{"id":277,"date":"2023-07-06T23:03:43","date_gmt":"2023-07-06T23:03:43","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/"},"modified":"2023-07-06T23:03:43","modified_gmt":"2023-07-06T23:03:43","slug":"contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/","title":{"rendered":"Transpos matriks (atau transpos)"},"content":{"rendered":"<p>Pada halaman ini kita akan melihat cara menghitung <strong>matriks transposisi (atau transposisi)<\/strong> . Anda juga akan melihat latihan yang terselesaikan sehingga Anda tidak ragu lagi tentang cara mengubah urutan matriks.<\/p>\n<h2 class=\"wp-block-heading\"> Bagaimana cara menghitung matriks yang ditransposisi (atau transposisi)?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>Matriks transpos<\/strong> , disebut juga matriks transpos, adalah matriks yang diperoleh dengan <strong>mengubah baris menjadi kolom<\/strong> . Matriks yang ditransposisi direpresentasikan dengan memberi tanda \u201ct\u201d di kanan atas matriks (A <sup>t<\/sup> ).<\/p>\n<p> <strong>Misalnya<\/strong> , mari kita transpos 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-8613db3e71f21d9ee2c4dc003600e32a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} 2 &amp; 3 &amp; 1 \\\\[1.1ex] 4 &amp; 5 &amp; 0   \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"120\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Untuk mengubah urutan matriks A, cukup <strong>ubah baris demi kolom<\/strong> . Dengan kata lain, baris pertama matriks menjadi kolom pertama matriks dan baris kedua matriks menjadi kolom kedua 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-e7cf9e274915aef7e44582556d188197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^t= \\begin{pmatrix} 2 &amp; 4 \\\\[1.1ex] 3 &amp; 5 \\\\[1.1ex] 1 &amp; 0   \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"103\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Berikut beberapa contoh cara mencari matriks yang ditransposisikan:<\/p>\n<h2 class=\"wp-block-heading\"> Contoh matriks yang ditransposisikan<\/h2>\n<h3 class=\"wp-block-heading\"> Contoh 1 <\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e3a8e6d458b2d60aabcedfe33c0297a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B= \\begin{pmatrix} 1 &amp; 5\\\\[1.1ex] 7 &amp; 2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"96\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-321fc68b5d5d3c546461c29b80102a82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^t= \\begin{pmatrix} 1 &amp; 7\\\\[1.1ex] 5 &amp; 2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"102\" 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\">Contoh 2 <\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8295b1417a32fc9378584f87c67abc05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C= \\begin{pmatrix} -1 &amp; 4 &amp; 3 \\\\[1.1ex] 5 &amp; 3 &amp; 2 \\\\[1.1ex] 6 &amp; 0 &amp; 9  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"137\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5274e4fc9bdc5939e3a5a08e6a8e41b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C^t= \\begin{pmatrix} -1 &amp; 5 &amp; 6 \\\\[1.1ex] 4 &amp; 3 &amp; 0 \\\\[1.1ex] 3 &amp; 2 &amp; 9  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"143\" 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:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\"> Contoh 3 <\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e2d2268ed4a7fee24a06a7a7f7cd76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle D= \\begin{pmatrix} 2 &amp; 6 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"126\" style=\"vertical-align: -7px;\"><\/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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f1c2184833ec63a43162fde532f6e593_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle D^t= \\begin{pmatrix}2 \\\\[1.1ex] 6 \\\\[1.1ex] -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" 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\">Contoh 4 <\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d83760eb84d950a0d31727e522d88f5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E= \\begin{pmatrix} 9 &amp; 0  \\\\[1.1ex] 2 &amp; -1 \\\\[1.1ex] 5 &amp; 3   \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"112\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c01a100ebae58a267a286f88010a796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E^t= \\begin{pmatrix} 9 &amp; 2 &amp; 5  \\\\[1.1ex] 0 &amp; -1 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"140\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Salah satu kegunaan transpos matriks adalah <a href=\"https:\/\/mathority.org\/id\/matriks-terbalik\/\">untuk menghitung invers matriks dengan rumus matriks terlampir atau dengan determinan<\/a> . Meskipun untuk menggunakan metode ini Anda juga perlu mengetahui cara menyelesaikan determiner, pada halaman tertaut Anda akan menemukan penjelasan keseluruhan prosedur dan Anda juga dapat melihat contoh dan latihan yang diselesaikan langkah demi langkah.<\/p>\n<h2 class=\"wp-block-heading\"> Sifat-sifat matriks yang ditransposisikan<\/h2>\n<p> Matriks yang ditransposisikan mempunyai ciri-ciri sebagai berikut:<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Sifat involusional:<\/span><\/strong> Transpos matriks yang ditransposisi sama dengan matriks aslinya.<\/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-a776188cca22c35019064e846b61b4b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(A^t\\right)^t = A\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"76\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Sifat distributif:<\/span><\/strong> menjumlahkan dua matriks kemudian mentransposisi hasilnya sama dengan mentransposisi setiap matriks terlebih dahulu kemudian menjumlahkannya: <\/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-aff76a8cf7355ea147e7a885b034b462_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(A+B\\right)^t = A^t+B^t\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Sifat linier (hasil kali matriks):<\/span><\/strong> Mengalikan dua matriks kemudian mentransposisi hasilnya sama dengan mentransposisi setiap matriks terlebih dahulu lalu mengalikannya tetapi urutan perkaliannya bergantian:<\/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-32a851b103c6805a1bf495dbdc04ddc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(A\\cdot B\\right)^t = B^t\\cdot A^t\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Sifat linier (konstan):<\/span><\/strong> Mentransposisi hasil perkalian matriks dengan konstanta sama dengan mengalikan matriks yang sudah ditransposisikan dengan konstanta.<\/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-802c2bde61d7e419e73a5d5424661aec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(c\\cdot A\\right)^t = c\\cdot A^t\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Matriks simetris:<\/span><\/strong> Jika transpos suatu matriks sama dengan matriks tanpa transpos, maka matriks tersebut dikatakan <strong>matriks simetris:<\/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-d15c8f7ea597b852f92fdb47dbdb8c80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{pmatrix} 7 &amp; 1 &amp; 3 \\\\[1.1ex] 1 &amp; 4 &amp; 2 \\\\[1.1ex] 3 &amp; 2 &amp; 5  \\end{pmatrix} \\right.^t = \\begin{pmatrix} 7 &amp; 1 &amp; 3 \\\\[1.1ex] 1 &amp; 4 &amp; 2 \\\\[1.1ex] 3 &amp; 2 &amp; 5  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"89\" width=\"202\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong><span style=\"color:#1976d2;\">Sifat antisimetris:<\/span><\/strong> Jika ketika mentransposisi suatu matriks matematika, kita memperoleh matriks yang sama tetapi semua elemennya berubah tanda, maka itu adalah <strong>matriks antisimetris:<\/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-5fcd7cfe60e5570bb668945b81540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{pmatrix} 0 &amp; 2 &amp; 4 \\\\[1.1ex] -2 &amp; 0 &amp; 6 \\\\[1.1ex] -4 &amp; -6 &amp; 0  \\end{pmatrix}\\right.^t = \\begin{pmatrix} 0 &amp; -2 &amp; -4 \\\\[1.1ex] 2 &amp; 0 &amp; -6 \\\\[1.1ex] 4 &amp; 6 &amp; 0  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"89\" width=\"257\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada halaman ini kita akan melihat cara menghitung matriks transposisi (atau transposisi) . Anda juga akan melihat latihan yang terselesaikan sehingga Anda tidak ragu lagi tentang cara mengubah urutan matriks. Bagaimana cara menghitung matriks yang ditransposisi (atau transposisi)? Matriks transpos , disebut juga matriks transpos, adalah matriks yang diperoleh dengan mengubah baris menjadi kolom . &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Transpos matriks (atau transpos)<\/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-277","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>Transpos matriks (atau transpos) - 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-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Transpos matriks (atau transpos) - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada halaman ini kita akan melihat cara menghitung matriks transposisi (atau transposisi) . Anda juga akan melihat latihan yang terselesaikan sehingga Anda tidak ragu lagi tentang cara mengubah urutan matriks. Bagaimana cara menghitung matriks yang ditransposisi (atau transposisi)? Matriks transpos , disebut juga matriks transpos, adalah matriks yang diperoleh dengan mengubah baris menjadi kolom . &hellip; Transpos matriks (atau transpos) Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T23:03:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8613db3e71f21d9ee2c4dc003600e32a_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Transpos matriks (atau transpos)\",\"datePublished\":\"2023-07-06T23:03:43+00:00\",\"dateModified\":\"2023-07-06T23:03:43+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\"},\"wordCount\":299,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Lukisan\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\",\"url\":\"https:\/\/mathority.org\/id\/contoh-matriks-yang-ditransposisikan-atau-ditransposisikan-dan-latihan-yang-diselesaikan\/\",\"name\":\"Transpos matriks (atau transpos) - 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Anda juga akan melihat latihan yang terselesaikan sehingga Anda tidak ragu lagi tentang cara mengubah urutan matriks. Bagaimana cara menghitung matriks yang ditransposisi (atau transposisi)? 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