{"id":7796,"date":"2020-01-31T15:57:12","date_gmt":"2020-01-31T20:57:12","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=7796"},"modified":"2020-02-02T23:35:09","modified_gmt":"2020-02-03T04:35:09","slug":"2019-2020-termino-2-e2-tema-2","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1003\/2019-2020-termino-2-e2-tema-2\/","title":{"rendered":"Tema 2"},"content":{"rendered":"
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\r\n Examen | 2019-2020 | T\u00e9rmino 2 | Segunda Evaluaci\u00f3n | Tema 2\r\n <\/div>\r\n <\/div>\n
\n

Considere \\mathcal{P}_3 (\\mathbb{R})<\/span> el conjunto de todos los polinomios de grado menor o igual a tres, con coeficientes reales. Considere en \\mathcal{P}_3 (\\mathbb{R})<\/span> la aplicaci\u00f3n \\langle \\cdot | \\cdot \\rangle : \\mathcal{P}_3 (\\mathbb{R}) \\times \\mathcal{P}_3 (\\mathbb{R}) \\longrightarrow \\mathbb{R}<\/span> definido por \\footnotesize{\\langle a_0+a_1x+a_2x^2+a_3x^3 | b_0+b_1x+b_2x^2+b_3x^3 \\rangle = a_0b_0+4a_1b_1+2a_2b_2+a_3b_3}<\/span><\/p>\n\n\n\n\n\n\n
a)<\/td>\nVerifique que \\langle \\cdot | \\cdot \\rangle<\/span> es un producto interno en \\mathcal{P}_3 (\\mathbb{R})<\/span>.<\/td>\n<\/tr>\n
b)<\/td>\nPara el operador en T:\\mathcal{P}_3 (\\mathbb{R})\\longrightarrow \\mathcal{P}_3 (\\mathbb{R})<\/span> definido por T(p(x))=p(-1)+p(0)x^2<\/span>, determine una base para la imagen de T<\/span>.<\/td>\n<\/tr>\n
c)<\/td>\nDetermine el complemento ortogonal del n\u00facleo (o kernel) de T<\/span>.<\/td>\n<\/tr>\n
d)<\/td>\nEncuentre la proyecci\u00f3n ortogonal del vector r(x)=1+x+2x^2+3x^3<\/span> sobre el n\u00facleo de T<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Considere el conjunto de todos los polinomios de grado menor o igual a tres, con coeficientes reales. Considere en la aplicaci\u00f3n definido por a) Verifique que es un producto interno en . b) Para el operador en definido por , determine una base para la imagen de . c) Determine el complemento ortogonal del n\u00facleo … 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":[1430169],"tags":[],"class_list":["post-7796","post","type-post","status-publish","format-standard","hentry","category-segunda-evaluacion-termino-2-2019-2020"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/7796","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=7796"}],"version-history":[{"count":15,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/7796\/revisions"}],"predecessor-version":[{"id":7811,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/7796\/revisions\/7811"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/media?parent=7796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/categories?post=7796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/tags?post=7796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}