{"id":296,"date":"2023-07-06T17:07:12","date_gmt":"2023-07-06T17:07:12","guid":{"rendered":"https:\/\/mathority.org\/id\/luas-suatu-matriks-sebagai-fungsi-parameter-contoh-dan-latihan-penyelesaian-matriks-2x2-3x3-3x4-4x4\/"},"modified":"2023-07-06T17:07:12","modified_gmt":"2023-07-06T17:07:12","slug":"luas-suatu-matriks-sebagai-fungsi-parameter-contoh-dan-latihan-penyelesaian-matriks-2x2-3x3-3x4-4x4","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/luas-suatu-matriks-sebagai-fungsi-parameter-contoh-dan-latihan-penyelesaian-matriks-2x2-3x3-3x4-4x4\/","title":{"rendered":"Rentang array berdasarkan parameter"},"content":{"rendered":"<p>Di halaman ini, Anda akan melihat cara menghitung <strong>peringkat tabel berdasarkan parameter.<\/strong> Anda juga akan menemukan contoh langkah demi langkah dan latihan yang diselesaikan tentang cara mencari rentang matriks berdasarkan satu parameter.<\/p>\n<p> Untuk memahami sepenuhnya tata cara mempelajari pangkat matriks dengan parameter, penting bagi Anda untuk mengetahui <a href=\"https:\/\/mathority.org\/id\">cara menghitung pangkat suatu matriks berdasarkan determinan<\/a> . Jadi kami menyarankan Anda mempelajari dua hal ini terlebih dahulu sebelum melanjutkan membaca.<\/p>\n<h2 class=\"wp-block-heading\"> Cara menghitung rentang array berdasarkan parameter. Contoh:<\/h2>\n<ul>\n<li> Menentukan rentang matriks A berdasarkan nilai parameter yang berbeda\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/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-0aa5688f2845a0225149f448466c943c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\begin{pmatrix} a+1 &amp; -1 &amp; a+1 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; a  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"198\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Matriks A paling banyak mempunyai rangking 3, karena merupakan matriks orde 3. Oleh karena itu, hal pertama yang perlu kita lakukan adalah <strong>menyelesaikan determinan seluruh matriks 3&#215;3<\/strong> dengan<a href=\"https:\/\/mathority.org\/id\/contoh-aturan-sarrus-determinan-3x3-dan-latihan-penyelesaiannya\/\">aturan Sarrus<\/a> , untuk melihat apakah dapat menduduki peringkat 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-835a881061438326519f4660b4c394fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} a+1 &amp; -1 &amp; a+1 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; a  \\end{vmatrix} &amp; =-a(a+1)+0+0+a+1-0-0 \\\\ &amp; =-a^2-a+a+1  \\\\[1.5ex] &amp; =-a^2+1 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"150\" width=\"429\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Hasil determinan merupakan fungsi dari parameter<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> . <strong>Oleh karena itu, kami menetapkan hasilnya sama dengan 0<\/strong> untuk melihat kapan tabel tersebut akan berada di peringkat 2 dan kapan akan berada di peringkat 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-7cf08fe725290ac099f54916fa4c5dcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -a^2+1 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"93\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Dan kami menyelesaikan persamaan 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-18b6f04242243eeefa0cd5892b29f4d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a^2 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" 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-ad7c0d92bbec913193a85949c7a0bfa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\sqrt{a^2} = \\sqrt{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -1px;\"><\/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-1191c881d84f673236382966b4e709ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{a = \\pm 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> apakah itu +1 atau -1, determinan 3\u00d73 akan menjadi 0 dan oleh karena itu, rank matriksnya tidak akan menjadi 3. Sebaliknya, ketika<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> berbeda dari +1 dan -1, determinannya akan berbeda dari 0 dan oleh karena itu, matriksnya akan mempunyai rangking 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-60e6f80d73c96b28458d7790d98d0a5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c}  \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq +1,-1 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"354\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sekarang mari kita lihat apa yang terjadi ketika<\/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-bbdf9897658213f9f2ad0b6a3d8d87cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{a=+1} :\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -2px;\"><\/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-53dde6f61dc01cac5c0a0705c44a7433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = +1 \\longrightarrow A= \\begin{pmatrix} 2 &amp; -1 &amp; 2 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; 1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"230\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Seperti yang kita lihat sebelumnya, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah 1 determinan matriksnya adalah 0. Oleh karena itu, matriks tersebut tidak mungkin berpangkat 3. Sekarang kita coba menghitung <a href=\"https:\/\/mathority.org\/id\/contoh-determinan-2x2-dan-latihan-penyelesaiannya\/\">determinan 2\u00d72<\/a> yang berbeda dengan 0 di dalam matriks, misalnya yang ada di pojok kiri atas:<\/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-d291f322f9d3f392e46568817e531a84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix} 2 &amp; -1 \\\\[1.1ex] 0 &amp; -1 \\end{vmatrix} =-2-0= -2 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Penentu orde 2 berbeda dengan 0. Jadi, bila parameternya<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> atau +1, <strong>pangkat matriksnya adalah 2:<\/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-d00c47041db87183749744eaf6789fd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c}  \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = +1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Setelah kita melihat rentang matriks kapan<\/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-910ad8735da02f7dffe9cd0fda341d6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a \\neq +1,-1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -4px;\"><\/p>\n<p> dan kapan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10f3012b6955e51b81c57a6e2e57b7df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"55\" style=\"vertical-align: -2px;\"><\/p>\n<p> Mari kita lihat apa yang terjadi ketika<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3d04c75a36ec68cca9920060cc558b99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{a = -1} :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" 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-f723d9c6b9f786b8c405ac7ec2d8bf1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -1 \\longrightarrow A=  \\begin{pmatrix} 0 &amp; -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; -1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"244\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Seperti yang kita lihat di awal, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> es -1 dan determinan matriksnya adalah 0. Oleh karena itu, tidak dapat diset ke rangking 3. Oleh karena itu, kita harus mencoba mencari determinan 2\u00d72 pada matriks yang berbeda dari 0, misalnya matriks yang lebih rendah bagian dari matriks. 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-cdc9bd6d9ad083e1e38f53079aebb5e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; -2  \\end{vmatrix} = 0-(-1)= 1\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Penentu dimensi 2 berbeda dengan 0. Jadi, bila parameternya<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> atau -1, <strong>peringkat tabelnya menjadi 2:<\/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-d12346bae2f327e7e1ee6c5276a599cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu kami menemukan 3 kasus berbeda di mana peringkat matriks A bergantung pada nilai yang diambil parameternya<\/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-4ae924c776e55c0f2987a783307cd9fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> Berikut <strong>ringkasannya<\/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-dc3a7ebea32c871ab7971a276decc60a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq +1,-1 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = +1 \\ \\longrightarrow \\ Rg(A)=2} \\\\[3ex]  \\color{black} \\bm{a = -1 \\ \\longrightarrow \\ Rg(A)=2} \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"167\" width=\"354\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sekarang setelah Anda mengetahui cara mendiskusikan rentang matriks yang bergantung pada parameter, Anda dapat berlatih melakukan latihan langkah demi langkah di bawah ini. Untuk mengatasinya, <a href=\"https:\/\/mathority.org\/id\/contoh-sifat-sifat-determinan-dan-latihan-2x2-3x3\/\">properti determiner<\/a> pasti akan membantu Anda, jadi jika Anda belum begitu paham tentangnya, saya menyarankan Anda untuk melihat terlebih dahulu halaman tertaut, di mana masing-masingnya dijelaskan dengan contoh.<\/p>\n<h2 class=\"wp-block-heading\"> Memperbaiki masalah rentang matriks berbasis parameter<\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Pelajari rentang tabel berikut berdasarkan nilai parameternya <\/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-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" 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-d7f53b08bcf2e2660dbb7c0aeb6fd369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 3 &amp; 1 &amp; a \\\\[1.1ex] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"136\" 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\"> Matriks A paling banyak mempunyai rangking 3, karena matriksnya berukuran 3\u00d73. Oleh karena itu, hal pertama yang perlu kita lakukan adalah menyelesaikan determinan seluruh matriks (dengan aturan Sarrus), untuk melihat apakah matriks tersebut dapat menduduki peringkat 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-d2539698cbcf9f06d2890d17da76174f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; 1 &amp; a \\\\[1.1ex] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{vmatrix}  =0-8+2a-4a+12-0 =-2a+4\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"382\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menetapkan hasilnya sama dengan 0 untuk melihat kapan array akan berada di peringkat 2 dan kapan peringkat 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-7042ae953fdcbe91d08fa963be26f7c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2a+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"94\" style=\"vertical-align: -2px;\"><\/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-90183d93145fd04e7a774c8a72bc3f1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2a=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"78\" 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-21d4999dede651fdb38c5b047b8e805d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a=\\cfrac{-4}{-2} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"97\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> berbeda dengan 2, determinan 3\u00d73 akan berbeda dengan 0 sehingga rank matriksnya adalah 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-a4c4e0bfd1194afe82d8807c033e7551_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq 2 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"310\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita lihat apa yang terjadi ketika <\/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-f2abbabd80372bf9bc248f12cebd5fb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=2 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-c131e19dd5d5c0d7826306103b4e118b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = 2 \\longrightarrow A= \\begin{pmatrix} 3 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"216\" 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-b97f01989b5e9679f95d300cd64f3735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} 3 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"164\" 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-77b38ebf03b8ed059edefd523c5ca1f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; 1  \\\\[1.1ex] 2 &amp; 2 \\end{vmatrix} = 6-2 = 4 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" 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-1f174f72890bce94d148e1f6e88681ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = 2 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"310\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami menemukan 2 kasus di mana rentang matriks A bervariasi dengan nilai yang diambil parameternya: <\/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-41e5cc7b6e9b3204f26e1c64e46f7057_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq 2 \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = 2\\ \\longrightarrow \\ Rg(A)=2}  \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"122\" width=\"304\" 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> Temukan rentang tabel berikut berdasarkan nilai parameter <\/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-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" 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-5b28f21cc2e7211d9dae9b6685b541fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] a &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; a \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"150\" 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\"> Matriks A paling banyak mempunyai rangking 3, karena matriksnya berukuran 3\u00d73. Oleh karena itu, hal pertama yang perlu kita lakukan adalah menyelesaikan determinan seluruh matriks (dengan aturan Sarrus), untuk melihat apakah matriks tersebut dapat menduduki peringkat 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-30c8c16fea09001059a5d66727fc7be3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] a &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; a \\end{vmatrix} &amp; =2a-12-2a+2+12-2a^2 \\\\ &amp;=2-2a^2\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"335\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menetapkan hasilnya sama dengan 0 untuk melihat kapan array akan berada di peringkat 2 dan kapan peringkat 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-28c4eeb004bd0bf3db692ee22c659a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2-2a^2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"89\" 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-e39820ff30d5df06ac09f254dcebeef0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2a^2=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"84\" 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-3c5cad133a274f40a2151ad9e9310825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a^2=\\cfrac{-2}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"74\" style=\"vertical-align: -12px;\"><\/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-8b5cd6314cc67aa83d49e16072e9314b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a^2=1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" 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-63f049dc27947cfc24afdd331acefe23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a=\\pm 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> berbeda dengan +1 dan -1, determinan 3\u00d73 akan berbeda dengan 0 sehingga rank matriksnya adalah 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-e7d26d825cd80ee861dd13168dafd408_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq +1, -1 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"354\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita lihat apa yang terjadi ketika <\/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-ee9005a2708f5bcb0f0fba0cefed3dfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=+1 :\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -2px;\"><\/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-7b95d408f076c4978c8605380a277cdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = +1 \\longrightarrow A= \\begin{pmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] 1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"244\" 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-fcd50b9549925b5011a6c20943c326ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] 1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; 1 \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" 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-03242296f208e07b9c4d634f0b7724cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}  2 &amp; 1 \\\\[1.1ex]  1 &amp; 3 \\end{vmatrix} = 6-1 = 5 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" 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-2550b439990981d1b74f72b1649a57e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = +1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita lihat apa yang terjadi ketika <\/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-53cc36b0e502c4e9a0aa575015035a8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=-1 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" 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-a2d16421400df26760d811229215ac83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -1 \\longrightarrow A= \\begin{pmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] -1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"258\" 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-ecd0b86cd6c59a0911f0c39ca7599806_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] -1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; -1  \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"191\" 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-378e43f0ef61ccabf82dacb5ac70466f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 2 &amp; 2  \\\\[1.1ex] -1 &amp; 1 \\end{vmatrix} =2-(-2) = 4 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" 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-d12346bae2f327e7e1ee6c5276a599cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami menemukan 3 kasus di mana rentang matriks A bervariasi bergantung pada nilai yang diambil parameternya: <\/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-6bf1904cee51914e041d94f588fed84d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq +1,-1 \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = +1\\ \\longrightarrow \\ Rg(A)=2} \\\\[3ex] \\color{black} \\bm{a = -1\\ \\longrightarrow \\ Rg(A)=2}  \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"167\" width=\"348\" 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\"> Latihan 3<\/h3>\n<p> Menghitung rentang tabel berikut berdasarkan nilai parameter <\/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-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" 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-090a99d3b4111785433e5c769589eb01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} a+1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; a-3  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"184\" 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\"> Matriks A paling banyak mempunyai rangking 3, karena matriksnya berukuran 3\u00d73. Oleh karena itu, hal pertama yang perlu kita lakukan adalah menyelesaikan determinan seluruh matriks (dengan aturan Sarrus), untuk melihat apakah matriks tersebut dapat menduduki peringkat 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-fec1cb52bb87fa2bccb40b70e1f21c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} a+1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; a-3 \\end{vmatrix} &amp; =(a+1)(a-3) +2+0-5+6(a+1)-0 \\\\ &amp; = a^2-3a+a-3 +2-5+6a+6 \\\\[1.5ex] &amp; =a^2+4a\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"150\" width=\"468\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menetapkan hasilnya sama dengan 0 untuk melihat kapan array akan berada di peringkat 2 dan kapan peringkat 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-f8e26b9f10414656086a0c25d28ea04f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a^2+4a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ini adalah persamaan kuadrat tidak lengkap, jadi kita ekstrak faktor persekutuannya:<\/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-3f6035239798b59504a776dac1f0e21a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a(a+4)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami menetapkan setiap suku sama dengan 0:<\/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-43b38da320da538e46c6b4515de48568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a(a+4)=0 \\longrightarrow \\begin{cases} \\bm{a = 0} \\\\[2ex] a+4=0  \\ \\longrightarrow \\ \\bm{a=-4}\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"328\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami memperoleh 0 dan -4 sebagai solusi. Oleh karena itu, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> berbeda dari 0 dan -4, determinan 3\u00d73 akan berbeda dari 0 sehingga rank matriksnya adalah 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-15908960ef2cfcd2105c4b901fb6cb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq 0, -4 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"340\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita lihat apa yang terjadi ketika <\/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-d229e6228a70e103acbec8ca88c12d7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=0 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-d97b25f01cb00d4677da0de5b4340ddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = 0 \\longrightarrow A= \\begin{pmatrix} 1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"230\" 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-9e0f3c315588dff8274873001f727a69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} 1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -3 \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" 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-c132b22650c707d9f410c3d9c1e8da35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 1  \\\\[1.1ex] 0 &amp; 1 \\end{vmatrix} = 1-0 = 1 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" 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-d33aeec452b54112a958bfeadf014fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = 0 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"310\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita lihat apa yang terjadi ketika <\/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-0287c5c8b769f316fb7d382ea3332fa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=-4 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" 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-9ce7e40d9d78ecddc5ee81fc799c8767_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -4 \\longrightarrow A= \\begin{pmatrix} -3 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -7  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"244\" 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-52d15d0bceeb1dbbc415fb4825ce9a05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} -3 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -7 \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" 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-d45971f1dbda32405246de38bb68bd92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -3 &amp; 1 \\\\[1.1ex] 0 &amp; 1\\end{vmatrix} =-3-0 = -3 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" 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-0551d4c8535193e378fc38c2e5580157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -4 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami menemukan 3 kasus di mana rentang matriks A bervariasi bergantung pada nilai yang diambil parameternya: <\/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-844f152985a2d84be1456501dfdc16e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq 0,-4 \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = 0\\ \\longrightarrow \\ Rg(A)=2} \\\\[3ex] \\color{black} \\bm{a = -4\\ \\longrightarrow \\ Rg(A)=2}  \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"167\" width=\"334\" 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> Tentukan luas matriks berdimensi 3\u00d74 berikut sesuai dengan nilai parameternya <\/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-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" 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-4da7907bd0e8f80006ea47d2437b3f3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} -1&amp;-3&amp;-2&amp;1\\\\[1.1ex] 4&amp;12&amp;8&amp;-4\\\\[1.1ex] 2&amp;6&amp;4&amp;a \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"203\" 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\"> Matriks A paling banyak berada pada peringkat 3, karena kita tidak dapat menghitung <a href=\"https:\/\/mathority.org\/id\/penentu-4x4-dengan-contoh-pelengkap-dan-latihan-yang-diselesaikan\/\">determinan 4\u00d74<\/a> apa pun. Oleh karena itu, hal pertama yang perlu kita lakukan adalah menyelesaikan semua kemungkinan determinan orde 3 (dengan aturan Sarrus), untuk melihat apakah determinan tersebut dapat 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-c2db025b8ecf4323d4a912d84a215d8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -1&amp;-3&amp;-2\\\\[1.1ex] 4&amp;12&amp;8\\\\[1.1ex] 2&amp;6&amp;4 \\end{vmatrix} &amp; =-48-48-48+48+48+48 =\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"395\" 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-e40592bf6f8bfd13cb68a1fd0393cebb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -1&amp;-3&amp;1\\\\[1.1ex] 4&amp;12&amp;-4\\\\[1.1ex] 2&amp;6&amp;a \\end{vmatrix} &amp; =-12a+24+24-24-24+12a=\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"414\" 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-ce1c28ae4120f0b37059b763e576d2eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -1&amp;-2&amp;1\\\\[1.1ex] 4&amp;8&amp;-4\\\\[1.1ex] 2&amp;4&amp;a \\end{vmatrix} &amp; =-8a+16+16-16-16+8a=\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"396\" 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-668e9096b00b90ee4cc48d272b17e7bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -3&amp;-2&amp;1\\\\[1.1ex] 12&amp;8&amp;-4\\\\[1.1ex] 6&amp;4&amp;a \\end{vmatrix} &amp; =-24a+48+48-48-48+24a=\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"414\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Hasil semua kemungkinan determinan orde 3 adalah 0, berapa pun nilainya<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> . Jadi matriksnya tidak akan pernah berada pada peringkat 3, karena tidak peduli berapa pun nilainya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> bahwa tidak akan pernah ada determinan 3\u00d73 selain 0.<\/p>\n<p class=\"has-text-align-left\"> Jadi sekarang kita coba determinan berdimensi 2 \u00d7 2. Namun semua determinan berorde 2 juga menghasilkan 0 kecuali yang 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-c4408f1ccf562196943209356e50e892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} 8&amp;-4\\\\[1.1ex] 4&amp;a \\end{vmatrix} &amp; =8a+16 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita atur hasilnya sama dengan 0 dan selesaikan persamaannya: <\/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-f5494bb524be48bc22a1cb054556c3a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 8a+16=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -2px;\"><\/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-8a6fc020bc84c4ba3f1989065a2207fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 8a=-16\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"74\" 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-02680bced4f2a76a7d23c5b9e6a2ecbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a=\\cfrac{-16}{8} =-2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"120\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> berbeda dengan -2, determinan 2\u00d72 akan berbeda dengan 0 sehingga rank matriksnya adalah 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-04b3447f6e823c3e11b66919654e7a5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq -2 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita lihat apa yang terjadi ketika <\/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-0e72cd3ad115f5d34fb5077b4d7d278a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=-2 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" 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-6ecbf63b188b46c05e67741cee83d7a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -2 \\longrightarrow A= \\begin{pmatrix} -1&amp;-3&amp;-2&amp;1\\\\[1.1ex] 4&amp;12&amp;8&amp;-4\\\\[1.1ex] 2&amp;6&amp;4&amp;-2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"297\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Seperti yang kita lihat sebelumnya, kapan<\/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-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah -2, semua determinan berorde 2 adalah 0. Oleh karena itu, tidak mungkin ada rank 2. Dan karena terdapat paling sedikit satu determinan 1\u00d71 yang berbeda dari 0, maka rank matriksnya adalah 1:<\/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-eb1cee57ae9619b3e4fdbf2357893425_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -2 \\ \\longrightarrow \\ Rg(A)=1} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami menemukan 2 kasus di mana rentang matriks A bervariasi dengan nilai yang diambil parameternya: <\/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-2bdfb67894431a4a08a3e791dcda0313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq -2 \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = -2\\ \\longrightarrow \\ Rg(A)=1}   \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"122\" width=\"317\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini, Anda akan melihat cara menghitung peringkat tabel berdasarkan parameter. Anda juga akan menemukan contoh langkah demi langkah dan latihan yang diselesaikan tentang cara mencari rentang matriks berdasarkan satu parameter. Untuk memahami sepenuhnya tata cara mempelajari pangkat matriks dengan parameter, penting bagi Anda untuk mengetahui cara menghitung pangkat suatu matriks berdasarkan determinan . &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/luas-suatu-matriks-sebagai-fungsi-parameter-contoh-dan-latihan-penyelesaian-matriks-2x2-3x3-3x4-4x4\/\"> <span class=\"screen-reader-text\">Rentang array berdasarkan parameter<\/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":[36],"tags":[],"class_list":["post-296","post","type-post","status-publish","format-standard","hentry","category-kalkulator"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Rentang array berdasarkan parameter -<\/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\/luas-suatu-matriks-sebagai-fungsi-parameter-contoh-dan-latihan-penyelesaian-matriks-2x2-3x3-3x4-4x4\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rentang array berdasarkan parameter -\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini, Anda akan melihat cara menghitung peringkat tabel berdasarkan parameter. 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