{"id":745,"date":"2021-11-27T22:41:19","date_gmt":"2021-11-27T22:41:19","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=745"},"modified":"2022-02-08T20:48:20","modified_gmt":"2022-02-08T20:48:20","slug":"clase-digital-4-metodo-de-gauss-jordan","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-4-metodo-de-gauss-jordan\/","title":{"rendered":"Clase digital 4: M\u00e9todo de Gauss &#8211; Jordan"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover\" 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-747\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk.jpg\" style=\"object-position:19% 4%\" data-object-fit=\"cover\" data-object-position=\"19% 4%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1068\" class=\"wp-block-cover__image-background wp-image-747\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk.jpg\" style=\"object-position:19% 4%\" data-object-fit=\"cover\" data-object-position=\"19% 4%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk-1024x684.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk-768x513.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk-1536x1025.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/7acuhoezuyk-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\">M\u00e9todo de Gauss &#8211; Jordan<\/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\">Siempre es un gusto saludarte y saber que tienes el \u00e1nimo para continuar, te invito a seguir en este camino formativo en tu cuarta clase titulada el M\u00e9todo de Gauss &#8211; Jordan y su utilidad al calcular el valor de las inc\u00f3gnitas en un sistema de ecuaciones del curso <strong>\u00c1lgebra Lineal<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El m\u00e9todo de Gauss &#8211; Jordan hace uso de las operaciones elementales dado que, al conservarse el valor de las inc\u00f3gnitas, es posible obtener sistemas de ecuaciones m\u00e1s simples y as\u00ed obtener los valores de manera directa.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ya hemos definido las componentes de toda matriz y su nomenclatura, as\u00ed como los conceptos de matriz triangular que es una representaci\u00f3n clave para resolver cualquier sistema de ecuaciones por muy complejo que sea, de una manera mucho m\u00e1s simple, o bien, determinar si dicho sistema es indeterminado o inconsistente.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez definidos los conceptos clave, abordamos el procedimiento est\u00e1ndar para aplicar el M\u00e9todo de Gauss &#8211; Jordan, aunque debe quedar claro que en algunos sistemas de ecuaciones es posible omitir pasos o cambiar el orden, por ejemplo, permutando renglones para facilitar el procedimiento. A pesar de lo anterior, se recomienda conocer el procedimiento tradicional, toda vez que esto facilitar\u00e1 una futura programaci\u00f3n de sistemas de ecuaciones a nivel general.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Te invito a continuar la sesi\u00f3n, \u00a1mucho \u00e9xito!<\/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\">Recordemos que un sistema de ecuaciones se puede representar como una matriz aumentada:<\/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-11.23.38.png\" alt=\"\" class=\"wp-image-748\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"556\" height=\"111\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.23.38.png\" alt=\"\" class=\"wp-image-748\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.23.38.png 556w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.23.38-300x60.png 300w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">El <strong>m\u00e9todo de Gauss \u2013 Jordan <\/strong>consiste en aplicar <strong>operaciones elementale<\/strong>s para obtener una matriz triangular superior:<\/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-11.24.09.png\" alt=\"\" class=\"wp-image-749\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"769\" height=\"186\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.24.09.png\" alt=\"\" class=\"wp-image-749\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.24.09.png 769w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.24.09-300x73.png 300w\" sizes=\"auto, (max-width: 769px) 100vw, 769px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Los pasos generales son:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Divide todo el primer rengl\u00f3n entre la componente a<sub>11<\/sub>.<\/li><li>Convierte todos los dem\u00e1s valores de esa columna en ceros:<ol><li>Al segundo rengl\u00f3n (R2) se le restar\u00e1 el primer rengl\u00f3n multiplicado por la componente a<sub>21<\/sub>.<\/li><li>Al tercer rengl\u00f3n (R3) se le restar\u00e1 el primer rengl\u00f3n multiplicado por la componente a<sub>31<\/sub>.<\/li><\/ol><\/li><li>Divide todo el segundo rengl\u00f3n entre la componente a<sub>22<\/sub>.&nbsp;<\/li><li>Repite todo el proceso para las dem\u00e1s columnas hasta obtener la forma deseada.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Teniendo la matriz triangular superior, podemos convertirla a la forma tradicional y resolver de <strong>forma escalonada <\/strong>para determinar el valor de las inc\u00f3gnitas:<\/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-11.24.54.png\" alt=\"\" class=\"wp-image-750\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"702\" height=\"201\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.24.54.png\" alt=\"\" class=\"wp-image-750\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.24.54.png 702w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.24.54-300x86.png 300w\" sizes=\"auto, (max-width: 702px) 100vw, 702px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Revisemos el siguiente ejemplo:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Poseemos un sistema de 3 ecuaciones y 3 inc\u00f3gnitas y lo convertimos a su representaci\u00f3n matricial:<\/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-11.25.27.png\" alt=\"\" class=\"wp-image-753\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"573\" height=\"111\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.25.27.png\" alt=\"\" class=\"wp-image-753\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.25.27.png 573w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.25.27-300x58.png 300w\" sizes=\"auto, (max-width: 573px) 100vw, 573px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Antes que nada, revisemos la nomenclatura:<\/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-11.25.59.png\" alt=\"\" class=\"wp-image-754\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"686\" height=\"247\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.25.59.png\" alt=\"\" class=\"wp-image-754\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.25.59.png 686w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.25.59-300x108.png 300w\" sizes=\"auto, (max-width: 686px) 100vw, 686px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Como primer paso dividimos el primer rengl\u00f3n R<sub>1<\/sub> entre la componente a<sub>11&nbsp;<\/sub>:<\/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-11.26.36.png\" alt=\"\" class=\"wp-image-755\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"682\" height=\"252\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.26.36.png\" alt=\"\" class=\"wp-image-755\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.26.36.png 682w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.26.36-300x111.png 300w\" sizes=\"auto, (max-width: 682px) 100vw, 682px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Como segundo paso se requiere \u00abconvertir\u00bb las componentes inferiores de la componente a<sub>11<\/sub> en ceros (0):<\/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-11.27.15.png\" alt=\"\" class=\"wp-image-756\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"718\" height=\"241\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.27.15.png\" alt=\"\" class=\"wp-image-756\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.27.15.png 718w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.27.15-300x101.png 300w\" sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Al tercer rengl\u00f3n (R<sub>3<\/sub>) se le restar\u00e1 el primer rengl\u00f3n multiplicado por la componente a<sub>31<\/sub>.<\/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-11.27.51.png\" alt=\"\" class=\"wp-image-759\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"691\" height=\"217\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.27.51.png\" alt=\"\" class=\"wp-image-759\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.27.51.png 691w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.27.51-300x94.png 300w\" sizes=\"auto, (max-width: 691px) 100vw, 691px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se procede a dividir el segundo rengl\u00f3n R<sub>2<\/sub> entre la componente a<sub>22&nbsp;<\/sub>:<\/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-11.28.25.png\" alt=\"\" class=\"wp-image-761\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"717\" height=\"226\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.28.25.png\" alt=\"\" class=\"wp-image-761\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.28.25.png 717w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.28.25-300x95.png 300w\" sizes=\"auto, (max-width: 717px) 100vw, 717px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora se repite todo el proceso para las dem\u00e1s columnas hasta obtener la forma deseada.&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-11.28.59.png\" alt=\"\" class=\"wp-image-763\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"721\" height=\"426\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.28.59.png\" alt=\"\" class=\"wp-image-763\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.28.59.png 721w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.28.59-300x177.png 300w\" sizes=\"auto, (max-width: 721px) 100vw, 721px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente, convertimos al sistema convencional de ecuaciones:<\/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-11.29.34.png\" alt=\"\" class=\"wp-image-764\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"681\" height=\"229\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.29.34.png\" alt=\"\" class=\"wp-image-764\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.29.34.png 681w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-11.29.34-300x101.png 300w\" sizes=\"auto, (max-width: 681px) 100vw, 681px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se observa que una vez que nos encontramos en esta forma triangular es posible obtener los resultados de forma escalonada, es decir, el valor de Z se obtiene directamente y su valor se sustituye en la ecuaci\u00f3n superior, obteniendo el valor de Y. Ambos valores (Z y Y) se sustituyen en la primera ecuaci\u00f3n y se obtiene el valor de X.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En conclusi\u00f3n, hemos visto que el <strong>m\u00e9todo de Gauss \u2013 Jordan <\/strong>consiste en aplicar <strong>operaciones elementale<\/strong>s para obtener una matriz triangular superior.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El procedimiento est\u00e1ndar es el siguiente:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Divide todo el primer rengl\u00f3n entre la componente a<sub>11<\/sub>.<\/li><li>Convierte todos los dem\u00e1s valores de esa columna en ceros:<ol><li>Al segundo rengl\u00f3n (R2) se le restar\u00e1 el primer rengl\u00f3n multiplicado por la componente a<sub>21<\/sub>.<\/li><li>Al tercer rengl\u00f3n (R3) se le restar\u00e1 el primer rengl\u00f3n multiplicado por la componente a<sub>31<\/sub>.<\/li><\/ol><\/li><li>Divide todo el segundo rengl\u00f3n entre la componente a<sub>22<\/sub>.&nbsp;<\/li><li>Repite todo el proceso para las dem\u00e1s columnas hasta obtener la forma deseada.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Teniendo la matriz triangular superior, podemos convertirla a la forma tradicional y resolver de <strong>forma escalonada <\/strong>para determinar el valor de las inc\u00f3gnitas:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hasta aqu\u00ed se concluye la clase. \u00a1Te felicito, vas muy bien! Te recuerdo que depende mucho de tu entusiasmo por aprender. No olvides hacer y mandar como corresponde la tarea asignada. Te espero en tu pr\u00f3xima clase, hasta entonces.<\/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! Siempre es un gusto saludarte y saber que tienes el \u00e1nimo para continuar, te invito a seguir en este camino formativo en tu cuarta clase titulada el M\u00e9todo de Gauss &#8211; Jordan y su utilidad al calcular el valor de las inc\u00f3gnitas en un sistema de ecuaciones del curso \u00c1lgebra Lineal. El m\u00e9todo &#8230; <a title=\"Clase digital 4: M\u00e9todo de Gauss &#8211; Jordan\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-4-metodo-de-gauss-jordan\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 4: M\u00e9todo de Gauss &#8211; Jordan\">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-745","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\/745","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=745"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/745\/revisions"}],"predecessor-version":[{"id":7310,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/745\/revisions\/7310"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=745"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=745"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=745"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}