{"id":6949,"date":"2019-09-06T14:20:37","date_gmt":"2019-09-06T19:20:37","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=6949"},"modified":"2019-09-06T14:20:37","modified_gmt":"2019-09-06T19:20:37","slug":"2019-2020-termino-1-e2-tema-1","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-1-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 | 2019-2020 | T\u00e9rmino 1 | Segunda Evaluaci\u00f3n | Tema 1\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">A continuaci\u00f3n encontrar\u00e1 cinco afirmaciones. Indique, rellenando el c\u00edrculo correspondiente, si la proposici\u00f3n es verdadera o falsa y en cada caso demuestre si la proposici\u00f3n es verdadera o construya un contraejemplo si la proposici\u00f3n es falsa.<\/p>\n<table style=\"border: none\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">a.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"81%\">Si <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> son matrices con los mismos valores propios y las mismas multiplicidades, entonces <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> son semejantes.<\/td>\n<td style=\"text-align: center;border: none\" width=\"2%\"><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">V<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">F<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border: none\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">b.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"81%\">Sea <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span> un espacio vectorial definido sobre un campo <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{K}<\/span>, con producto interno <span class=\"wp-katex-eq\" data-display=\"false\">\\langle \\cdot|\\cdot \\rangle<\/span>. Si <span class=\"wp-katex-eq\" data-display=\"false\">S=\\{ v_1,v_2,v_3 \\}<\/span> es un conjunto ortogonal, formado por vectores no nulos, entonces <span class=\"wp-katex-eq\" data-display=\"false\">S<\/span> es un conjunto linealmente independiente.<\/td>\n<td style=\"text-align: center;border: none\" width=\"2%\"><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">V<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">F<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border: none\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">c.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"81%\">Si <span class=\"wp-katex-eq\" data-display=\"false\">T:V \\longrightarrow W<\/span> es una transformaci\u00f3n lineal, <span class=\"wp-katex-eq\" data-display=\"false\">U<\/span> un subespacio de W, entonces <span class=\"wp-katex-eq\" data-display=\"false\">H=\\{ v\\in V : T(v) \\in U \\}<\/span> es un subespacio de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>.<\/td>\n<td style=\"text-align: center;border: none\" width=\"2%\"><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">V<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">F<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border: none\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">d.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"81%\">Si <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> es una matriz cuadrada de orden <span class=\"wp-katex-eq\" data-display=\"false\">n<\/span>, entonces <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> es diagonalizable si y s\u00f3lo si es sim\u00e9trica.<\/td>\n<td style=\"text-align: center;border: none\" width=\"2%\"><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">V<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">F<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border: none\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">e.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"81%\">Haciendo uso de formas cuadr\u00e1ticas, se puede verificar que <span class=\"wp-katex-eq\" data-display=\"false\">x^2+4xy+y^2=9<\/span> corresponde a la ecuaci\u00f3n de una elipse en el plano.<\/td>\n<td style=\"text-align: center;border: none\" width=\"2%\"><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">V<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<td style=\"text-align: center;border: none\" width=\"6%\">F<br \/>\n<span class=\"wp-katex-eq\" data-display=\"false\">\\bigcirc<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>A continuaci\u00f3n encontrar\u00e1 cinco afirmaciones. Indique, rellenando el c\u00edrculo correspondiente, si la proposici\u00f3n es verdadera o falsa y en cada caso demuestre si la proposici\u00f3n es verdadera o construya un contraejemplo si la proposici\u00f3n es falsa. a. Si y son matrices con los mismos valores propios y las mismas multiplicidades, entonces y son semejantes. V &hellip; <a href=\"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-1-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":[1430163],"tags":[],"class_list":["post-6949","post","type-post","status-publish","format-standard","hentry","category-segunda-evaluacion-termino-1-2019-2020"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/6949","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=6949"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/6949\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=6949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=6949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=6949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}