{"id":814,"date":"2021-11-27T22:46:48","date_gmt":"2021-11-27T22:46:48","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=814"},"modified":"2022-02-08T20:48:59","modified_gmt":"2022-02-08T20:48:59","slug":"clase-digital-11-propiedades-de-las-determinantes","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-11-propiedades-de-las-determinantes\/","title":{"rendered":"Clase digital 11: Propiedades de las determinantes"},"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-815\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/jexauncfefs.jpg\" style=\"object-position:69% 70%\" data-object-fit=\"cover\" data-object-position=\"69% 70%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1200\" class=\"wp-block-cover__image-background wp-image-815\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/jexauncfefs.jpg\" style=\"object-position:69% 70%\" data-object-fit=\"cover\" data-object-position=\"69% 70%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/jexauncfefs.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/jexauncfefs-300x225.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/jexauncfefs-1024x768.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/jexauncfefs-768x576.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/jexauncfefs-1536x1152.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\">Propiedades de las determinantes<\/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\">No sabes la alegr\u00eda que tengo al saber que sigues perseverando en tu educaci\u00f3n. Te comento que est\u00e1s a pocas clases de lograr el objetivo de este curso y con ello subes un pelda\u00f1o m\u00e1s en tu aprendizaje. \u00a1Qu\u00e9 emoci\u00f3n no crees! Pues bien, para completar todo este proceso formativo te invito a empezar esta sesi\u00f3n que es la n\u00famero once denominada Propiedades de las determinantes del curso <strong>\u00c1lgebra Lineal.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para la gran mayor\u00eda de veces, aplicar el M\u00e9todo de Factores directamente sobre una matriz compleja (refiri\u00e9ndonos a dimensiones de 5&#215;5 o m\u00e1s, incluso mucho m\u00e1s), dar\u00e1 como resultado un n\u00famero grande de operaciones que debemos resolver. Notaremos que en matrices de 50 x 50, 500 x 500 o incluso m\u00e1s, el conjunto de operaciones necesarias para obtener todos los factores es bastante grande que se vuelve poco funcional resolverlas, con el riesgo de los errores en c\u00e1lculos que esto implica.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es por ello, que se vuelve imperante conocer las propiedades de las determinantes para simplificar la matriz a una m\u00e1s simple y as\u00ed resolverla, afectando \u00fanicamente los valores directos de las determinantes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez aclarado lo anterior, te invito a proseguir.<\/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\">&nbsp;1) Si aplicamos la operaci\u00f3n elemental <strong>\u201csuma de renglones\u201d <\/strong>a una matriz conservar\u00e1 el valor de su determinante.<\/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-12.23.48.png\" alt=\"\" class=\"wp-image-816\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"560\" height=\"245\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.23.48.png\" alt=\"\" class=\"wp-image-816\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.23.48.png 560w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.23.48-300x131.png 300w\" sizes=\"auto, (max-width: 560px) 100vw, 560px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2) <\/strong>Si aplicamos la operaci\u00f3n elemental <strong>\u201cPermuta\u201d <\/strong>entre dos renglones de una matriz cambiar\u00e1 el signo de su determinante.<\/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-12.24.46.png\" alt=\"\" class=\"wp-image-818\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"216\" height=\"204\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.24.46.png\" alt=\"\" class=\"wp-image-818\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3) <\/strong>Si aplicamos la operaci\u00f3n elemental <strong>\u201cMultiplicaci\u00f3n por escalar\u201d <\/strong>en un rengl\u00f3n de la matriz, la determinante se multiplicar\u00e1 por el mismo escalar.&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-12.25.32.png\" alt=\"\" class=\"wp-image-820\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"544\" height=\"200\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.25.32.png\" alt=\"\" class=\"wp-image-820\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.25.32.png 544w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.25.32-300x110.png 300w\" sizes=\"auto, (max-width: 544px) 100vw, 544px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4) <\/strong>La determinante de una <strong>matriz triangular <\/strong>(superior o inferior) es igual al producto de su diagonal principal.<\/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-12.26.22.png\" alt=\"\" class=\"wp-image-822\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"223\" height=\"144\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.26.22.png\" alt=\"\" class=\"wp-image-822\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Calcular la siguiente determinante (mediante operaciones elementales):<\/em><\/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-12.26.54.png\" alt=\"\" class=\"wp-image-823\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"342\" height=\"251\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.26.54.png\" alt=\"\" class=\"wp-image-823\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.26.54.png 342w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.26.54-300x220.png 300w\" sizes=\"auto, (max-width: 342px) 100vw, 342px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 1)<\/strong> <em>Aplicar el <\/em><strong><em>M\u00e9todo de Gauss <\/em><\/strong><em>para obtener una matriz triangular (superior o inferior)<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Aplicamos el M\u00e9todo est\u00e1ndar de Gauss (convertir la primera componente en 1):<\/em><\/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-12.28.05.png\" alt=\"\" class=\"wp-image-825\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"526\" height=\"286\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.28.05.png\" alt=\"\" class=\"wp-image-825\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.28.05.png 526w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.28.05-300x163.png 300w\" sizes=\"auto, (max-width: 526px) 100vw, 526px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Aplicamos el M\u00e9todo est\u00e1ndar de Gauss (ahora convertimos los elementos debajo del primer pivote en ceros):<\/em><\/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-12.28.35.png\" alt=\"\" class=\"wp-image-827\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"516\" height=\"282\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.28.35.png\" alt=\"\" class=\"wp-image-827\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.28.35.png 516w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.28.35-300x164.png 300w\" sizes=\"auto, (max-width: 516px) 100vw, 516px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Aplicamos el M\u00e9todo est\u00e1ndar de Gauss (convertimos la componente central en 1):<\/em><\/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-12.29.01.png\" alt=\"\" class=\"wp-image-828\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"434\" height=\"170\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.29.01.png\" alt=\"\" class=\"wp-image-828\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.29.01.png 434w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.29.01-300x118.png 300w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Aplicamos el M\u00e9todo est\u00e1ndar de Gauss (convertimos en cero el n\u00famero debajo de dicho pivote):<\/em><\/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-12.29.29.png\" alt=\"\" class=\"wp-image-830\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"541\" height=\"181\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.29.29.png\" alt=\"\" class=\"wp-image-830\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.29.29.png 541w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.29.29-300x100.png 300w\" sizes=\"auto, (max-width: 541px) 100vw, 541px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 2)<\/strong> <em>Revisar TODAS las operaciones elementales realizadas en el paso 1<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Las operaciones elementales realizadas fueron las siguientes:<\/em><\/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-12.30.01.png\" alt=\"\" class=\"wp-image-831\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"155\" height=\"170\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.30.01.png\" alt=\"\" class=\"wp-image-831\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Recordemos que las sumas de renglones no afectan la determinante, pero s\u00ed las <\/em><strong><em>multiplicaciones por escalares<\/em><\/strong><em>. Las seleccionamos<\/em>:<\/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-12.30.31.png\" alt=\"\" class=\"wp-image-833\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"211\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.30.31.png\" alt=\"\" class=\"wp-image-833\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 3)<\/strong> <em>Multiplicar las componentes de la <\/em><strong><em>diagonal<\/em><\/strong><em> de la matriz triangular<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Multiplicamos los componentes de la diagonal:<\/em><\/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-12.31.05.png\" alt=\"\" class=\"wp-image-835\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"520\" height=\"212\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.31.05.png\" alt=\"\" class=\"wp-image-835\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.31.05.png 520w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.31.05-300x122.png 300w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 4)<\/strong> <em>Multiplicar la determinante modificada por el rec\u00edproco de cada escalar multiplicado durante el paso 1.&nbsp;<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Los escalares que se multiplicaron durante el M\u00e9todo de Gauss se encierran en un rect\u00e1ngulo rojo.<\/em><\/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-12.31.42.png\" alt=\"\" class=\"wp-image-836\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"138\" height=\"194\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.31.42.png\" alt=\"\" class=\"wp-image-836\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Los rec\u00edprocos de los escalares son:<\/em><\/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-12.32.13.png\" alt=\"\" class=\"wp-image-838\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"432\" height=\"114\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.32.13.png\" alt=\"\" class=\"wp-image-838\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.32.13.png 432w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.32.13-300x79.png 300w\" sizes=\"auto, (max-width: 432px) 100vw, 432px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Entonces:<\/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-12.32.41.png\" alt=\"\" class=\"wp-image-839\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"533\" height=\"149\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.32.41.png\" alt=\"\" class=\"wp-image-839\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.32.41.png 533w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.32.41-300x84.png 300w\" sizes=\"auto, (max-width: 533px) 100vw, 533px\" \/><\/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\">En conclusi\u00f3n, repasemos lo siguiente: Consideremos una matriz A y su determinante.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Si a dicha matriz A, le aplicamos una suma de renglones, observaremos que su determinante es la misma.&nbsp;<\/li><li>Si a dicha matriz A, le aplicamos una permuta de renglones, entonces su determinante cambia de signo.&nbsp;<\/li><li>Si a la matriz A, le multiplicamos un rengl\u00f3n por un escalar, entonces la determinante se multiplicar\u00e1 por dicho escalar.&nbsp;<\/li><li>Si tenemos una matriz triangular (superior o inferior) su determinante es igual al producto de sus componentes.&nbsp;<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">A partir de estas propiedades, es posible simplificar las operaciones para obtener el valor de una determinante.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hemos llegado al final de la clase, me siento muy feliz de que hayas llegado hasta aqu\u00ed. \u00a1Te felicito, tienes una gran voluntad! Para cerrar la clase te invito a realizar la tarea asignada y mandarla como corresponde. Te espero en tu pr\u00f3xima sesi\u00f3n, 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! No sabes la alegr\u00eda que tengo al saber que sigues perseverando en tu educaci\u00f3n. Te comento que est\u00e1s a pocas clases de lograr el objetivo de este curso y con ello subes un pelda\u00f1o m\u00e1s en tu aprendizaje. \u00a1Qu\u00e9 emoci\u00f3n no crees! Pues bien, para completar todo este proceso formativo te invito a &#8230; <a title=\"Clase digital 11: Propiedades de las determinantes\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-11-propiedades-de-las-determinantes\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 11: Propiedades de las determinantes\">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-814","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\/814","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=814"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/814\/revisions"}],"predecessor-version":[{"id":7312,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/814\/revisions\/7312"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=814"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=814"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}