{"id":841,"date":"2021-11-27T22:47:16","date_gmt":"2021-11-27T22:47:16","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=841"},"modified":"2022-02-08T20:38:30","modified_gmt":"2022-02-08T20:38:30","slug":"clase-digital-12-metodo-de-cramer","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-12-metodo-de-cramer\/","title":{"rendered":"Clase digital 12: M\u00e9todo de Cramer"},"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-842\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/vt-dbtf8kb0.jpg\" style=\"object-position:60% 75%\" data-object-fit=\"cover\" data-object-position=\"60% 75%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"896\" class=\"wp-block-cover__image-background wp-image-842\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/vt-dbtf8kb0.jpg\" style=\"object-position:60% 75%\" data-object-fit=\"cover\" data-object-position=\"60% 75%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/vt-dbtf8kb0.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/vt-dbtf8kb0-300x168.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/vt-dbtf8kb0-1024x573.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/vt-dbtf8kb0-768x430.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/vt-dbtf8kb0-1536x860.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\">M\u00e9todo de Cramer<\/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!&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Me complace enormemente saber de ti, espero que compartas mi emoci\u00f3n y te sumes con una gran actitud y \u00e1nimo a esta clase 12 titulada M\u00e9todo de Cramer del curso <strong>\u00c1lgebra Lineal.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El M\u00e9todo de Cramer, nos permite obtener el valor de las inc\u00f3gnitas en un sistema de ecuaciones haciendo uso de las determinantes. Esta es una de las aplicaciones que poseen las determinantes. Si la determinante es cero, podemos definir que nos encontramos con un sistema de ecuaciones indeterminado.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cuento con que esta clase sea de gran apoyo para ti.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\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\">Otra manera de encontrar el valor de las inc\u00f3gnitas de un sistema de ecuaciones es mediante el M\u00e9todo de Cramer.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como ejemplo consideremos las siguientes:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>Ecuaci\u00f3n &nbsp; 1)<\/strong> 5x + 2y + z = 20<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Ecuaci\u00f3n &nbsp; 2)<\/strong> 2x + y + 2z = 10<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Ecuaci\u00f3n &nbsp; 3)<\/strong> 4x + y + 3z = 17<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si las convertimos a un sistema matricial:<\/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-12.39.04.png\" alt=\"\" class=\"wp-image-843\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"74\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.39.04.png\" alt=\"\" class=\"wp-image-843\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.39.04.png 309w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.39.04-300x72.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Del lado izquierdo de la ecuaci\u00f3n se tienen tres columnas con los coeficientes de las inc\u00f3gnitas (C), mientras que al lado derecho se tiene una columna de resultados (R).<\/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-12.39.49.png\" alt=\"\" class=\"wp-image-844\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"293\" height=\"89\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.39.49.png\" alt=\"\" class=\"wp-image-844\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Para obtener el valor de las inc\u00f3gnitas aplicamos las f\u00f3rmulas siguientes:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>X = D1\/D<\/strong><br><strong>Y = D2\/D<\/strong><br><strong>Z = D3\/D<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Donde D, D1, D2 y D3 son determinantes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para obtener D se requieren las tres primeras columnas (marcadas en azul) e ignoramos la columna amarilla.&nbsp;<\/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-12.40.29.png\" alt=\"\" class=\"wp-image-845\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"99\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.40.29.png\" alt=\"\" class=\"wp-image-845\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La determinante D equivale a:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D = [(5) (1) (3) + (2) (1) (1) + (4) (2) (2)] \u2013 [(5) (2) (1) + (2) (2) (3) + (1) (1) (4)]<br><strong>D = 7<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para obtener D1 es necesario sustituir la columna de resultados (color amarillo) en la columna C1.<\/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-12.41.08.png\" alt=\"\" class=\"wp-image-846\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"98\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.41.08.png\" alt=\"\" class=\"wp-image-846\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora obtenemos la determinante D1:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D1 = [(20) (1) (3) + (10) (1) (1) + (17) (2) (2)] \u2013 [(20) (2) (1) + (10) (2) (3) + (1) (1) (17)]<br><strong>D1 = 21<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En el caso de D2 dejamos la columna C1 en su lugar y sustituimos la columna C2 por R.<\/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-12.41.42.png\" alt=\"\" class=\"wp-image-847\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"98\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.41.42.png\" alt=\"\" class=\"wp-image-847\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se obtiene la determinante D2:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>D2 = 14<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Del mismo modo para D3 sustituimos la columna C3 por la columna R.<\/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-12.42.14.png\" alt=\"\" class=\"wp-image-848\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"99\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.42.14.png\" alt=\"\" class=\"wp-image-848\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se obtiene la determinante D3:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>D3 = 7<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sustituyendo en las f\u00f3rmulas:<\/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-12.42.45.png\" alt=\"\" class=\"wp-image-849\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"269\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.42.45.png\" alt=\"\" class=\"wp-image-849\" \/><\/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 recordemos lo siguiente:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para el M\u00e9todo de Cramer es necesario recurrir a las determinantes y aplicar las siguientes f\u00f3rmulas:<\/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-12.43.13.png\" alt=\"\" class=\"wp-image-850\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"105\" height=\"279\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.43.13.png\" alt=\"\" class=\"wp-image-850\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Donde la determinante D es la que se obtiene al considerar la matriz formada s\u00f3lo por los coeficientes de las inc\u00f3gnitas.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Los valores D1, D2 y D3 son las determinantes que se obtienen al sustituir la columna de los coeficientes de la inc\u00f3gnita correspondiente por la columna de resultados (constantes).&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Te felicito por tu logro! Te invito a continuar con tu proceso formativo realizando y mandando la actividad asignada a esta clase. \u201cPerseverar es sin\u00f3nimo de tenacidad, no decaigas sigue perseverando en tu educaci\u00f3n\u201d Te encuentro en la siguiente clase. Hasta luego.<\/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!&nbsp; Me complace enormemente saber de ti, espero que compartas mi emoci\u00f3n y te sumes con una gran actitud y \u00e1nimo a esta clase 12 titulada M\u00e9todo de Cramer del curso \u00c1lgebra Lineal. El M\u00e9todo de Cramer, nos permite obtener el valor de las inc\u00f3gnitas en un sistema de ecuaciones haciendo uso de las &#8230; <a title=\"Clase digital 12: M\u00e9todo de Cramer\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-12-metodo-de-cramer\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 12: M\u00e9todo de Cramer\">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-841","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\/841","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=841"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/841\/revisions"}],"predecessor-version":[{"id":7247,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/841\/revisions\/7247"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}