{"id":885,"date":"2020-04-23T04:44:18","date_gmt":"2020-04-23T04:44:18","guid":{"rendered":"https:\/\/people.utm.my\/halinawati4\/?p=885"},"modified":"2020-04-23T04:48:19","modified_gmt":"2020-04-23T04:48:19","slug":"linear-combination-linear-dependence-and-linear-independence","status":"publish","type":"post","link":"https:\/\/people.utm.my\/halinawati4\/linear-combination-linear-dependence-and-linear-independence\/","title":{"rendered":"LINEAR COMBINATION, LINEAR DEPENDENCE AND LINEAR INDEPENDENCE"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"885\" class=\"elementor elementor-885\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4bcc98b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4bcc98b\" 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-dcc5f63\" data-id=\"dcc5f63\" 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-07f27d2 elementor-widget elementor-widget-text-editor\" data-id=\"07f27d2\" 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><p>Basic understanding of linear combination is:\n\n<p>(scalar)(x) + (scalar)(y) + (scalar)(z)\n\n<p> Or\n\n<p> (scalar)(x<font size=\"1\">1<\/font>) + (scalar)(x<font size=\"1\">2<\/font>) + (scalar)(x<font size=\"1\">3<\/font>) +\u2026.+ (scalar)(x<font size=\"1\">n<\/font>)\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-ea503fd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ea503fd\" 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-8355fe5\" data-id=\"8355fe5\" 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-89d7846 elementor-widget elementor-widget-text-editor\" data-id=\"89d7846\" 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<p style=\"color:white\"><font size=\"4\">a linear combination of the vectors would be any combination of them using addition and scalar multiplication. A few examples would be:\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-3ecdb7a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3ecdb7a\" 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-6b3447c\" data-id=\"6b3447c\" 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-e6b6116 elementor-widget elementor-widget-image\" data-id=\"e6b6116\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"491\" height=\"298\" src=\"https:\/\/people.utm.my\/halinawati4\/wp-content\/uploads\/sites\/1201\/2020\/04\/Multiplying-vector-by-a-scalar-1.png\" class=\"attachment-large size-large wp-image-869\" alt=\"\" srcset=\"https:\/\/people.utm.my\/halinawati4\/wp-content\/uploads\/sites\/1201\/2020\/04\/Multiplying-vector-by-a-scalar-1.png 491w, https:\/\/people.utm.my\/halinawati4\/wp-content\/uploads\/sites\/1201\/2020\/04\/Multiplying-vector-by-a-scalar-1-300x182.png 300w\" sizes=\"100vw\" \/>\t\t\t\t\t\t\t\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-18131ff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"18131ff\" 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-376dba2\" data-id=\"376dba2\" 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-17d6ac7 elementor-widget elementor-widget-text-editor\" data-id=\"17d6ac7\" 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<p style=\"color:white\"><font>Here I shared my video slide.<\/p>\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-894cbb5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"894cbb5\" 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-166ebf1\" data-id=\"166ebf1\" 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-570ff39 elementor-widget elementor-widget-video\" data-id=\"570ff39\" 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\/04\/Lecture-2-part-3.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-d797fc5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d797fc5\" 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-826c26f\" data-id=\"826c26f\" 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-ef6b7d7 elementor-widget elementor-widget-text-editor\" data-id=\"ef6b7d7\" 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<p style=\"color:white\"><font>Here some video on youtube discussing about linear vector combination, linear dependence and linear independence.<\/p>\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-219c666 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"219c666\" 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-4ac44d0\" data-id=\"4ac44d0\" 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-304c9ab elementor-widget elementor-widget-video\" data-id=\"304c9ab\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/WJlQzgS_itI&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-969ab71 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"969ab71\" 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-dec2a86\" data-id=\"dec2a86\" 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-397fc2e elementor-widget elementor-widget-video\" data-id=\"397fc2e\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/OYp6XbibVt4&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-eb80910 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"eb80910\" 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-681dbbe\" data-id=\"681dbbe\" 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-515169a elementor-widget elementor-widget-video\" data-id=\"515169a\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/kzjVqg0Xxhk&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-7d4b3db elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d4b3db\" 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-4cc94b8\" data-id=\"4cc94b8\" 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-7460a6e elementor-widget elementor-widget-video\" data-id=\"7460a6e\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/Bn547nOfs3w&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-6ab2f9d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6ab2f9d\" 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-7f8655b\" data-id=\"7f8655b\" 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-f1a1e9c elementor-widget elementor-widget-video\" data-id=\"f1a1e9c\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/XI2kYIxhe-o&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-ec846ca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ec846ca\" 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-f6d328d\" data-id=\"f6d328d\" 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-b629b35 elementor-widget elementor-widget-text-editor\" data-id=\"b629b35\" 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<p style=\"color:white\"><font>If this video still cannot help you, you can find another video on youtube that can help you to understand. Anyway, please leave a comment below so that I know you read and watch the video that I put it here. <\/p>\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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Basic understanding of linear combination is: (scalar)(x) + (scalar)(y) + (scalar)(z) Or (scalar)(x1) + (scalar)(x2) + (scalar)(x3) +\u2026.+ (scalar)(xn) a linear combination of the vectors would be any combination of them using addition and scalar multiplication. A few examples would be: Here I shared my video slide. https:\/\/people.utm.my\/halinawati4\/files\/2020\/04\/Lecture-2-part-3.mp4 Here some video on youtube discussing about &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/people.utm.my\/halinawati4\/linear-combination-linear-dependence-and-linear-independence\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;LINEAR COMBINATION, LINEAR DEPENDENCE AND LINEAR INDEPENDENCE&#8221;<\/span><\/a><\/p>\n","protected":false},"author":16047,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-885","post","type-post","status-publish","format-standard","hentry","category-computational-mathematic"],"_links":{"self":[{"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/posts\/885","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=885"}],"version-history":[{"count":4,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/posts\/885\/revisions"}],"predecessor-version":[{"id":890,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/posts\/885\/revisions\/890"}],"wp:attachment":[{"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/media?parent=885"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/categories?post=885"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/people.utm.my\/halinawati4\/wp-json\/wp\/v2\/tags?post=885"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}