{"id":6993,"date":"2019-09-07T11:30:49","date_gmt":"2019-09-07T16:30:49","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=6993"},"modified":"2019-09-07T11:30:49","modified_gmt":"2019-09-07T16:30:49","slug":"2019-2020-termino-1-e2-tema-3","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-1-e2-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 | Segunda 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\">V<\/span> el espacio vectorial real de todas las matrices cuadradas de orden <span class=\"wp-katex-eq\" data-display=\"false\">2<\/span>, con las operaciones usuales. Se define, en <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>, el producto interno <span class=\"wp-katex-eq\" data-display=\"false\">\\langle A|B \\rangle=tr(B^T A)<\/span> (esto es, la traza del producto entre la transpuesta de la matriz <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> y la matriz <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span>). Considerando el subespacio <span class=\"wp-katex-eq katex-display\" data-display=\"true\">H=\\begin{Bmatrix} \\begin{pmatrix} \\begin{array}{cc} a&amp;b\\\\b&amp;c \\end{array}\\end{pmatrix} : a+c=0 \\, , \\, \\forall a,b,c\\in \\mathbb{R} \\end{Bmatrix}<\/span>de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/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 ortonormal para <span class=\"wp-katex-eq\" data-display=\"false\">H<\/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%\">El complemento ortogonal de <span class=\"wp-katex-eq\" data-display=\"false\">H<\/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%\">La proyecci\u00f3n del vector <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{pmatrix} \\begin{array}{rr} 1&amp;2\\\\2&amp;-1 \\end{array} \\end{pmatrix}<\/span> sobre <span class=\"wp-katex-eq\" data-display=\"false\">H<\/span>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Sea el espacio vectorial real de todas las matrices cuadradas de orden , con las operaciones usuales. Se define, en , el producto interno (esto es, la traza del producto entre la transpuesta de la matriz y la matriz ). Considerando el subespacio de , determine: a. Una base ortonormal para . b. El complemento &hellip; <a href=\"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-1-e2-tema-3\/\" class=\"more-link\">Sigue leyendo <span class=\"screen-reader-text\">Tema 3<\/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-6993","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\/6993","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=6993"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/6993\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=6993"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=6993"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=6993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}