-dan-3x3-serta-latihan-penyelesaiannya\/\">pangkat matriks<\/a> , jika Anda penasaran.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada halaman ini kita akan melihat cara mengalikan suatu bilangan dengan matriks. Anda juga memiliki contoh yang akan membantu Anda memahaminya dengan sempurna dan menyelesaikan latihan sehingga Anda dapat berlatih. Anda juga akan menemukan semua properti hasil kali skalar dan matriks. Bagaimana cara mengalikan suatu bilangan dengan matriks? Untuk mengalikan suatu bilangan dengan matriks , &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/perkalian-suatu-bilangan-dengan-matriks-2x2-dan-3x3-contoh-dan-latihan-soalnya\/\"> <span class=\"screen-reader-text\">Mengalikan suatu bilangan dengan 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-280","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 suatu bilangan dengan 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\/perkalian-suatu-bilangan-dengan-matriks-2x2-dan-3x3-contoh-dan-latihan-soalnya\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Perkalian suatu bilangan dengan matriks - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada halaman ini kita akan melihat cara mengalikan suatu bilangan dengan matriks. 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