{"id":6742,"date":"2019-07-08T08:11:11","date_gmt":"2019-07-08T13:11:11","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=6742"},"modified":"2019-07-08T08:11:11","modified_gmt":"2019-07-08T13:11:11","slug":"2019-2020-termino-1-e1-tema-4","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-1-e1-tema-4\/","title":{"rendered":"Tema 4"},"content":{"rendered":"
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\r\n Examen | 2019-2020 | T\u00e9rmino 1 | Primera Evaluaci\u00f3n | Tema 4\r\n <\/div>\r\n <\/div>\n
\n

Se sabe que W=(\\mathbb{R}^2,+,\\cdot)<\/span> y V=(\\mathbb{R}^2,\\oplus,\\odot)<\/span> son espacios vectoriales reales siendo +<\/span> y \\cdot<\/span> las operaciones usuales en \\mathbb{R}^2<\/span>; adem\u00e1s, \\oplus<\/span> y \\odot<\/span> las operaciones definidas por\\begin{pmatrix} a\\\\b \\end{pmatrix} \\oplus \\begin{pmatrix} c\\\\d \\end{pmatrix}=\\begin{pmatrix} a+c+1\\\\b+d \\end{pmatrix}\\qquad \\alpha\\odot \\begin{pmatrix} a\\\\b \\end{pmatrix}=\\begin{pmatrix} \\alpha a + \\alpha -1\\\\\\alpha b \\end{pmatrix}<\/span>Bajo estas condiciones, se define la funci\u00f3n T:V\\longrightarrow W<\/span>, definida por T\\begin{pmatrix} a\\\\b \\end{pmatrix}=\\begin{pmatrix} a\\\\b \\end{pmatrix}<\/span>.<\/p>\n\n\n\n\n\n\n\n
a.<\/td>\nDetermine T\\begin{pmatrix} \\begin{pmatrix} 1\\\\1 \\end{pmatrix} \\oplus \\begin{pmatrix} -1\\\\-1 \\end{pmatrix} \\end{pmatrix}<\/span>, T\\begin{pmatrix} 1\\\\1 \\end{pmatrix}+T\\begin{pmatrix} -1\\\\-1 \\end{pmatrix}<\/span>.<\/td>\n<\/tr>\n
b.<\/td>\nDetermine T\\begin{pmatrix} \\alpha \\odot \\begin{pmatrix} a\\\\b \\end{pmatrix} \\end{pmatrix}<\/span> y \\alpha \\cdot T\\begin{pmatrix} a\\\\b \\end{pmatrix}<\/span>, si \\begin{pmatrix} a\\\\b \\end{pmatrix} \\in V<\/span> y \\alpha \\in \\mathbb{R}<\/span>.<\/td>\n<\/tr>\n
c.<\/td>\n\u00bfCu\u00e1l es el elemento neutro de la adici\u00f3n en V<\/span>?<\/td>\n<\/tr>\n
d.<\/td>\nSi \\textbf{0}_{V}<\/span> es el elemento neutro de V<\/span>. \u00bfT(\\textbf{0}_{V})<\/span> es igual al elemento neutro de W<\/span>?<\/td>\n
e.<\/td>\n\u00bfT<\/span> es una transformaci\u00f3n lineal?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Se sabe que y son espacios vectoriales reales siendo y las operaciones usuales en ; adem\u00e1s, y las operaciones definidas porBajo estas condiciones, se define la funci\u00f3n , definida por . a. Determine , . b. Determine y , si y . c. \u00bfCu\u00e1l es el elemento neutro de la adici\u00f3n en ? d. Si … Sigue leyendo Tema 4<\/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":[1430162],"tags":[],"class_list":["post-6742","post","type-post","status-publish","format-standard","hentry","category-primera-evaluacion-termino-1-2019-2020"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/6742","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=6742"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/6742\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=6742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=6742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=6742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}