{"id":4127,"date":"2018-04-18T12:00:00","date_gmt":"2018-04-18T17:00:00","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=4127"},"modified":"2018-04-18T12:00:00","modified_gmt":"2018-04-18T17:00:00","slug":"2016-2017-termino-2-e2-tema-1","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2016-2017-termino-2-e2-tema-1\/","title":{"rendered":"Tema 1"},"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 | 2016-2017 | T\u00e9rmino 2 | Segunda Evaluaci\u00f3n | Tema 1\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">Califique las siguientes proposiciones como verdaderas o falsas, justifique su respuesta. Puede escribir un contraejemplo si considera que la proposici\u00f3n es falsa.<\/p>\n<p style=\"text-align: justify\">a. Si <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> es una matriz de tama\u00f1o <span class=\"wp-katex-eq\" data-display=\"false\">n\\times n<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">u<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">v<\/span> son vectores de <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}^n<\/span>, entonces se cumple que <span class=\"wp-katex-eq\" data-display=\"false\">\\langle Av,u \\rangle=\\langle v,A^T u \\rangle<\/span>.<br \/>\n<b>Nota:<\/b> <span class=\"wp-katex-eq\" data-display=\"false\">\\langle u,v \\rangle<\/span> representa el producto interno.<\/p>\n<p style=\"text-align: justify\">b. Sea <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span> un espacio vectorial y <span class=\"wp-katex-eq\" data-display=\"false\">T<\/span> un operador lineal definido sobre <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>, entonces se cumple que <span class=\"wp-katex-eq\" data-display=\"false\">Nu(T^2) \\subseteq Nu(T)<\/span>.<\/p>\n<p style=\"text-align: justify\">c. Sea <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> matrices semejantes, entonces las matrices <span class=\"wp-katex-eq\" data-display=\"false\">A^T<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">B^T<\/span> tambi\u00e9n lo son.<\/p>\n<p style=\"text-align: justify\">d. Sea <span class=\"wp-katex-eq\" data-display=\"false\">T:V\\longrightarrow W<\/span> una transformaci\u00f3n lineal. Si <span class=\"wp-katex-eq\" data-display=\"false\">\\{v_1,v_2,...,v_n\\}<\/span> es un conjunto linealmente independiente en <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>, entonces el conjunto <span class=\"wp-katex-eq\" data-display=\"false\">\\{T(v_1),T(v_2),...,T(v_n)\\}<\/span> es linealmente independiente en <span class=\"wp-katex-eq\" data-display=\"false\">W<\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Califique las siguientes proposiciones como verdaderas o falsas, justifique su respuesta. Puede escribir un contraejemplo si considera que la proposici\u00f3n es falsa. a. Si es una matriz de tama\u00f1o , y son vectores de , entonces se cumple que . Nota: representa el producto interno. b. Sea un espacio vectorial y un operador lineal definido &hellip; <a href=\"https:\/\/blog.espol.edu.ec\/matg1049\/2016-2017-termino-2-e2-tema-1\/\" class=\"more-link\">Sigue leyendo <span class=\"screen-reader-text\">Tema 1<\/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":[1416687],"tags":[],"class_list":["post-4127","post","type-post","status-publish","format-standard","hentry","category-segunda-evaluacion-termino-2-2016-2017"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/4127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/users\/609"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/comments?post=4127"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/4127\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=4127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=4127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=4127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}