{"id":838,"date":"2020-03-25T10:00:49","date_gmt":"2020-03-25T10:00:49","guid":{"rendered":"https:\/\/people.utm.my\/halinawati4\/?p=838"},"modified":"2020-03-25T10:04:40","modified_gmt":"2020-03-25T10:04:40","slug":"solving-a-system-of-linear-equations-using-the-inverse-of-a-matrix-and-factorization","status":"publish","type":"post","link":"https:\/\/people.utm.my\/halinawati4\/solving-a-system-of-linear-equations-using-the-inverse-of-a-matrix-and-factorization\/","title":{"rendered":"Solving a System of Linear Equations Using the Inverse of a Matrix and Factorization"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"838\" class=\"elementor elementor-838\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-58e9116 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"58e9116\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-de55ad8\" data-id=\"de55ad8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-438a498 elementor-widget elementor-widget-text-editor\" data-id=\"438a498\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3> We can solve our system linear equations by transforming the system linear equation into the matrix form. We already learn to solve it using REF and RREF. Now we will learn how to solve it using the inverse matrix and Factorization Matrix.\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-34d05a2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"34d05a2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-98def48\" data-id=\"98def48\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bdb96c2 elementor-widget elementor-widget-heading\" data-id=\"bdb96c2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Solving a System of Linear Equation using the Inverse<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ac4c371 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ac4c371\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-45fd04a\" data-id=\"45fd04a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fee20cc elementor-widget elementor-widget-video\" data-id=\"fee20cc\" data-element_type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/people.utm.my\/halinawati4\/files\/2020\/03\/Lecture-1-part-5.mp4\" controls=\"\" preload=\"metadata\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d208ab3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d208ab3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-afda5d0\" data-id=\"afda5d0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f32ddd1 elementor-widget elementor-widget-text-editor\" data-id=\"f32ddd1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h4> Video below is to make you understand more how to solving the linear equation using Inverse Matrix.\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6ecb985 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6ecb985\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-9eeb067\" data-id=\"9eeb067\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6374015 elementor-widget elementor-widget-video\" data-id=\"6374015\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/PTN8rganLWo&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0506efe\" data-id=\"0506efe\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-573de9d elementor-widget elementor-widget-video\" data-id=\"573de9d\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/hu6B1d3vvqU&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b15acd0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b15acd0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-faecf03\" data-id=\"faecf03\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e4c2077 elementor-widget elementor-widget-text-editor\" data-id=\"e4c2077\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h4>And here the video to solve using Factorization. \n<p> 1. LU decomposition <p> 2. Doolittle Factorization <p> 3. Crout Factorization.\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bba6855 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bba6855\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b78badd\" data-id=\"b78badd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1efb715 elementor-widget elementor-widget-video\" data-id=\"1efb715\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/o8PiWO8C3zs&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c1536e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c1536e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-01b9ec8\" data-id=\"01b9ec8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6214fa9 elementor-widget elementor-widget-video\" data-id=\"6214fa9\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/BFYFkn-eOQk&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-2a6afce\" data-id=\"2a6afce\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c6ad07d elementor-widget elementor-widget-video\" data-id=\"c6ad07d\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/vR25PDWrcpk&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-deb37a5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"deb37a5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-11647a1\" data-id=\"11647a1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5e43961 elementor-widget elementor-widget-video\" data-id=\"5e43961\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/gA7m5lttIcU&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-f00d127\" data-id=\"f00d127\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-82d9345 elementor-widget elementor-widget-video\" data-id=\"82d9345\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/DXhw98XSOs0&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6fc8f96 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6fc8f96\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-47b2d11\" data-id=\"47b2d11\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f1894bb elementor-widget elementor-widget-video\" data-id=\"f1894bb\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/sGV9fs5Yn0M&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>We can solve our system linear equations by transforming the system linear equation into the matrix form. We already learn to solve it using REF and RREF. Now we will learn how to solve it using the inverse matrix and Factorization Matrix. Solving a System of Linear Equation using the Inverse https:\/\/people.utm.my\/halinawati4\/files\/2020\/03\/Lecture-1-part-5.mp4 Video below is &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/people.utm.my\/halinawati4\/solving-a-system-of-linear-equations-using-the-inverse-of-a-matrix-and-factorization\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Solving a System of Linear Equations Using the Inverse of a Matrix and Factorization&#8221;<\/span><\/a><\/p>\n","protected":false},"author":16047,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[42,43,41],"class_list":["post-838","post","type-post","status-publish","format-standard","hentry","category-computational-mathematic","tag-factorization","tag-lu-factorization","tag-solving-linear-equation-using-inverse-matrix"],"_links":{"self":[{"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/posts\/838","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/users\/16047"}],"replies":[{"embeddable":true,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/comments?post=838"}],"version-history":[{"count":4,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/posts\/838\/revisions"}],"predecessor-version":[{"id":843,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/posts\/838\/revisions\/843"}],"wp:attachment":[{"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/media?parent=838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/categories?post=838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/tags?post=838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}