{"id":3846,"date":"2018-04-09T12:03:31","date_gmt":"2018-04-09T17:03:31","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=3846"},"modified":"2018-04-09T12:17:19","modified_gmt":"2018-04-09T17:17:19","slug":"2017-2018-termino-2-e3-tema-4","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1003\/2017-2018-termino-2-e3-tema-4\/","title":{"rendered":"Tema 4"},"content":{"rendered":"<div class='dropshadowboxes-container ' style='width:auto;'>\r\n                            <div class='dropshadowboxes-drop-shadow dropshadowboxes-rounded-corners dropshadowboxes-inside-and-outside-shadow dropshadowboxes-lifted-bottom-left dropshadowboxes-effect-default' style=' border: 1px solid #dddddd; height:; background-color:#ffffff;    '>\r\n                            Examen | 2017-2018 | T\u00e9rmino 2 | Tercera Evaluaci\u00f3n | Tema 4\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">Considere <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{P}_3<\/span>, el espacio vectorial de todos los polinomios de grado menor o igual a <span class=\"wp-katex-eq\" data-display=\"false\">3<\/span>, con el producto interno definido por:<span class=\"wp-katex-eq katex-display\" data-display=\"true\">\\footnotesize{\\langle a_0+a_1x+a_2x^2+a_3x^3,b_0+b_1x+b_2x^2+b_3x^3 \\rangle=a_3b_3+2a_2b_2+4a_1b_1+a_0b_0}<\/span>Considere adem\u00e1s la transformaci\u00f3n <span class=\"wp-katex-eq\" data-display=\"false\">T:\\mathbb{P}_3 \\longrightarrow \\mathbb{P}_3<\/span> definida por <span class=\"wp-katex-eq\" data-display=\"false\">T(p)=p(-1)+p(0)x^2<\/span>.<\/p>\n<p style=\"text-align: justify\">a. Determine una base para la imagen de <span class=\"wp-katex-eq\" data-display=\"false\">T<\/span>.<\/p>\n<p style=\"text-align: justify\">b. Determine una base para el complemento ortogonal del n\u00facleo de la transformaci\u00f3n lineal <span class=\"wp-katex-eq\" data-display=\"false\">T<\/span>.<\/p>\n<p style=\"text-align: justify\">c. Encuentre la proyecci\u00f3n ortogonal de <span class=\"wp-katex-eq\" data-display=\"false\">r(x)=3x^3+2x^2+x+1<\/span> sobre el n\u00facleo de <span class=\"wp-katex-eq\" data-display=\"false\">T<\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Considere , el espacio vectorial de todos los polinomios de grado menor o igual a , con el producto interno definido por:Considere adem\u00e1s la transformaci\u00f3n definida por . a. Determine una base para la imagen de . b. Determine una base para el complemento ortogonal del n\u00facleo de la transformaci\u00f3n lineal . c. Encuentre la &hellip; <a href=\"https:\/\/blog.espol.edu.ec\/matg1003\/2017-2018-termino-2-e3-tema-4\/\" class=\"more-link\">Sigue leyendo <span class=\"screen-reader-text\">Tema 4<\/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":[1416679],"tags":[],"class_list":["post-3846","post","type-post","status-publish","format-standard","hentry","category-tercera-evaluacion-termino-2"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3846","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=3846"}],"version-history":[{"count":14,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3846\/revisions"}],"predecessor-version":[{"id":3860,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3846\/revisions\/3860"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/media?parent=3846"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/categories?post=3846"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/tags?post=3846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}