{"id":835,"date":"2021-03-19T18:00:33","date_gmt":"2021-03-19T16:00:33","guid":{"rendered":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=835"},"modified":"2021-03-24T21:22:40","modified_gmt":"2021-03-24T19:22:40","slug":"sistema-de-ecuaciones-lineales-con-parametro","status":"publish","type":"post","link":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=835","title":{"rendered":"Sistema de ecuaciones lineales con par\u00e1metro"},"content":{"rendered":"<p>Ya estuvimos analizando el Teorema de Rouch\u00e9, que clasifica sistemas de ecuaciones lineales seg\u00fan su soluci\u00f3n a trav\u00e9s del rango de matrices; concretamente, comparando los de la matriz de coeficientes y de la matriz ampliada.<\/p>\n<p>Vamos a insistir en \u00e9l y resolver un t\u00edpico ejercicio en el que se estudia un sistema en el que aparecen coeficientes literales.<\/p>\n<p>Aqu\u00ed el enunciado:<\/p>\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\nClasifiquemos el siguiente sistema de ecuaciones lineales seg\u00fan los valores del par\u00e1metro \\(\\lambda\\):\\[\\left\\{ \\begin{array}{lcr} 2x+3y-4z&#038;=&#038;1\\\\[1mm] 4x+6y-\\lambda z&#038; =&#038; 4\\\\[1mm] \\phantom{2}x+\\phantom{2}y+\\phantom{2}z&#038; =&#038; 10 \\end{array} \\right.\\]<\/fieldset>\n<p>Si tienes dudas o quieres comprobar tu discusi\u00f3n, una resoluci\u00f3n detallada est\u00e1 en el siguiente v\u00eddeo:<\/p>\n<div style=\"text-align: center;\">\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/dvQfC5avC94\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<\/div>\n<p>Observemos que s\u00f3lo han aparecido dos casos (en ninguno era compatible indeterminado) y que no se ha resuelto. Aunque podr\u00edamos resolver mediante la Regla de Cramer f\u00e1cilmente cuando es compatible determinado (la soluci\u00f3n queda expresada en funci\u00f3n del coeficiente \\(\\lambda\\)).<\/p>\n<p>Gracias y espero que haya sido \u00fatil la publicaci\u00f3n. Hasta la vista.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ya estuvimos analizando el Teorema de Rouch\u00e9, que clasifica sistemas de ecuaciones lineales seg\u00fan su soluci\u00f3n a trav\u00e9s del rango de matrices; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"post-templates\/post_nosidebar.php","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[65,67,50],"class_list":["post-835","post","type-post","status-publish","format-standard","hentry","category-matematicas-ii","tag-algebra","tag-sistemas-de-ecuaciones","tag-video"],"_links":{"self":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/835","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=835"}],"version-history":[{"count":2,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/835\/revisions"}],"predecessor-version":[{"id":837,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/835\/revisions\/837"}],"wp:attachment":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}