{"id":872,"date":"2021-11-27T22:48:01","date_gmt":"2021-11-27T22:48:01","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=872"},"modified":"2022-02-08T20:36:03","modified_gmt":"2022-02-08T20:36:03","slug":"clase-digital-14-combinaciones-lineales","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-14-combinaciones-lineales\/","title":{"rendered":"Clase digital 14: Combinaciones lineales"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-873\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/xnqvgsbxgv4.jpg\" style=\"object-position:65% 36%\" data-object-fit=\"cover\" data-object-position=\"65% 36%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1000\" class=\"wp-block-cover__image-background wp-image-873\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/xnqvgsbxgv4.jpg\" style=\"object-position:65% 36%\" data-object-fit=\"cover\" data-object-position=\"65% 36%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/xnqvgsbxgv4.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/xnqvgsbxgv4-300x188.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/xnqvgsbxgv4-1024x640.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/xnqvgsbxgv4-768x480.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/xnqvgsbxgv4-1536x960.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Combinaciones lineales<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Qu\u00e9 gusto&nbsp;encontrarte nuevamente en este curso, te doy la bienvenida a la clase 14 titulada Combinaciones lineales del curso <strong>\u00c1lgebra Lineal<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Debo decirte que es muy satisfactorio saber que sigues vigente en tu proceso formativo, te invito a que contin\u00faes en \u00e9l. Por otro lado y sin desviarnos del tema que nos une, ser\u00e1 necesario recordar sobre las reglas para la suma de matrices, la multiplicaci\u00f3n por un escalar y los espacios vectoriales.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Veremos que algunos vectores pueden obtenerse a partir de otros mediante multiplicaci\u00f3n de escalares y suma de vectores.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dado lo anterior, entremos en materia. \u00a1\u00c9xito!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Recuerda<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Para que los vectores se puedan sumar deben ser del mismo tama\u00f1o.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.31.12.png\" alt=\"\" class=\"wp-image-886\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"502\" height=\"248\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.31.12.png\" alt=\"\" class=\"wp-image-886\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.31.12.png 502w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.31.12-300x148.png 300w\" sizes=\"auto, (max-width: 502px) 100vw, 502px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Recuerda<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Si multiplicas un escalar por un vector, se debe multiplicar el n\u00famero a cada componente del vector. Por ejemplo, si <strong>c = 2<\/strong>.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.36.10.png\" alt=\"\" class=\"wp-image-888\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"409\" height=\"139\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.36.10.png\" alt=\"\" class=\"wp-image-888\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.36.10.png 409w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.36.10-300x102.png 300w\" sizes=\"auto, (max-width: 409px) 100vw, 409px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"combinaciones-lineales\">Combinaciones lineales<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>Se dice que un vector es una <strong>combinaci\u00f3n lineal <\/strong>si puede representarse como la suma de otros vectores multiplicados por escalares.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.06.png\" alt=\"\" class=\"wp-image-889\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"662\" height=\"197\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.06.png\" alt=\"\" class=\"wp-image-889\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.06.png 662w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.06-300x89.png 300w\" sizes=\"auto, (max-width: 662px) 100vw, 662px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>En algunas ocasiones no sabremos el valor de los escalares, por lo que debemos calcularlos.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.43.png\" alt=\"\" class=\"wp-image-890\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"688\" height=\"184\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.43.png\" alt=\"\" class=\"wp-image-890\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.43.png 688w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.37.43-300x80.png 300w\" sizes=\"auto, (max-width: 688px) 100vw, 688px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>Para eso los convertimos a un sistema de ecuaciones algebraico:<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.38.12.png\" alt=\"\" class=\"wp-image-891\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"161\" height=\"120\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.38.12.png\" alt=\"\" class=\"wp-image-891\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto, el escalar alfa es 2, el escalar beta es 1 y el escalar gamma es 1.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lo mismo aplica en la suma de matrices:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.38.42.png\" alt=\"\" class=\"wp-image-892\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"518\" height=\"147\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.38.42.png\" alt=\"\" class=\"wp-image-892\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.38.42.png 518w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-13.38.42-300x85.png 300w\" sizes=\"auto, (max-width: 518px) 100vw, 518px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>Se dice que <strong>la Matriz C es una combinaci\u00f3n lineal de la Matriz A y de la Matriz B<\/strong>.&nbsp;<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Para concluir la clase repasemos lo siguiente:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se dice que un vector es una <strong>combinaci\u00f3n lineal <\/strong>si puede representarse como la suma de otros vectores multiplicados por escalares.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si un vector no puede representarse de esta manera se dice que es linealmente independiente a dichos vectores.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es as\u00ed como llegamos al t\u00e9rmino de esta clase. Espero que todas tus dudas se hayan disipado con la informaci\u00f3n propuesta. Para finalizar la clase debes hacer la actividad correspondiente. \u00a1Vas muy bien, ya casi terminas este trayecto formativo felicidades! Te espero en la siguiente clase.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n <\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>Grossman, S. I. (2004). Algebra Lineal y sus Aplicaciones. (5<sup>a<\/sup> ed.). M\u00e9xico: McGraw-Hill.<\/li><li>Anton, H. (2011). Introducci\u00f3n al Algebra Lineal. (5<sup>a<\/sup> ed.). M\u00e9xico: Limusa Wiley.<\/li><li>Campbell, H. G. (1980). Linear Algebra with Applications. Atlanta: Prentice-Hall.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Qu\u00e9 gusto&nbsp;encontrarte nuevamente en este curso, te doy la bienvenida a la clase 14 titulada Combinaciones lineales del curso \u00c1lgebra Lineal. Debo decirte que es muy satisfactorio saber que sigues vigente en tu proceso formativo, te invito a que contin\u00faes en \u00e9l. Por otro lado y sin desviarnos del tema que nos une, &#8230; <a title=\"Clase digital 14: Combinaciones lineales\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-14-combinaciones-lineales\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 14: Combinaciones lineales\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[10,11],"tags":[41,61,62],"class_list":["post-872","post","type-post","status-publish","format-standard","hentry","category-ingenieria-civil","category-uda-algebra-lineal","tag-clase-digital","tag-jorge-arturo-gutierrez-camarena","tag-neli04035"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/872","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=872"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/872\/revisions"}],"predecessor-version":[{"id":7230,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/872\/revisions\/7230"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=872"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=872"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}