{"id":3323,"date":"2017-11-30T21:42:04","date_gmt":"2017-12-01T02:42:04","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=3323"},"modified":"2017-11-30T21:42:04","modified_gmt":"2017-12-01T02:42:04","slug":"2017-2018-termino-2-e1-tema-1","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2017-2018-termino-2-e1-tema-1\/","title":{"rendered":"Tema 1"},"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 | Primera Evaluaci\u00f3n | Tema 1\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">Califique, justificando cada respuesta, como verdadero o falso las siguientes proposiciones.<\/p>\n<p style=\"text-align: justify\">a. El conjunto soluci\u00f3n del sistema <span class=\"wp-katex-eq\" data-display=\"false\">\\left\\{\\begin{array}{c} x_1+x_2=1 \\\\ x_3+x_4=0 \\end{array}\\right.<\/span> es un subespacio vectorial de <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}^4<\/span>.<\/p>\n<p style=\"text-align: justify\">b. Sean <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span> un espacio vectorial sobre un campo <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{K}<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">W<\/span> un subespacio de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>. Si <span class=\"wp-katex-eq\" data-display=\"false\">v\\notin W<\/span> entonces, <span class=\"wp-katex-eq\" data-display=\"false\">v+w \\notin W<\/span> para cada <span class=\"wp-katex-eq\" data-display=\"false\">w<\/span> de <span class=\"wp-katex-eq\" data-display=\"false\">W<\/span>.<\/p>\n<p style=\"text-align: justify\">c. Sean <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span> un espacio vectorial sobre un campo <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{K}<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> subconjuntos de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>. Entonces <span class=\"wp-katex-eq\" data-display=\"false\">Gen(A\\cap B)=Gen(A) \\cap Gen(B)<\/span>.<\/p>\n<p style=\"text-align: justify\">d. Si <span class=\"wp-katex-eq\" data-display=\"false\">\\{u,v\\}<\/span> es un conjunto linealmente independiente de un espacio vectorial <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>, entonces <span class=\"wp-katex-eq\" data-display=\"false\">\\{u+v,u+w,v+w\\}<\/span> es un conjunto linealmente independiente para todo vector no nulo <span class=\"wp-katex-eq\" data-display=\"false\">w<\/span> de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>.<\/p>\n<p style=\"text-align: justify\">e. Sea <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> una matriz cuadrada. Si el espacio columna de <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> es igual al espacio rengl\u00f3n de <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span>, entonces <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> es una matriz sim\u00e9trica.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Califique, justificando cada respuesta, como verdadero o falso las siguientes proposiciones. a. El conjunto soluci\u00f3n del sistema es un subespacio vectorial de . b. Sean un espacio vectorial sobre un campo y un subespacio de . Si entonces, para cada de . c. Sean un espacio vectorial sobre un campo , y subconjuntos de . &hellip; <a href=\"https:\/\/blog.espol.edu.ec\/matg1049\/2017-2018-termino-2-e1-tema-1\/\" class=\"more-link\">Sigue leyendo <span class=\"screen-reader-text\">Tema 1<\/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":[1416677],"tags":[],"class_list":["post-3323","post","type-post","status-publish","format-standard","hentry","category-primera-evaluacion-termino-2"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/3323","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=3323"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/3323\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=3323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=3323"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=3323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}