{"id":782,"date":"2021-11-27T22:45:09","date_gmt":"2021-11-27T22:45:09","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=782"},"modified":"2022-02-08T19:05:19","modified_gmt":"2022-02-08T19:05:19","slug":"clase-digital-7-inversa-de-matrices","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-7-inversa-de-matrices\/","title":{"rendered":"Clase digital 7: Inversa de matrices"},"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-783\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis.jpg\" style=\"object-position:61% 48%\" data-object-fit=\"cover\" data-object-position=\"61% 48%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1067\" class=\"wp-block-cover__image-background wp-image-783\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis.jpg\" style=\"object-position:61% 48%\" data-object-fit=\"cover\" data-object-position=\"61% 48%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis-1024x683.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis-1536x1024.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/ag-pvymsbis-272x182.jpg 272w\" 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\">Inversa de matrices<\/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\">\u00a1Qu\u00e9 emoci\u00f3n volvernos a encontrar! Espero que sigas con ese mismo \u00edmpetu de la primera clase y sigas aprendiendo, por lo tanto te invito a esta s\u00e9ptima clase titulada INVERSA DE MATRICES del curso <strong>\u00c1lgebra Lineal.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para esta sesi\u00f3n se pretende definir las condiciones para poder obtener la inversa de matrices y aclarar que no todas las matrices son invertibles. Es necesario hacer uso de esta t\u00e9cnica puesto que no existen las divisiones entre matrices y la obtenci\u00f3n de la inversa nos proporcionar\u00e1 una herramienta \u00fatil para la resoluci\u00f3n de ecuaciones lineales.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez definida la inversa de matrices, podremos ser capaces de hacer uso de estas t\u00e9cnicas para la resoluci\u00f3n de ecuaciones lineales.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Adelante y con mucho \u00e1nimo, empecemos la clase!<\/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\">No existen las divisiones de matrices, pero en su lugar es posible multiplicar por la inversa de la matriz de inter\u00e9s.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Poseemos una matriz cuadrada de 3 renglones X 3 columnas (3&#215;3):<\/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-11.48.51.png\" alt=\"\" class=\"wp-image-784\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"338\" height=\"161\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.48.51.png\" alt=\"\" class=\"wp-image-784\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.48.51.png 338w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.48.51-300x143.png 300w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>Lo primero que necesitamos hacer es convertirla en matriz aumentada, con la matriz identidad del lado derecho.<\/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-11.49.33.png\" alt=\"\" class=\"wp-image-785\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"527\" height=\"175\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.49.33.png\" alt=\"\" class=\"wp-image-785\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.49.33.png 527w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.49.33-300x100.png 300w\" sizes=\"auto, (max-width: 527px) 100vw, 527px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>La idea es aplicar operaciones elementales de manera similar al M\u00e9todo de Gauss \u2013 Jordan, hasta obtener la siguiente forma:<\/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-11.50.06.png\" alt=\"\" class=\"wp-image-786\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"252\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.50.06.png\" alt=\"\" class=\"wp-image-786\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.50.06.png 587w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.50.06-300x129.png 300w\" sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><\/noscript><\/figure><\/div>\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\">No existen las divisiones de matrices. Sin embargo, es posible hacer uso de una herramienta an\u00e1loga que consiste en multiplicar por la inversa de una matriz.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para ello es necesario representar la matriz de inter\u00e9s en una matriz aumentada, colocando del lado derecho, una matriz identidad.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se debe aplicar el M\u00e9todo de Gauss &#8211; Jordan para que del lado izquierdo quede la matriz identidad y lo que quede del lado derecho ser\u00e1 la inversa.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>NOTA<\/em>: No todas las matrices son invertibles.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hemos llegado al final de la sesi\u00f3n y no me resta m\u00e1s que felicitarte por llegar hasta esta parte del curso. Te invito a que contin\u00faes con tu proceso formativo realizando la tarea asignada y mandarla como corresponde. Te encuentro pr\u00f3ximamente.<\/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! \u00a1Qu\u00e9 emoci\u00f3n volvernos a encontrar! Espero que sigas con ese mismo \u00edmpetu de la primera clase y sigas aprendiendo, por lo tanto te invito a esta s\u00e9ptima clase titulada INVERSA DE MATRICES del curso \u00c1lgebra Lineal. Para esta sesi\u00f3n se pretende definir las condiciones para poder obtener la inversa de matrices y aclarar &#8230; <a title=\"Clase digital 7: Inversa de matrices\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-7-inversa-de-matrices\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 7: Inversa de matrices\">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-782","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\/782","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=782"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/782\/revisions"}],"predecessor-version":[{"id":6980,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/782\/revisions\/6980"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=782"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}