{"id":308652,"date":"2022-11-25T18:40:00","date_gmt":"2022-11-25T11:40:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=308652"},"modified":"2023-02-06T10:23:38","modified_gmt":"2023-02-06T03:23:38","slug":"matriks","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/matriks\/","title":{"rendered":"Pengertian Matriks, Jenis, dan Contoh Soal dengan Pembahasan"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"853\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-monstera-6238036-1.webp\" alt=\"Pengertian Matriks, Jenis, dan Contoh Soal dengan Pembahasan\" class=\"wp-image-308658\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-monstera-6238036-1.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-monstera-6238036-1-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-monstera-6238036-1-1200x800.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-monstera-6238036-1-1170x780.webp 1170w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-monstera-6238036-1-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-monstera-6238036-1-263x175.webp?crop=1 263w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, saat belajar SPLDV atau SPLTV pasti kamu akan bertemu beberapa persamaan yang memuat beberapa variabel, kan? Biasanya, kamu diminta untuk menentukan nilai setiap variabelnya. Salah satu cara yang bisa kamu gunakan untuk menyelesaikan SPLDV maupun SPLTV adalah matriks. Apa yang dimaksud dengan matriks serta apa saja jenis-jenisnya? Yuk, simak artikel selengkapnya berikut ini.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Pengertian Matriks<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Matriks adalah angka-angka yang disusun sedemikian sehingga menyerupai persegipanjang berdasarkan urutan baris dan kolom. Angka-angka yang menyusun matriks disebut sebagai unsur atau elemen. Umumnya, matriks berada di dalam tanda kurung dan dinyatakan sebagai huruf kapital. Sementara itu, unsur atau elemen dinyatakan sebagai huruf kecil serta memiliki indeks. Indeks tersebut menyatakan letak baris dan kolom unsur. Baris adalah susunan angka yang arahnya horizontal atau mendatar. Sementara kolom adalah susunan angka yang arahnya vertikal. Perhatikan contoh matriks berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/snuHYKQBMKWYnkjU6B6ap1UnWSklqjgy5q1GhBVWN59CsCOt6NAOW7p27U2_QyijF_YFK30gQiWBkNZE73_rUxvAOnk098rCCrGEwu7620EdQmNpC5FTtyey_nyhWqP12D7ZAqbSYRyUKnWbRaVhF72fwYQSa2FB0QPACBivKeEkH8bXCEHVKmiqtXRx-OiF8qpQT68uog\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari contoh di atas, <em>a<sub>11<\/sub><\/em>, <em>a<sub>12<\/sub>, a<sub>13<\/sub><\/em>, \u2026, <em>a<sub>33<\/sub> <\/em>disebut sebagai unsur. Sementara indeks 11 \u2013 33 menunjukkan letak baris dan kolom unsur <em>a<\/em>. Misalnya <em>a<sub>11<\/sub><\/em> berarti elemen <em>a<\/em> berada di baris ke-1 dan kolom ke-1, <em>a<sub>12<\/sub><\/em> berarti elemen <em>a<\/em> berada di baris ke-1 dan kolom ke-2, dan seterusnya. Nah, banyaknya baris dan kolom di dalam matriks disebut sebagai ordo. Kira-kira, matriks P di atas termasuk ordo berapa ya Quipperian?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Jenis-Jenis Matriks<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Adapun jenis-jenis matriks adalah sebagai berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1. Matriks baris<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Matriks baris adalah matriks yang hanya memiliki satu baris dengan beberapa kolom. Perhatikan contoh matriks baris berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/KBes_eDJRhpJClvIfZXnV2IemCs1OUcY6PNEdUat9LdyNYjqxmW8VB0LPGygs96RZP95LDsyEatJmHeYpMpu4v60vPpDAGCBsAqBi99XochRA1MqhfFAAb0h9bKiA5o3gNKliqkQMxDT0-Tf5OgTKVyGgjmIph7uzzQHd962Dygu6z7Zxh0SfBXbG6x2hMuim-C4sgc9HQ\" alt=\"\" width=\"94\" height=\"59\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Berdasarkan contoh di atas, baik matriks P, Q, maupun R semuanya termasuk matriks baris. Namun, ordo ketiganya berbeda karena jumlah kolomnya berbeda. Matriks P memiliki ordo 1 \u00d7 3, matriks Q memiliki ordo 1 \u00d7 4, dan matriks R memiliki ordo 1 \u00d7 2.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. Matriks kolom<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Matriks kolom adalah matriks yang hanya memiliki satu kolom dengan beberapa baris. Ya, pada prinsipnya sama sih dengan sebelumnya. Perhatikan contoh matriks kolom berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/NZUB7j52iI7-4gAEPlKFQ9TLWNPNi3kdPGV1hh7NdkxRUyGP4a7mRyQw9avUyrUp_gXGXDnH3764TEeM7TSMpSf8xJOQxobdUn7--BYPbLlhWknp86JCXNHq0sNKohquOTKO6GoCS9hWnlRT7qi5YE3LuwBVlXV2bVOV7E5LgPu6a2Bz6ThjkjfLP7ahKqaJGaBmV5Q_Ow\" alt=\"\" width=\"50\" height=\"173\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ketiga matriks di atas memiliki kolom yang sama, yaitu satu. Namun, baris ketiganya berbeda. Dengan demikian, ordonya juga pasti berbeda. Matriks P memiliki ordo 3 \u00d7 1, Q memiliki ordo 4 \u00d7 1, dan R memiliki ordo 2 \u00d7 1.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.<\/strong> <strong>Matriks nol<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Matriks nol adalah matriks yang bernilai nol di semua elemennya. Perhatikan contoh matriks nol berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/Gj7yxnB6FJUrY6dYtLaV169uJ7A7WaYlh30CrwpNyGaGXlPcK9BbgE_ilkoXotmn9DL96oKpEeFah5fx484zhS5f3BtasfkH2zlFRbrtVT-bLYE3mPwZ_TVU-XXiTOVKMeqB8Q9gKTJRvB2yj94auKa4YJJpOa3tegBIeFEd3c_Ll15r5WZ7SYAdex6uTTcOMMU7km7_HA\" alt=\"\" width=\"82\" height=\"102\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>4. Matriks persegi<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Merupakan matriks yang memiliki jumlah baris yang sama dengan kolomnya, seperti matriks ordo 2 \u00d7 2, 3 \u00d7 3, dan seterusnya. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/OqxeztVe3l3sS-ftWb6UpAKtPZuH8VcoC6KZ09ZMohU924bTXnBST8JVC2mOWXRbzZ-KXSq84ZaBt4gOiJnL1APUoAiMtSsYew8pZwnje8yZtg__Yu-yoMZLEgoIQEBktHRdiqH2d1x5JQ5dUffHNR5cPTcuQny-yKWP1T7NOUfHq5PN0mEWveCkPZpqLFVYLqHskN7kcg\" alt=\"\" width=\"111\" height=\"156\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>5.<\/strong> <strong>Matriks segitiga atas<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Merupakan bentuk matriks persegi yang elemen di bawah diagonal utamanya bernilai nol, sehingga seolah-olah berbentuk segitiga. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/tcEZ5TRyjxBEn9QsKddrEqvrC6HA2wIy2IE2Nm4bkIoGgSGXqKN7o9iptIRZMBtOkoI6lPKpf3s5I6J5Je1-7hUtGHtnsgRTiIbCL7RpH3hXrsmEDcNtYw4GpeI41uYfgy0ZJLqxXkXbVDdDkBfCoM7FNXiZ2z2MOXa_PGuOqsvZCE9WQ3C60tp0pNg5h17QExM59xmVzA\" alt=\"\" width=\"103\" height=\"71\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Matriks segitiga atas biasanya digunakan sebagai dasar untuk mencari determinan dengan metode reduksi baris.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>6.<\/strong> <strong>Matriks segitiga bawah<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Merupakan matriks persegi yang elemen di atas diagonal utamanya bernilai nol. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/yf6CnpImXKOMeGfGBOfbwYq-6uTg78bWSF3m1t9CMc_BN__9pQQz9GDRYLFcdxN78TtDpIBQotS_H3GSZXlNs7UnY5TosmqQ3Rf3FjkTD57lrRYNIXTIV2q7trWNFtcoI9NvmjjUCFJiCz7KAppTZEigdp1nb3VDwZW_KVvCNEr-aZO-WWHfMOgg6mE-LBno6ykfyFLmlw\" alt=\"\" width=\"111\" height=\"72\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>7.<\/strong> <strong>Matriks diagonal<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Merupakan matriks persegi yang semua elemennya bernilai nol, kecuali diagonal utamanya. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/_-9Mf8VnjnJN-_KTFzk5X2Yo1IrLVkjJfzIl53Cw57TwCt9PIxJ1hhjHCq55torTx-UhiFlu0nlvkb8ZQ4jI4MQ9uhn4ljGL0XZeIcg25De3z-0lxYo7x8shXh0xTgeP6yiHJZp-J5ll5cuZpN2NqL5nq7ai8izQ86N-TcnCgZlbl2UXL8cVG7r-dOgGxmSWN0_N5NdYww\" alt=\"\" width=\"101\" height=\"69\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>8.<\/strong> <strong>Matriks identitas<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Merupakan matriks diagonal yang setiap elemen diagonal utamanya bernilai satu. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/Ps4w6oxkUYq9qu2Ns8KSwn9fO0xP4xR4k-H0_15ta5YtZJeApoIJQD4w--1A7vxg2Zls7u9rJBcwGkKh0T9QJv8xFyZfP_ojDPqpi5qtPFhNfSRlgbr1ktD0aTc58XmAQqQMmEqlfhQQ6Ac5LphJ8ygTkNgwvZ8UhGaLlkNkQg4RV7GnwmDIOj-7_vgHKWDy6mQroQwEtQ\" alt=\"\" width=\"83\" height=\"106\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>9.<\/strong> <strong>Matriks singular<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Merupakan matriks yang determinannya bernilai nol. Artinya, kamu bisa menentukan singularitas matriks melalui perhitungan karena tidak bisa dilihat secara visual hanya dari bentuk matriksnya saja. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/kJ3a2ioXRPhV42y0F-DjFomFFdl5FnAIOuRKdpCpP6EV2G1duQgoZcJiEmkC7AmSKWT-8pwikFjLYyWJZvlZMwDJzBXR1Oo_zJgWXZ0hMhYwmYwuBbwYEnzUWjfb9SNXE9ymb4qrMbZGlEeePugBrDSfHxYIyNa3bKMio7gI0r_9YKa8GtW0iQ6T-rh7B6tUOnwkQNN2-w\" alt=\"\" width=\"69\" height=\"45\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Matriks P&nbsp; termasuk singular karena determinannya bernilai nol.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Det P = (2 \u00d7 8) \u2013 (4 \u00d7 4)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 16 \u2013 16<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Sifat-Sifat Matriks<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Sifat-sifat matriks berlaku pada saat matriks dioperasikan dengan matriks lain. Adapun sifat-sifatnya adalah sebagai berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Sifat penjumlahan matriks<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Penjumlahan hanya berlaku pada matriks yang memiliki ordo sama. Jika ordo antarmatriksnya berbeda, maka tidak bisa dilakukan penjumlahan. Misalnya, penjumlahan antarmatriks ordo 2 \u00d7 2, antarmatriks 3 \u00d7 3, dan seterusnya. Penjumlahan ini memenuhi sifat-sifat berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sifat komutatif, yaitu sifat yang memenuhi A + B = B + A.<\/li>\n\n\n\n<li>Sifat asosiatif, yaitu sifat yang memenuhi (A + B) + C = A + (B + C).<\/li>\n\n\n\n<li>Sifat matriks nol, yaitu sifat yang memenuhi A + 0 = A.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Sifat pengurangan matriks<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sama seperti penjumlahan, pengurangan hanya berlaku untuk matriks berordo sama. Namun, sifat-sifat penjumlahan tidak berlaku pada pengurangan, kecuali sifat pengurangan dengan matriks nol, yaitu A \u2013 0 = A.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Sifat perkalian matriks<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Perkalian antara dua matriks bisa dilakukan jika jumlah kolom matriks pertama sama dengan jumlah baris matriks kedua. Misalnya matriks ordo 2 x 3 bisa dikalikan dengan ordo 3 x 2, matriks ordo 3 x 1 bisa dikalikan ordo 1 x 3, dan seterusnya. Ingat, ketentuan ini tidak bisa dibalik, ya. Pada perkalian matriks berlaku sifat-sifat berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sifat asosiatif, yaitu (A \u00d7 B) \u00d7 C = A \u00d7 (B \u00d7 C).<\/li>\n\n\n\n<li>Sifat distributif, yaitu A \u00d7 (B + C) = (A \u00d7 B) + (A \u00d7 C).<\/li>\n\n\n\n<li>Perkalian dengan matriks nol akan menghasilkan matriks nol, yaitu A \u00d7 0 = 0.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Cara Menghitung Matriks<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Cara menghitung matriks tentu tidak lepas dari operasi penjumlahan, pengurangan, dan perkalian. Lantas, bagaimana cara menghitungnya?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Cara menghitung hasil penjumlahan matriks<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Hasil penjumlahan matriks diperoleh dengan menjumlahkan elemen-elemen yang seletak. Misalnya elemen pada baris ke-1 dan kolom ke-1 dijumlahkan dengan elemen yang sama. Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui dua buah matriks seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/25BJBogEGnMTf7WLcm4ch3tq2ygjsticdpUuPI-oIfThly251m1aARlkto3SsnGXw_B3-nz4HKQqrYR5Vw6Pv2RTeiRIAhEQZG1XNQsLYXtfk7vPezr4nWBShpGF4SKBJuRJRDjAjPPAClQqOVoDoPLPvN2Mi9OOW84pcnMY2juIUjf1TvENKHEZaIkp5RkxVi11A8i-Pg\" alt=\"\" width=\"99\" height=\"115\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan hasil penjumlahan kedua matriks tersebut!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jangan lupa untuk menjumlahkan elemen yang seletak.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/6prJssJC9Zqks49_MCtQcO9Tkv6g9aSUg4haFQ-OoEKD3tmao8hfYE7da3_WuSPhuMtSIi26R-57W6q-NzqpCrDDt67HOqfJX5VKzma9SrMZIZUPeY60xk0vwS0e5WQ-IWtEGZZ6jT7dQ0QKH9o_5e-aqr66dD8mUXW4tNpXl3DWdmeiSNELPHh0cQ1Od5iyFKhryaxigg\" alt=\"\" width=\"199\" height=\"166\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, hasil penjumlahannya adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/ueVys0qBLbZdThrO_KTSUUz3JxLiPwI8VS0RESvKKZf8tPffclmE7Vou-6Jgdsxu5W7akVuVDoRbOjQ9NlmH4CFvU-50wAYyZlXv79ScRS6Q_P4vNu0zenE1cZAFtvKkKJutk0M1sViUferwWxeLrlOaag9h-kHvkKI7wB2PJCU-kfmzBybCRTHlTpUP_hd7_fKHpnEahg\" alt=\"\" width=\"109\" height=\"57\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Cara menghitung hasil pengurangan matriks<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Cara menghitung hasil pengurangan matriks sama dengan penjumlahan, yaitu mengurangkan elemen yang seletak. Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui dua matriks seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/25BJBogEGnMTf7WLcm4ch3tq2ygjsticdpUuPI-oIfThly251m1aARlkto3SsnGXw_B3-nz4HKQqrYR5Vw6Pv2RTeiRIAhEQZG1XNQsLYXtfk7vPezr4nWBShpGF4SKBJuRJRDjAjPPAClQqOVoDoPLPvN2Mi9OOW84pcnMY2juIUjf1TvENKHEZaIkp5RkxVi11A8i-Pg\" alt=\"\" width=\"102\" height=\"118\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan hasil pengurangan P \u2013 Q!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Berikut ini hasil pengurangannya.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/d2Ox1ybm_tUh7uF-2B3EGLcpITIwoZKz1hMC123SBVZBo0rNRnMVJPrptUaPcLtdKmvkVVZ5YM4v44ZvRKjAPgIt6Ig4KaybAB9RuyEmMB-NqIXEgSb-hbPLe_GQCOskwemaNeymxO0OfJ0fphwK3oJoVoGKmT-dn41rAG3lsi2pe1p-AQ_kAbqIrxmd2tDE3RTXk9gelg\" alt=\"\" width=\"208\" height=\"172\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, hasil pengurangannya adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/tLWvJZbyDV_nPFmJNuMCAJiwcJ_8e66mxAylc505MVAwi3rb6vTTPnWIMPw8LI2bXhAhNtP2BlqsbiH0zTSqIKv5pJMwJZrp1J1Vi5DQaSOUPcSL7gWXQhqHs6TaDTR4GQopeQNm8qtDSIMPn7tlXNrnciM06K_GU2N3Ng7iD_5CPyegF6LWsWoJAb16mDl-WwfBFQAlBw\" alt=\"\" width=\"116\" height=\"61\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Cara menghitung hasil perkalian matriks<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Cara menghitung perkalian antara dua matriks adalah dengan mengalikan semua elemen baris matriks pertama dengan semua elemen kolom di matriks kedua secara berurutan. Perhatikan ilustrasi berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/N78HI3TFYQKN6zeyM_nKdsfqshXkhPUvQEwZX0z9PazxfAGI2vBmeT2WEVG7HmQXWbUGdUE75ES4zTo-z3HuBLNDevynFpuGlhE1hFCXfdJ7QwXfqUEzt0qRmcEQVLYNE4Nw4uP3JJMhxKvFn3JDxpsljEd7YhEkRYUXkSStwcx__Qi8rDIWuoaVY8ici3acAeAJwj3oTg\" alt=\"\" width=\"249\" height=\"263\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Sampai sini, apakah Quipperian sudah paham cara menghitung hasil operasi matriks?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Transpose Matriks<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Saat belajar materi ini, tak lengkap rasanya jika belum belajar transpose. Apa sih transpose matriks itu? Transpose matriks adalah matriks baru yang dihasilkan oleh perpindahan elemen baris menjadi elemen kolom. Penulisan transpose matriks biasanya dinyatakan sebagai indeks (superscript) pada matriks awalnya, misal A<sup>T<\/sup>, P<sup>T<\/sup>, B<sup>T<\/sup>, dan seterusnya. Perhatikan ilustrasi berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/60ec2aZfvuUqErMBSAuRlWgHK9tX2cycY3oG714Wwtf9UHlfC85ULQDtfljcOydRUAB1cMHA2dDvxqUKVYkScDWwjw7lfxZSa0Fu4I8muuPpuDSohcCnhm6nGbOkSS_v0d6F1zjtTpFZaBOvt1fxp8kcbWYMi_mLCTaM_NJF8pWQMytn0u_4QsJKzobQBb78zOGw7-5_Jg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari ilustrasi di atas, perpindahan elemen baris menjadi kolom ditandai dengan warna garis putus-putus yang sama.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Soal Matriks<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mengasah pemahamanmu tentang pembahasan kali ini, yuk simak contoh soal berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh soal 1<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui persamaan matriks seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/czdvpHyvPUrIHE99d1pZKkY2_UY7ffQCFYuDYT4-L7tv0d6ftm78CMiz3c7Q01m3HegL0EJWZ__Pb0PzrkqBWHCx-9RtAweD5OvBSx-ssvE4kctyWZDveTphC5Pbin3N0wq622iSRSDZX615-zYP8qfPUsoZrKULL-ACBYe8CETMBK3CfDXv7ra5Da99NAEHUPKPKj9vMA\" alt=\"\" width=\"118\" height=\"46\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan nilai <em>x<\/em> \u2013 <em>y<\/em>!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pada soal di atas, berlaku perkalian matriks. Oleh sebab itu, kamu harus menguraikan hasil perkaliannya.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/W-nL9xUguCYA4enfwt8zgp7DpKeQespFVRi1oBjDQvco_N_97p5YuChmb8gehCuOoRUIc7euvTFY-itnYkVenrXuoxCUTSSaYJnkchKVxfE7m7OMOyzliUVjfFU4zkQ2ZtmKCsB1NCLV5G_izNB3DgKuWhNrQzCJ5GCkEkjeTn-rLo-hJUuqPZ58czdcfaRugYT3vWAduA\" alt=\"\" width=\"124\" height=\"120\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, <em>x<\/em> \u2013 <em>y<\/em> = 2 \u2013 4 = -2.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh soal 2<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui data ketersediaan beberapa merek vaksin di enam puskesmas.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Puskesmas<\/th><th>Vaksin A<\/th><th>Vaksin B<\/th><th>Vaksin C<\/th><th>Vaksin D<\/th><\/tr><\/thead><tbody><tr><td>Kecamatan 1<\/td><td>Tidak ada<\/td><td>120 sasaran<\/td><td>100 sasaran<\/td><td>Tidak ada<\/td><\/tr><tr><td>Keamatan 2<\/td><td>10 sasaran<\/td><td>Tidak ada<\/td><td>50 sasaran<\/td><td>10 sasaran<\/td><\/tr><tr><td>Kecamatan 3<\/td><td>138 sasaran<\/td><td>88 sasaran<\/td><td>Tidak ada<\/td><td>5 sasaran<\/td><\/tr><tr><td>Kecamatan 4<\/td><td>Tidak ada<\/td><td>100 sasaran<\/td><td>70 sasaran<\/td><td>Tidak ada<\/td><\/tr><tr><td>Kecamatan 5<\/td><td>1 sasaran<\/td><td>Tidak ada<\/td><td>Tidak ada<\/td><td>128 sasaran<\/td><\/tr><tr><td>Kecamatan 6<\/td><td>20 sasaran<\/td><td>90 sasaran<\/td><td>50 sasaran<\/td><td>TIdak ada<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Buatlah bentuk matriks dari data di atas!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk membuat matriks, kamu hanya perlu melihat banyaknya baris dan kolom yang tertera pada tabel. Data pada tabel di atas akan membentuk matriks ordo 6 \u00d7 4 seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/WcKxXYSpgqmsi-HMyHbDzK6DNkoloaSzxnDFb0QNycZiG8BES0p_pHdZSbias2vD94ruH2BFAmErNaQCKfo9MBB1QOsvxmMyfX_6nkSYcbPivIldyFkJTVE7wakaBspS5BBAvVZxfxdFLrajSYPyEG4fru3o8fmfxaRnFVU3n5_bHriJcf-arHolJfQ8FCNJoMdqJk_acg\" alt=\"\" width=\"155\" height=\"143\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ternyata, cara membuatnya sangat mudah kan?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh soal 3<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui dua transpose matriks seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/FuoloP51PorZ6QBfeYeLunOX1Br0NxPTGKQEmG9l34sBvVNNT_VPDT1bczoES9mCPXLqmm4hg6OGgzlLDMhVD6QqTAV8PMQYRydSJguTy9NBGHXwYUi8fy-xXVWoGpoeDZd2gZkR2f5SSh0oamO3i41BOT-4O3OHOBJ9leW78gwLGQGPqofv3wBJ5mNMJCodBLY82eEXjg\" alt=\"\" width=\"128\" height=\"95\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Berapakah hasil perkalian antara D dan E?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, kamu harus mencari komposisi matriks awalnya, yaitu D dan E.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/vQHxybzFHOGK76ETjjLxeH8YkpUOkzSKRroAHyNld4GdxMN5BXw4bfdvnG5yFYLZGFRCcNeQ_aYb_Gb1ssOXqKHrVvYnYn_Ger-_RyuY-i3WXc547kunRDKuZ526hhtXjd4atyiUslLy9IExj7yyx739q6DxCYMyM5-BYSpTUz3jmzNbMbK9soOSopZXjxZlL1BA5YdMMg\" alt=\"\" width=\"123\" height=\"155\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, hasil perkalian antara D dan E adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/Jc0zWm8_Yxw0J-DtMnimzSRi7QrZhIS7yCfjPUvpOAx2XwGfnlWjBSKEbrv-XpjXY03OrLUqjco-Z-atmIK6G_r9tIvyh8YxNuNpeaWDMH8ck0XW3-OiDW0l2muwz44iXCzZp3zoD1XxRGeJFtJyA__L3Fm8cbHlRaI2yUQw24d1Dca460_8uzK9VZ-oudAEMLImP-AzTA\" alt=\"\" width=\"175\" height=\"316\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat, ya. Untuk melihat materi lengkapnya, yuk buruan gabung <a href=\"https:\/\/www.quipper.com\/id\/video\/\">Quipper Video.<\/a> Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, saat belajar SPLDV atau SPLTV pasti kamu akan bertemu beberapa persamaan yang memuat beberapa variabel, kan? Biasanya, kamu diminta untuk menentukan nilai&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":308658,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[679384825],"ppma_author":[679386823,679386836],"class_list":["post-308652","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-11"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Matriks, Jenis, dan Contoh Soal dengan Pembahasan - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Matriks adalah angka-angka yang disusun sedemikian sehingga menyerupai persegipanjang berdasarkan urutan baris dan kolom.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/matriks\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pengertian Matriks, Jenis, dan Contoh Soal dengan Pembahasan - 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