{"id":7336,"date":"2019-09-18T22:07:33","date_gmt":"2019-09-19T03:07:33","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=7336"},"modified":"2019-09-18T22:07:33","modified_gmt":"2019-09-19T03:07:33","slug":"2019-2020-termino-1-e3-tema-3","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-1-e3-tema-3\/","title":{"rendered":"Tema 3"},"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 | Tercera Evaluaci\u00f3n | Tema 3\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">Sea <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> una matriz cuadrada de orden <span class=\"wp-katex-eq\" data-display=\"false\">3<\/span>, con entradas reales y cuyos subespacios propios son <span class=\"wp-katex-eq\" data-display=\"false\">E_{\\lambda_1}=\\{ (x,y,z)\\in \\mathbb{R}^3 \\ :\\ x+y=0\\ ,\\ z=0 \\}<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">E_{\\lambda_2}=\\{ (x,y,z)\\in \\mathbb{R}^3 \\ :\\ x-y-2z=0 \\}<\/span>. Determine:<\/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=\"95%\">Una base para <span class=\"wp-katex-eq\" data-display=\"false\">E_{\\lambda_1}<\/span>.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">b.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"95%\">Una base para <span class=\"wp-katex-eq\" data-display=\"false\">E_{\\lambda_2}<\/span>.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">c.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"95%\">Si la matriz <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> es diagonalizable.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">d.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"95%\">Si la matriz <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> es diagonalizable ortogonalmente.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"5%\">e.<\/td>\n<td style=\"text-align: justify;border: none\" width=\"95%\">El complemento ortogonal de <span class=\"wp-katex-eq\" data-display=\"false\">E_{\\lambda_2}<\/span>, considerando en <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}^3<\/span> el producto interno can\u00f3nico.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Sea una matriz cuadrada de orden , con entradas reales y cuyos subespacios propios son y . Determine: a. Una base para . b. Una base para . c. Si la matriz es diagonalizable. d. Si la matriz es diagonalizable ortogonalmente. e. El complemento ortogonal de , considerando en el producto interno can\u00f3nico.<\/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":[1430164],"tags":[],"class_list":["post-7336","post","type-post","status-publish","format-standard","hentry","category-tercera-evaluacion-termino-1-2019-2020"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/7336","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=7336"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/7336\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=7336"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=7336"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=7336"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}