{"id":3390,"date":"2017-12-01T01:02:11","date_gmt":"2017-12-01T06:02:11","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=3390"},"modified":"2017-12-01T01:22:28","modified_gmt":"2017-12-01T06:22:28","slug":"2017-2018-termino-2-e1-tema-5","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1003\/2017-2018-termino-2-e1-tema-5\/","title":{"rendered":"Tema 5"},"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 5\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\"><span class=\"wp-katex-eq\" data-display=\"false\">V=\\left\\{\\left(\\begin{array}{rr} a &amp; b \\\\ c &amp; 0 \\end{array}\\right):\\ a\\in \\mathbb{R}^+\\ \\wedge\\ b,c \\in \\mathbb{R} \\right\\}<\/span> es un espacio vectorial sobre <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}<\/span>, con las siguientes operaciones:<span class=\"wp-katex-eq katex-display\" data-display=\"true\">\\begin{aligned}\\begin{pmatrix}a_1 &amp; b_1 \\\\ c_1 &amp; 0\\end{pmatrix}\\oplus \\begin{pmatrix} a_2 &amp; b_2 \\\\ c_2 &amp; 0\\end{pmatrix} &amp;= \\begin{pmatrix} a_1a_2 &amp; b_1+b_2+7 \\\\ c_1+c_2 &amp; 0 \\end{pmatrix} \\\\  \\\\ \\alpha \\odot \\begin{pmatrix} a &amp; b \\\\ c &amp; 0\\end{pmatrix} &amp;= \\begin{pmatrix} a^{\\alpha} &amp; \\alpha b+7\\alpha-7 \\\\ \\alpha c &amp; 0 \\end{pmatrix} \\end{aligned}<\/span>Determine:<\/p>\n<p style=\"text-align: justify\">a. El vector nulo de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>.<\/p>\n<p style=\"text-align: justify\">b. El vector opuesto de un elemento <span class=\"wp-katex-eq\" data-display=\"false\">\\left(\\begin{array}{rr}a &amp; b \\\\ c &amp; 0 \\end{array}\\right)<\/span> de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span>.<\/p>\n<p style=\"text-align: justify\">c. Los valores de <span class=\"wp-katex-eq\" data-display=\"false\">a<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">x<\/span> tal que <span class=\"wp-katex-eq\" data-display=\"false\">\\left(\\begin{array}{rr}a &amp; 2 \\\\ 1 &amp; 0 \\end{array}\\right)<\/span> sea una combinaci\u00f3n lineal de los vectores <span class=\"wp-katex-eq\" data-display=\"false\">\\left(\\begin{array}{rr}1 &amp; 0 \\\\ x &amp; 0 \\end{array}\\right)<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">\\left(\\begin{array}{rr}1 &amp; 1 \\\\ 3x &amp; 0 \\end{array}\\right)<\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>es un espacio vectorial sobre , con las siguientes operaciones:Determine: a. El vector nulo de . b. El vector opuesto de un elemento de . c. Los valores de y tal que sea una combinaci\u00f3n lineal de los vectores y .<\/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-3390","post","type-post","status-publish","format-standard","hentry","category-primera-evaluacion-termino-2"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3390","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=3390"}],"version-history":[{"count":12,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3390\/revisions"}],"predecessor-version":[{"id":3403,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/posts\/3390\/revisions\/3403"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/media?parent=3390"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/categories?post=3390"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1003\/wp-json\/wp\/v2\/tags?post=3390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}