{"id":7865,"date":"2020-02-19T00:04:50","date_gmt":"2020-02-19T05:04:50","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=7865"},"modified":"2020-02-19T00:04:50","modified_gmt":"2020-02-19T05:04:50","slug":"2019-2020-termino-2-e3-tema-3","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-2-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 2 | 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 tres con entradas reales y cuyos subespacios propios son<span class=\"wp-katex-eq katex-display\" data-display=\"true\">\\begin{aligned} E_{\\lambda_1}&amp;=\\begin{Bmatrix}  \\begin{pmatrix} x\\\\y\\\\z \\end{pmatrix} \\in \\mathbb{R}^3 \\ : \\ \\begin{aligned} x-y+z&amp;=0 \\end{aligned} \\end{Bmatrix}\\\\ \\\\ E_{\\lambda_2}&amp;=\\begin{Bmatrix}  \\begin{pmatrix} x\\\\y\\\\z \\end{pmatrix} \\in \\mathbb{R}^3 \\ : \\ \\begin{aligned} -x-y+z&amp;=0 \\\\ -2y&amp;=0\\end{aligned} \\end{Bmatrix}\\end{aligned}<\/span>Determine:<\/p>\n<table style=\"border: none\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"6%\">a)<\/td>\n<td style=\"text-align: justify;border: none\" width=\"94%\">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\">b)<\/td>\n<td style=\"text-align: justify;border: none\">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\">c)<\/td>\n<td style=\"text-align: justify;border: none\">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\">d)<\/td>\n<td style=\"text-align: justify;border: none\">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\">e)<\/td>\n<td style=\"text-align: justify;border: none\">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 tres con entradas reales y cuyos subespacios propios sonDetermine: 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":[1430170],"tags":[],"class_list":["post-7865","post","type-post","status-publish","format-standard","hentry","category-tercera-evaluacion-termino-2-2019-2020"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/7865","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=7865"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/7865\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=7865"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=7865"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=7865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}