{"id":84,"date":"2018-03-15T14:37:59","date_gmt":"2018-03-15T17:37:59","guid":{"rendered":"http:\/\/www.professores.uff.br\/renatadefreitas\/?page_id=84"},"modified":"2018-03-15T14:49:39","modified_gmt":"2018-03-15T17:49:39","slug":"gan-00007-introducao-a-algebra-linear-2016-1","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/renatadefreitas\/gan-00007-introducao-a-algebra-linear-2016-1\/","title":{"rendered":"GAN 00007 &#8211; Introdu\u00e7\u00e3o \u00e0 \u00c1lgebra Linear, 2016-1"},"content":{"rendered":"<p><strong>Info<\/strong><\/p>\n<p>Turma A1, ter\u00e7as e quintas, 16h-18h, sala H-201 Gragoat\u00e1<br \/>\nCurso: Estat\u00edstica<br \/>\nProfa. Renata de Freitas<\/p>\n<p><strong>Calend\u00e1rio:<\/strong><\/p>\n<p>27 de abril &#8211; <a href=\"https:\/\/dl.dropboxusercontent.com\/u\/55173600\/IC-Seminarios\/ic-seminarios.html\">Encontro de IC<\/a><\/p>\n<p>30 de maio &#8211; A Quarta Dimens\u00e3o &#8211; Aula Inaugural de 2016-1<\/p>\n<p>Folga<\/p>\n<p>26 de maio &#8211; Corpus Christi<br \/>\n11 de julho, segunda, 9-11h e 11-13h &#8211; Aula extra (sala G 304)<\/p>\n<p>Verifica\u00e7\u00f5es da aprendizagem:<\/p>\n<p>02 de junho &#8211; V1<br \/>\n12 de julho &#8211; V2<br \/>\n19 de julho &#8211; 2a chamada<br \/>\n26 de julho &#8211; VS<br \/>\nA vista de prova da VS ser\u00e1 no dia 28 de julho, quinta, \u00e0s 16h, no GAN (IME, Campus do Valonguinho, 4o. andar).<\/p>\n<p>Resultados:<a href=\"https:\/\/dl.dropboxusercontent.com\/u\/55537685\/2016-1_IntAlgLin_resultados.html\"> V1 e V2<\/a>,<a href=\"https:\/\/dl.dropboxusercontent.com\/u\/55537685\/2016-1_IntAlgLin_notas.txt\"> m\u00e9dias<\/a> (notas lan\u00e7adas no IdUFF).<\/p>\n<hr \/>\n<p><strong>Monitoria<\/strong><br \/>\nReiner dos Santos Filho (reinerhenrique41 @ gmail.com)<br \/>\nSala 506, Bl. G, Campus do Gragoat\u00e1<br \/>\nSegundas &#8211; 13h-15h30min, ter\u00e7as &#8211; 11h30min-15h30min, sextas &#8211; 08h-10h30min<\/p>\n<hr \/>\n<p><strong>Refer\u00eancias<\/strong><\/p>\n<p>H. Anton, C. Rorres, \u00c1lgebra Linear com Aplica\u00e7\u00f5es, d\u00e9cima edi\u00e7\u00e3o, Bookman, 2012. *** livro-texto ***<\/p>\n<p>J. L. Boldrini et al., \u00c1lgebra Linear, Harbra, 1978.<\/p>\n<p>C. A. Callioli, H. Domingues, R. C. F. Costa, \u00c1lgebra Linear e Aplica\u00e7\u00f5es, Atual, 1993.<\/p>\n<p>J. Colombo, J. Koiller, \u00c1lgebra Linear (texto em prepara\u00e7\u00e3o), GAN\/IME-UFF, 2014: <a href=\"http:\/\/w3.impa.br\/~koiller\/NotasAlgLinear\">NotasColomboKoiller_EM_PREPARACAO.pdf.<\/a><\/p>\n<p>*** Para cada erro encontrado no texto Colombo-Koiller, o primeiro aluno que reportar o erro para o email freitas @ vm.uff.br ganha 0,1 ponto na nota da primeira prova. ***<\/p>\n<p>A. Hefez, C. Fernandez, Introdu\u00e7\u00e3o \u00e0 \u00c1lgebra Linear, SBM, 2012 (Cole\u00e7\u00e3o PROFMAT).<\/p>\n<p>E. L. Lima, \u00c1lgebra Linear, SBM, 1996 (Cole\u00e7\u00e3o Matem\u00e1tica Universit\u00e1ria).<\/p>\n<p>S. Lipschutz, M.L. Lipson, \u00c1lgebra Linear, quarta edi\u00e7\u00e3o, Bookman, 2011 (Cole\u00e7\u00e3o Schaum).<\/p>\n<p>D. Poole, \u00c1lgebra Linear, Pioneira Thomson Learning, 2004.<\/p>\n<p>M. L. Villela, \u00c1lgebra Linear I (manuscrito): <a href=\"https:\/\/dl.dropboxusercontent.com\/u\/55537685\/alglinear1-mod1.pdf\">M\u00f3dulo 1<\/a>, <a href=\"https:\/\/dl.dropboxusercontent.com\/u\/55537685\/alglinear1-mod2.pdf\">M\u00f3dulo 2<\/a>, <a href=\"https:\/\/dl.dropboxusercontent.com\/u\/55537685\/alglinear1-mod3.pdf\">M\u00f3dulo 3<\/a>, IME-UFF, 2010.<\/p>\n<hr \/>\n<p><strong>Exerc\u00edcios<\/strong><\/p>\n<p><strong>26\/4\/2016:<\/strong> Anton-Rorres: pp. 30-31 (8a ed.), pp. 9-10 (10a ed.).<\/p>\n<p><strong>28\/4\/2016:<\/strong> Anton-Rorres: pp. 37-41 (8a ed.), pp. 22-25 (10a ed.).<\/p>\n<p><strong>3\/5\/2016:<\/strong> Anton-Rorres &#8211; Se\u00e7\u00e3o 1.3: pp. 46-49 (8a ed.), Se\u00e7\u00e3o 1.4: pp. 54-56 (8a ed.).<\/p>\n<p><strong>Matrizes:<\/strong><\/p>\n<ul>\n<li>Hefez-Fernandez, Cap\u00edtulo 1, Exerc\u00edcios 2.1, 2.2, 2.3, 2.4, 2.6, 2.8, 2.9, 2.10, 2.12, 2.13, 2.14.<\/li>\n<li>Callioli-Domingues-Costa, Parte 1, Cap\u00edtulo 1, Se\u00e7\u00f5es 5 e 6 &#8211; Exerc\u00edcios Resolvidos e Exerc\u00edcios Propostos.<\/li>\n<\/ul>\n<p><strong>Escalonamento de matrizes e resolu\u00e7\u00e3o de sistemas:<\/strong><\/p>\n<ul>\n<li>Hefez-Fernandez, Cap\u00edtulo 2, Exerc\u00edcios 1.1 (a), 1.4 (a)(b)(c), 1.6, 2.1, 2.2, 2.8, 2.9.<\/li>\n<li>Callioli-Domingues-Costa, Parte 1, Cap\u00edtulo 1, Se\u00e7\u00f5es 1 a 4 &#8211; Exerc\u00edcios Resolvidos e Exerc\u00edcios Propostos.<\/li>\n<li>Villela, M\u00f3dulo 1 &#8211; Exerc\u00edcios 1, 3, 4 (pp. 34-36).<\/li>\n<li>Colombo-Koiller, Cap\u00edtulo 1 &#8211; Exerc\u00edcios Propostos (pp. 29-31).<br \/>\n<strong>5\/5\/2016:<\/strong> Anton-Rorres &#8211; Se\u00e7\u00e3o 1.5: pp. 59-61 (8a ed.), pp. 58-60 (10a ed.), Se\u00e7\u00e3o 1.6: pp. 64-66 (8a ed.), pp. 65-66 (10a ed.), Exerc\u00edcios suplementares do cap\u00edtulo 1: pp. 71-73 (8a ed.), pp. 91-92 (10a ed.).<\/li>\n<\/ul>\n<p><strong>Nota\u00e7\u00e3o matricial para sistemas lineares:<\/strong><\/p>\n<ul>\n<li>Hefez-Fernandez, Cap\u00edtulo 1, Exerc\u00edcio 2.15; Cap\u00edtulo 2, Exerc\u00edcios 2.3, 2.4, 2.5.<\/li>\n<li>Villela, M\u00f3dulo 1 &#8211; Exerc\u00edcio 2 (p. 35).<\/li>\n<\/ul>\n<p><strong>Matrizes elementares:<\/strong><\/p>\n<ul>\n<li>Hefez-Fernandez, Cap\u00edtulo 1, Exerc\u00edcio 1.9.<\/li>\n<\/ul>\n<p><strong>Inversas e determinantes:<\/strong><\/p>\n<ul>\n<li>Steinbruch-Winterle, Ap\u00eandice (Determinantes, Invers\u00e3o de matrizes) &#8211; Problemas Resolvidos e Problemas Propostos.<\/li>\n<li>Callioli-Domingues-Costa, Parte 1, Cap\u00edtulo 1, Se\u00e7\u00f5es 7 e 8 &#8211; Exerc\u00edcios Resolvidos e Exerc\u00edcios Propostos.<\/li>\n<li>Colombo-Koiller, Cap\u00edtulo 6 &#8211; Exerc\u00edcios Propostos (pp. 153-161).<\/li>\n<\/ul>\n<p><strong>17\/5\/2016:<\/strong> Anton-Rorres &#8211; pp. 188-191 (10a ed.), itens 1, 7, 8, 11, 12, 15, 18, 19, 20; <a href=\"http:\/\/www.professores.uff.br\/renatadefreitas\/wp-content\/uploads\/sites\/171\/2018\/03\/unnamed-file.pdf\">Exerc\u00edcio 1 do Simulado.<\/a><\/p>\n<p><strong>19\/5\/2016:<\/strong> Anton-Rorres &#8211; pp. 173-174 (8a ed.), itens 1(a), 1(b), 2, 3, 5-12, 14-18, 23(b), 23(c), 23(d), 24-26; Anton-Rorres &#8211; pp. 182-184 (8a ed.), itens 1(a), 1(b), 2, 3, 7-18, 20-22, 24, 25, 29, 34; <a href=\"http:\/\/www.professores.uff.br\/renatadefreitas\/wp-content\/uploads\/sites\/171\/2018\/03\/2016-1_AlgLin_S2.pdf\">Exerc\u00edcio 2 do Simulado.<\/a><\/p>\n<p><strong>24\/5\/2016:<\/strong><a href=\"http:\/\/www.professores.uff.br\/renatadefreitas\/wp-content\/uploads\/sites\/171\/2018\/03\/2016-1_AlgLin_S3.pdf\"> Exerc\u00edcio 3 do Simulado.<\/a><\/p>\n<p><strong>Combina\u00e7\u00e3o linear, depend\u00eancia e independ\u00eancia linear:<\/strong><\/p>\n<ul>\n<li>Hefez-Fernandez, Cap\u00edtulo 3, Exerc\u00edcios 1.1, 1.2, 1.3, 1.6, 1.8 at\u00e9 1.15, 2.2 at\u00e9 2.10.<\/li>\n<li>Villela, M\u00f3dulo 2 &#8211; Exerc\u00edcios pp. 55 e 56, itens 1,2,3,5,6,7,8,9,10,13.<\/li>\n<li>Callioli-Domingues-Costa, Parte 1, Cap\u00edtulo 3, Se\u00e7\u00e3o 1 &#8211; Exerc\u00edcios Resolvidos e Exerc\u00edcios Propostos.<\/li>\n<li>Colombo-Koiller, Cap\u00edtulo 2 e Cap\u00edtulo 3 (Se\u00e7\u00f5es 3.0, 3.1 e 3.3) &#8211; Exerc\u00edcios Propostos (pp. 58-64 e pp. 76-82).<\/li>\n<\/ul>\n<p><strong>Base de um espa\u00e7o vetorial:<\/strong><\/p>\n<ul>\n<li>Hefez-Fernandez, Cap\u00edtulo 3, Exerc\u00edcios 3.1, 3.3, 3.4, 3.5, 3.11, 3.13(a), 3.13(b), 3.14, 3.15, 3.16, 4.1, 4.2, 4.3, 4.4, 4.5.<\/li>\n<li>Villela, M\u00f3dulo 2 &#8211; Exerc\u00edcios pp. 63 e 64, itens 3,4,5,6,7,9,10; pp. 69 e 70, itens 1,2,3.<\/li>\n<li>Callioli-Domingues-Costa, Parte 1, Cap\u00edtulo 3, Se\u00e7\u00f5es 3, 4, 5 e 7 &#8211; Exerc\u00edcios Resolvidos e Exerc\u00edcios Propostos.<\/li>\n<li>Colombo-Koiller, Cap\u00edtulo 4 (Se\u00e7\u00f5es 4.2, 4.4 e 4.5) &#8211; Exerc\u00edcios Propostos (pp. 109-115).<\/li>\n<\/ul>\n<p><strong>14\/6\/2016:<\/strong> Anton-Rorres (8a ed.) &#8211; pp. 262-264, itens 1-34; pp. 267-268, itens 1-29; pp. 271-273, itens 1-25; pp. 277-280, itens 1-22; p. 287, itens 1, 5-8.<\/p>\n<p><strong>Transforma\u00e7\u00e3o linear, n\u00facleo, imagem:<\/strong><\/p>\n<ul>\n<li>Hefez-Fernandez, Cap\u00edtulos 5 e 6.<\/li>\n<li>Villela, M\u00f3dulo 3 &#8211; Exerc\u00edcios pp. 77 e 78, itens 1 a 7; pp. 84 a 86, itens 1 a 14; pp. 94 a 96, itens 1 a 15; pp. 104 a 106, itens 1 a 13.<\/li>\n<li>Callioli-Domingues-Costa, Parte 1, Cap\u00edtulo 4, Se\u00e7\u00f5es 1, 2 e 3; Cap\u00edtulo 5, Se\u00e7\u00e3o 2 &#8211; Exerc\u00edcios Resolvidos e Exerc\u00edcios Propostos.<\/li>\n<li>Colombo-Koiller, Cap\u00edtulo 5 &#8211; Exerc\u00edcios Propostos (pp. 138-139).<\/li>\n<\/ul>\n<p><strong>16\/6\/2016:<\/strong><\/p>\n<p>Considerando a correspond\u00eancia entre matrizes e transforma\u00e7\u00f5es lineares, dadas as matrizes A, B e C em cada item a seguir, explique a rela\u00e7\u00e3o entre as transforma\u00e7\u00f5es lineares associadas \u00e0s matrizes A e B com a transforma\u00e7\u00e3o linear associada \u00e0 matriz C.<\/p>\n<ol>\n<li>A=(aij) \u00e9 matriz de ordem 2&#215;3 tal que aij=i+j,<br \/>\nB=(bij) \u00e9 matriz de ordem 2&#215;3 tal que bij=1 se i+j \u00e9 par e bij=1 se i+j \u00e9 \u00edmpar,<br \/>\nC=A+B.<\/li>\n<li>A=(aij) \u00e9 matriz de ordem 2&#215;3 tal que aij=i+j,<br \/>\nB=(bij) \u00e9 matriz de ordem 3&#215;4 tal que bij=1 se i+j \u00e9 par e bij=1 se i+j \u00e9 \u00edmpar,<br \/>\nC=AB.<\/li>\n<li>A=(aij) \u00e9 matriz de ordem 2&#215;3 tal que aij=i+j,<br \/>\nC=7A.<\/li>\n<li>A=(aij) \u00e9 matriz de ordem 2&#215;2 tal que aij=i+j,<br \/>\nC \u00e9 a inversa de A.<\/li>\n<li>A=(aij) \u00e9 matriz de ordem 2&#215;2 tal que aij=i+j,<br \/>\nC=[detA].<\/li>\n<\/ol>\n<p><strong>21\/6\/2016:<\/strong> Anton-Rorres (8a ed.) &#8211; pp. 243-245, itens 1-23.<\/p>\n<p><strong>Auto-valores e auto-vetores:<\/strong><\/p>\n<ul>\n<li>Steinbruch-Winterle, Cap\u00edtulo 6 &#8211; Problemas Resolvidos e Problemas Propostos.<\/li>\n<li>Callioli-Domingues-Costa, Parte 2, Cap\u00edtulo 2, Se\u00e7\u00e3o 1 &#8211; Exerc\u00edcios Resolvidos e Exerc\u00edcios Propostos.<\/li>\n<\/ul>\n<p><strong>23\/06\/2016: <a href=\"http:\/\/www.professores.uff.br\/renatadefreitas\/wp-content\/uploads\/sites\/171\/2018\/03\/2016-1_AlgLin_E4.pdf\">pdf<\/a><\/strong><\/p>\n<p><strong>08\/07\/2016:<\/strong> <a href=\"http:\/\/www.professores.uff.br\/renatadefreitas\/wp-content\/uploads\/sites\/171\/2018\/03\/2016-1_IntAlgLin_S5.pdf\">Simulado para V2<\/a><\/p>\n<hr \/>\n<p><strong>V\u00eddeo<\/strong><\/p>\n<p>Uma aplica\u00e7\u00e3o de \u00c1lgebra Linear a ferramentas de busca na internet: <a href=\"https:\/\/www.youtube.com\/watch?v=DZ0hq2sQg28\">Isto \u00e9 Matem\u00e1tica, 1a temporada, epis\u00f3dio 2.<\/a><\/p>\n<hr \/>\n<p><strong>Ferramenta online<\/strong><\/p>\n<p>Para escalonamento e muito mais (site em ingl\u00eas): <a href=\"http:\/\/www.math.odu.edu\/~bogacki\/lat\/\">Linear Algebra Toolkit.<\/a><\/p>\n<p>Atualizada em 26\/7\/2016.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Info Turma A1, ter\u00e7as e quintas, 16h-18h, sala H-201 Gragoat\u00e1 Curso: Estat\u00edstica Profa. Renata de Freitas Calend\u00e1rio: 27 de abril &#8211; Encontro de IC 30 de maio &#8211; A Quarta Dimens\u00e3o &#8211; Aula Inaugural de 2016-1 Folga 26 de maio &#8211; Corpus Christi 11 de julho, segunda, 9-11h e 11-13h &#8211; Aula extra (sala G [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-84","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/pages\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/comments?post=84"}],"version-history":[{"count":3,"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/pages\/84\/revisions"}],"predecessor-version":[{"id":93,"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/pages\/84\/revisions\/93"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/media?parent=84"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/categories?post=84"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/renatadefreitas\/wp-json\/wp\/v2\/tags?post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}