{"id":7849,"date":"2020-02-17T15:46:21","date_gmt":"2020-02-17T20:46:21","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=7849"},"modified":"2020-02-18T23:31:10","modified_gmt":"2020-02-19T04:31:10","slug":"2019-2020-termino-2-e3-tema-2","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1003\/2019-2020-termino-2-e3-tema-2\/","title":{"rendered":"Tema 2"},"content":{"rendered":"
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\r\n Examen | 2019-2020 | T\u00e9rmino 2 | Tercera Evaluaci\u00f3n | Tema 2\r\n <\/div>\r\n <\/div>\n
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Considere el espacio vectorial real \\mathcal{P}_2(\\mathbb{R})<\/span> de los polinomios de grado menor o igual a dos con coeficiente reales. Se define el producto interno en \\mathcal{P}_2(\\mathbb{R})<\/span> por \\langle p | q \\rangle = a_1a_2+3b_1b_2+2c_1c_2<\/span>, donde p(x)=a_1+b_1x+c_1x^2<\/span> y q(x)=a_2+b_2x+c_2x^2<\/span>.<\/p>\n\n\n\n\n\n\n
a)<\/td>\nDetermine si los polinomios p(x)=1+x<\/span> y q(x)=x^2-x<\/span> son ortogonales respecto a este producto interno.<\/td>\n<\/tr>\n
b)<\/td>\nCalcule la proyecci\u00f3n ortogonal del polinomio p(x)=1+x+x^2<\/span> sobre el polinomio q(x)=1+x<\/span>.<\/td>\n<\/tr>\n
c)<\/td>\nVerifique que B=\\{ 1,x+1,x^2-1 \\}<\/span> es una base de \\mathcal{P}_2(\\mathbb{R})<\/span>.<\/td>\n<\/tr>\n
d)<\/td>\nHalle la matriz cambio de base, de la base can\u00f3nica a la base B<\/span> (mencionada en el literal c).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Considere el espacio vectorial real de los polinomios de grado menor o igual a dos con coeficiente reales. Se define el producto interno en por , donde y . a) Determine si los polinomios y son ortogonales respecto a este producto interno. b) Calcule la proyecci\u00f3n ortogonal del polinomio sobre el polinomio . c) Verifique … Sigue leyendo Tema 2<\/span><\/a><\/p>\n","protected":false},"author":609,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[1430170],"tags":[],"class_list":["post-7849","post","type-post","status-publish","format-standard","hentry","category-tercera-evaluacion-termino-2-2019-2020"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/7849","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/users\/609"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/comments?post=7849"}],"version-history":[{"count":13,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/7849\/revisions"}],"predecessor-version":[{"id":7862,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/7849\/revisions\/7862"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/media?parent=7849"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/categories?post=7849"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/tags?post=7849"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}