{"id":307478,"date":"2022-11-08T10:06:26","date_gmt":"2022-11-08T03:06:26","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=307478"},"modified":"2023-02-06T10:17:57","modified_gmt":"2023-02-06T03:17:57","slug":"operasi-matriks","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/operasi-matriks\/","title":{"rendered":"Pengertian Operasi Matriks, Jenis dan Contoh"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1920\" height=\"1280\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash.webp\" alt=\"\" class=\"wp-image-307507\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash.webp 1920w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash-1536x1024.webp 1536w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash-1200x800.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash-1170x780.webp 1170w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/antoine-dautry-_zsL306fDck-unsplash-263x175.webp?crop=1 263w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, untuk menyelesaikan permasalahan Matematika yang memuat lebih dari satu variabel, kamu bisa menggunakan matriks <em>lho<\/em>. Matriks bisa dioperasikan seperti operasi bilangan. Lalu, apa itu operasi matriks? Operasi matriks adalah operasi suatu bentuk matrik.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pada artikel ini, Quipper Blog akan mengajak Quipperian untuk belajar tentang operasi matriks beserta jenis-jenisnya. <em>Nah, <\/em>semakin penasaran kan? Yuk, simak selengkapnya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Apa Itu Operasi pada Matriks?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Operasi matriks adalah operasi suatu bentuk matriks, seperti penjumlahan, pengurangan, dan perkalian. Untuk penjumlahan dan pengurangan hanya bisa dilakukan pada matriks yang ordonya sama. Lalu, apakah yang dimaksud ordo? Ordo adalah banyaknya baris dan kolom suatu matriks. Umumnya, ordo dinyatakan sebagai bentuk perkalian antara baris dan kolom.&nbsp; Misalnya suatu matriks memiliki ordo 2 x 2. Artinya, memiliki 2 baris dan 2 kolom. Rumus matriks dilihat dari jumlah baris dan kolom, yaitu sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk lebih lebih jelasnya tentang matriks ordo 2 x 2, perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/N6F8LO4onr9gFSKMmmFV5_pOpS2V-ZEckGmD7VDppa-_0LZGojNXYoP2KN7d-mU_G0Vcrextu7LzkrqyRZEQeQJQRyBd1_ggqFdosRLLgc_k6iM3sAHPRG0lkoB7iVwzIg4eLDCWnlx0CaW4nn-JtICi1L8RInGJNAJUMMGgpYuCsAgJ5kgIEL7KHdGzaFt7UTeoQ24rYw\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Jenis Operasi Matriks?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Seperti pada pembahasan sebelumnya, jenis operasi matriks dibagi menjadi tiga, yaitu penjumlahan, pengurangan, dan perkalian. Penjabaran ketiga jenis operasi matriks tersebut adalah sebagai berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Penjumlahan Matriks<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Konsep penjumlahan matriks sama seperti penjumlahan pada bilangan. Salah satu syarat penjumlahan ini adalah matriks yang dijumlahkan memiliki ordo yang sama. Misalnya matriks P ordo 2 x 2 hanya bisa dijumlahkan dengan matriks lain yang ordonya juga 2 x 2, matriks Q ordo 3 x 3 hanya bisa dijumlahkan dengan matriks lain yang ordonya 3 x 3, dan seterusnya. Operasi penjumlahan ini juga memenuhi sifat-sifat berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sifat komutatif<br>Pada sifat ini berlaku A + B = B + A.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sifat asosiatif<br>Pada sifat ini berlaku (A + B) + C = A +(B + C)<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Matriks nol<br>Pada sifat ini berlaku A + 0 = A.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Jika dijumlahkan dengan lawannya akan menghasilkan matriks nol, yaitu A + (-A) = 0.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk lebih jelasnya, perhatikan contoh soal penjumlahan matriks berikut ini.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Contoh soal Penjumlahan Matriks 1<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui dua buah matriks, yaitu matriks A dan B seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/GmgrCqyMd8ENC6PTe1xw8pT_wECVoWvCJsFuZ-iZJbt1qJYb09Gaxe0YShEsCvgUOUoWYL1qQDDdnj6Ibllg7bj1ZSrx2aD8qiAvJy5cYF5J1gT-QwkkzVaVTnUTiCM3Qpm3QIJstj1Vyp55FDLr8_Y1RwCtZgMiryqMJOiessEopZYQyO6GzXs2ySha0BaROsn5NxYscg\" alt=\"\" width=\"88\" height=\"103\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan hasil penjumlahan matriks A dan B tersebut dan buktikan bahwa kedua matriks tersebut memenuhi sifat komutatif.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ingat, penjumlahan matriks dilakukan pada elemen yang baris dan kolomnya sama.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/7RbebSOlBPnhyneBIkSW2jilnmoHRByMZfyqpkIywie88Hu0TrpIk1OxURXKmgh-fovwH4rcfioCsqUeDWGWUlEs7Mt5AJ_SDY7sJwmsJXCwLlU4gBlJss9IkzttwsbwvJzTW5RNFgcU9g1ZS9lrcCMV2iAzcdYcCGLEOSNXku8822DLkY0zrjFKKmW0iEqnC1ahbR6NGg\" alt=\"\" width=\"171\" height=\"147\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, kamu harus mengoperasikan keduanya secara komutatif, yaitu B + A seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/Vv7HuqifyW_Y7SU9DdaIlSm4DUjZmjW2nxP3M6oAt12atgYAvheAP2zl3nEVIxcNEdZic1ktZeypQOxoby4LITsZMH-1VTjq0aKr_PSQbfWgsSSEmAuyW14Ct_dcdPqbExKBeN_rOqhg_eaHlLghMt3YQFgQhQVHt0jRdr9WtAmUtirt1THqbgrXcDPlu0q8T5pR6c0X_Q\" alt=\"\" width=\"171\" height=\"146\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ternyata, hasil A + B = B + A. Dengan demikian, kedua matriks tersebut memenuhi sifat komutatif.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, hasil penjumlahannya adalah <sub><\/sub>dan keduanya memenuhi sifat komutatif.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Contoh soal Penjumlahan Matriks 2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Andi dan ayahnya membuka usaha penjualan pakan ternak di dua tempat yang berbeda. Toko Andi berada di Semarang, sementara ayahnya di Solo. Keduanya menjual dua jenis pakan ternak yang sama, yaitu pakan konsentrat dan fermentasi. Biaya pembelian dan operasional setiap bulan keduanya ditunjukkan oleh tabel berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Toko Andi<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th><\/th><th colspan=\"2\"><center>Nama Pakan<\/center><\/th><\/tr><\/thead><tbody><tr><td>Biaya<\/td><td>Konsentrat<\/td><td>Fermentasi<\/td><\/tr><tr><td>Pembelian<\/td><td>Rp2.200.000<\/td><td>Rp3.000.000<\/td><\/tr><tr><td>Operasional<\/td><td>Rp50.000<\/td><td>Rp75.000<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Toko ayah<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th><\/th><th colspan=\"2\"><center>Nama Pakan<\/center><\/th><\/tr><\/thead><tbody><tr><td>Biaya<\/td><td>Konsentrat<\/td><td>Fermentasi<\/td><\/tr><tr><td>Pembelian<\/td><td>Rp2.200.000<\/td><td>Rp3.000.000<\/td><\/tr><tr><td>Operasional<\/td><td>Rp50.000<\/td><td>Rp75.000<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan total biaya yang diperlukan oleh Andi dan ayah setiap bulan!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, buatlah masing-masing matriks untuk toko Andi dan ayah.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Andi = <sub><\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ayah = <sub><\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total biaya yang diperlukan oleh Andi dan ayahnya setiap bulan adalah sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Andi + ayah =&nbsp; <sub><\/sub>+<sub><\/sub>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Andi + ayah =<sub><\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, total biayanya ditunjukkan oleh matriks di atas.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Pengurangan Matriks<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Konsep pengurangan pada matriks sama seperti penjumlahan, yaitu mengurangkan elemen yang letaknya sama atau seletak. Salah satu syarat yang harus dipenuhi juga sama, yaitu memiliki ordo yang sama. Pada pengurangan matriks ini, tidak berlaku sifat-sifat seperti halnya penjumlahan. Adapun contoh soal pengurangan matriks adalah sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Contoh soal<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dua buah matrik, yaitu sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/ziLC63emtQMzd2hpnWi6mJ6QqJbl2rGCWfWipDIth_4DtjhkFZcEzqGeNOmFvv6fktLTwjFOtLdSoLPiDOGmbHfVXh0Lr0UrJNW30y_MTvblOEhMGGVp0p9fl58lbxSaCVG-pxzjMokNoI14EiZjSmFB68FgG7AFgIQz1Iys-KkjG8_xxcXNtWWLSWROnumAqSFDXvx3Ng\" alt=\"\" width=\"82\" height=\"96\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan hasil pengurangan antara matriks A dan matriks B!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/diplDs0zErTcUo_xFyF8z2lhxEqO_w93kvDYi5SyF5w9axH5O4Spxypi1OZ_ZR-q1ZDoiNzJHz8ZubZPBrgBb6MpWez9qUHBGFzI3yuz6czuq3Hf7TyVvrDOTdU9zjgmS9Kaee95RSVv0k5OfYWjAmCuZsGbMk_WPUpZgmySvo_N99jCDikrjqnVVTe76GIILpV2ecmlag\" alt=\"\" width=\"150\" height=\"129\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, hasil pengurangannya adalah <sub><\/sub>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Perkalian Matriks<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Jika penjumlahan dan pengurangan berlaku pada dua buah matrik atau lebih yang ordonya sama, maka tidak demikian dengan perkalian. Perkalian matriks bisa berupa perkalian antara konstanta dan matriks serta perkalian antarmatriks, seperti berikut ini.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Perkalian antara konstanta dan matriks, yaitu seperti berikut.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/BbOGtktjjIJi5qGLWoue0eCgE0loFpnISsy9sQRNOV_jRvJ1K8ER9TI7DEqkIarU4n6V5j9IQtSj6-LAihgYkJaZQyWYCrEbbg43wvj4cWAkHhYQYjYF2ix-klV8GkfndEqnDRg5EHA9US4F1-CVPwgbTSWGJSznUH-ZeY0xfl2PwFAvrGHkOWTJUReuhaxYk7D1jtL_EQ\" alt=\"\" width=\"131\" height=\"111\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Perkalian antarmatriks<br>Perkalian antarmatriks lebih rumit daripada perkalian antara konstanta dan matriks. Penasaran? Cekidot!<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/neyDND-Km6kQnrUU2R8buZQmMw97aXvyZQIhhK_wyiiKevKzB9b0zwuapN8jKzRTr_Hsx0AshjzuxdGZm92XCIgzQBBxbspPjYpoHaQxsHWqim4n8w-_CtxoA0dmbcCmzvxStV8mh3CRC2OcQHKN-6VGcay3UoL8S5RpNMm5PqUqoUctQr5InxZr1B_aaj2Wf0ccrMIrRA\" alt=\"\" width=\"255\" height=\"162\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Perkalian ini memenuhi sifat-sifat berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sifat asosiatif<br>Pada sifat ini, berlaku (A \u00d7 B) \u00d7 C= A \u00d7 (B \u00d7 C)<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sifat distributif<br>Pada sifat ini, berlaku A \u00d7 (B + C) = (A \u00d7 B) + (A \u00d7 C)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Agar pemahamanmu semakin terasah, yuk simak contoh soal perkalian matriks berikut ini.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui perkalian matriks seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/jVdMsVFAn8ExZ6qtuzikVLU2Tb4H_Q1vpvyWgsXLahrqFhd2nwzm1i__RIh1UiQ0Yv-iflpVMQhUVYwZW5x2RY9XR5t3gyHK6-zleDLIcbP3mNwRGvyLhTI79gDSuKI0Z5ZnW5D1NFeF_Y79nIfVGvGWtMm7e5y8BbolQvR5JQWpm6VdC60aEIX0DOMeJEFr9EguxmTyTQ\" alt=\"\" width=\"128\" height=\"44\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan nilai 2<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\">Mula-mula, kamu harus mengalikan matriks ordo 2 x 2 dan 2 x 1 pada soal.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/s3ay34S7SxPd_2htsq72A4FcRcq6LjBL5gbXZWUHNExNOdE7O7WbA27PWOUoU01sR_dxgAFb9XPZXNc9QrhQpjq7OvnyZxkv21hXTlDA5exKR9ABr5KL52jEVTAOupG4Ah6Z39bH14TfWekeqPLvY2Jv7i8BuOlyBULDE6nhhQmciqhNLwWtMS5Fa9o2m4hXGtqMC8iPww\" alt=\"\" width=\"138\" height=\"148\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lakukan eliminasi pada persamaan (1) dan (2).<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/WpBI54PQN1id49WADRhvdjizTzz2_Cbza9Xpe9e8EQFyKoYQQzoZPwKGIjFEFmUvpNFbM5Z14aDcu2dKQMTGSNJyCku4zJi_EbB90oFGIDks5Ws8XZvbn-keCQplMItAoTSrXiz0UT1HoiDQTjCR_14En3j_qMaa_Ag5_SazkPXXHRLw9aFc6pLw07nUmOMwUrlHu2mJ1Q\" alt=\"\" width=\"236\" height=\"118\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Substitusikan nilai <em>y<\/em> = -1 ke persamaan (2). Dengan demikian, diperoleh:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/bYFKPIO4L74MJD1si_wSPUEWJea39liFk4CXEVBitLYPhyyprd0YJBtjmmqkg8MKzbpADF_C1e84CKQPmD9nO23-Wcpreihe1wOuOL_eJuS0Fm1fGXKY82LKLwEovls9MGKaCCRTTraDaeKNFahShK55H-cOPXJsHsIR3nVX_-pKTCk4pLr5r_2WNkSL94fTdngkZw0Gow\" alt=\"\" width=\"129\" height=\"94\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai 2<em>x<\/em> \u2013 <em>y<\/em> = 2(5) \u2013 (-1) = 11.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bisa bermanfaat, ya. Jika kamu ingin melihat video lengkapnya, silahkan gabung bareng Quipper Video. Bersama Quipper Video, belajar jadi lebih mudah dan menyenangkan. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, untuk menyelesaikan permasalahan Matematika yang memuat lebih dari satu variabel, kamu bisa menggunakan matriks lho. Matriks bisa dioperasikan seperti operasi bilangan. Lalu,&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":307507,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384865],"tags":[679384825],"ppma_author":[679386823,679386836],"class_list":["post-307478","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 v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Operasi Matriks, Jenis dan Contoh - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Belajar operasi matrik lengkap di sini. 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