{"id":3763,"date":"2018-04-06T09:44:26","date_gmt":"2018-04-06T14:44:26","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=3763"},"modified":"2018-04-06T10:12:58","modified_gmt":"2018-04-06T15:12:58","slug":"2017-2018-termino-2-e2-tema-3","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1003\/2017-2018-termino-2-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 | 2017-2018 | T\u00e9rmino 2 | Segunda Evaluaci\u00f3n | Tema 3\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">En el espacio de la matrices de entradas reales y orden <span class=\"wp-katex-eq\" data-display=\"false\">2<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">M_{2\\times 2}(\\mathbb{R})<\/span>, se define el producto interno <span class=\"wp-katex-eq\" data-display=\"false\">\\langle A,B \\rangle = Tr(B^T A)<\/span>. Sea <span class=\"wp-katex-eq\" data-display=\"false\">H=\\{A\\in M_{2\\times 2}(\\mathbb{R})\\;:\\;Tr(A)=0\\}<\/span>.<\/p>\n<p style=\"text-align: justify\">a. Sean <span class=\"wp-katex-eq\" data-display=\"false\">A=\\small{\\begin{pmatrix}k-2 &amp; 0\\\\ 1 &amp; s+2\\end{pmatrix}}<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">B=\\small{\\begin{pmatrix}2 &amp; 10\\\\ 0 &amp; -2\\end{pmatrix}}<\/span><span class=\"wp-katex-eq\" data-display=\"false\">\\in H<\/span>. Determine, de ser posible, los valores de <span class=\"wp-katex-eq\" data-display=\"false\">s<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">k<\/span> para que <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> sean matrices ortogonales.<\/p>\n<p style=\"text-align: justify\">b. Encuentre <span class=\"wp-katex-eq\" data-display=\"false\">H^{\\perp}<\/span>.<\/p>\n<p style=\"text-align: justify\">c. Encuentre la proyecci\u00f3n de <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> sobre <span class=\"wp-katex-eq\" data-display=\"false\">H^{\\perp}<\/span>, es decir, <span class=\"wp-katex-eq\" data-display=\"false\">Proy_{H^{\\perp}}B<\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>En el espacio de la matrices de entradas reales y orden , , se define el producto interno . Sea . a. Sean y . Determine, de ser posible, los valores de y para que y sean matrices ortogonales. b. Encuentre . c. Encuentre la proyecci\u00f3n de sobre , es decir, .<\/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":[1416678],"tags":[],"class_list":["post-3763","post","type-post","status-publish","format-standard","hentry","category-segunda-evaluacion-termino-2"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3763","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/users\/609"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/comments?post=3763"}],"version-history":[{"count":26,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3763\/revisions"}],"predecessor-version":[{"id":3789,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3763\/revisions\/3789"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/media?parent=3763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/categories?post=3763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/tags?post=3763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}