{"id":4031,"date":"2018-04-13T09:48:25","date_gmt":"2018-04-13T14:48:25","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=4031"},"modified":"2018-04-13T09:48:25","modified_gmt":"2018-04-13T14:48:25","slug":"2016-2017-termino-1-e3-tema-2","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2016-2017-termino-1-e3-tema-2\/","title":{"rendered":"Tema 2"},"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 | 2016-2017 | T\u00e9rmino 1 | Tercera Evaluaci\u00f3n | Tema 2\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">Sea el espacio vectorial de las matrices <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{M}_{3\\times 3}<\/span> se define la matriz <span class=\"wp-katex-eq\" data-display=\"false\">M<\/span> como sigue<span class=\"wp-katex-eq katex-display\" data-display=\"true\">M=\\begin{pmatrix}3&amp;2&amp;0\\\\2&amp;3&amp;0\\\\0&amp;0&amp;3 \\end{pmatrix}<\/span><\/p>\n<p style=\"text-align: justify\">a. Determine el valor de <span class=\"wp-katex-eq\" data-display=\"false\">\\alpha<\/span> para que la matriz<span class=\"wp-katex-eq katex-display\" data-display=\"true\">A=\\begin{pmatrix}13&amp;12&amp;0\\\\12&amp;13&amp;0\\\\0&amp;0&amp;\\alpha \\end{pmatrix}<\/span>pertenezca al subespacio generado por <span class=\"wp-katex-eq\" data-display=\"false\">M<\/span> e <span class=\"wp-katex-eq\" data-display=\"false\">I<\/span>.<br \/>\n<b>Nota:<\/b> <span class=\"wp-katex-eq\" data-display=\"false\">I<\/span> denota la matriz identidad.<\/p>\n<p style=\"text-align: justify\">b. Se define el subconjunto <span class=\"wp-katex-eq\" data-display=\"false\">E<\/span> de <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{M}_{3\\times 3}<\/span> como <span class=\"wp-katex-eq\" data-display=\"false\">E=\\footnotesize{\\{ aI+bM+cM^2\\; ; \\; a,b,c\\in \\mathbb{R} \\}}<\/span>. Demuestre que <span class=\"wp-katex-eq\" data-display=\"false\">E<\/span> es un subespacio vectorial.<\/p>\n<p style=\"text-align: justify\">c. \u00bfCu\u00e1l es la dimensi\u00f3n de <span class=\"wp-katex-eq\" data-display=\"false\">E<\/span>?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sea el espacio vectorial de las matrices se define la matriz como sigue a. Determine el valor de para que la matrizpertenezca al subespacio generado por e . Nota: denota la matriz identidad. b. Se define el subconjunto de como . Demuestre que es un subespacio vectorial. c. \u00bfCu\u00e1l es la dimensi\u00f3n de ?<\/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":[1416684],"tags":[],"class_list":["post-4031","post","type-post","status-publish","format-standard","hentry","category-tercera-evaluacion-termino-1"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/4031","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=4031"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/4031\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=4031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=4031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=4031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}