{"id":388299,"date":"2019-06-16T00:45:22","date_gmt":"2019-06-16T03:45:22","guid":{"rendered":"https:\/\/blog-estrategia.mystagingwebsite.com\/blog\/?p=388299"},"modified":"2019-06-16T03:43:51","modified_gmt":"2019-06-16T06:43:51","slug":"questao-comentada-01-afrfb","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/questao-comentada-01-afrfb\/","title":{"rendered":"Quest\u00e3o resolvida 01 (AFRFB)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Ol\u00e1, guerreiros e guerreiras!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tudo bem ?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Meu nome \u00e9 Carlos Vitor e sou <strong>Coach<\/strong> aqui no <strong>Estrat\u00e9gia Concursos<\/strong>. Tamb\u00e9m sou Servidor P\u00fablico Federal e Professor de Matem\u00e1tica. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">No artigo de hoje comentarei uma quest\u00e3o de <strong>MATRIZES\/DETERMINANTES<\/strong> que foi cobrada no concurso de <strong>Auditor Fiscal da Receita Federal do Brasil (AFRFB)<\/strong>, em 2012.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"text-align:center\"><strong>QUEST\u00c3O<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(AFRFB &#8211; 2012) <\/strong>As matrizes, A, B, C e D s\u00e3o quadradas de quarta ordem. A matriz B \u00e9 igual a \u00bd da matriz A, ou seja: B = \u00bd A. A matriz C \u00e9 igual a matriz transposta de B, ou seja C = BT.  A matriz D \u00e9 definida a partir da matriz C; a \u00fanica diferen\u00e7a entre essas duas matrizes \u00e9 que a matriz D tem como primeira linha a primeira linha de C multiplicada por 2. Sabendo-se que o determinante de A \u00e9 igual a 32, ent\u00e3o a soma dos determinantes das matrizes B, C e D \u00e9 igual a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) 6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e) 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"text-align:center\"><strong>RESOLU\u00c7\u00c3O<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De acordo\ncom o enunciado da quest\u00e3o, temos as seguintes informa\u00e7\u00f5es:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 As\nmatrizes A, B, C e D s\u00e3o quadradas de quarta ordem.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 O\ndeterminante da matriz A \u00e9 igual a 32, isto \u00e9, det A = 32<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 A matriz\nB \u00e9 igual a \u00bd da matriz A, ou seja: B = \u00bd A<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>PROPRIEDADE<\/strong>: <strong>Quando\nmultiplicamos uma matriz por uma constante, o determinante fica multiplicado\npor esta mesma constante elevada \u00e0 ordem da matriz.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De acordo\ncom a propriedade, vamos calcular o determinante da matriz B. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">det B = 1\/2 x 1\/2 x 1\/2 x 1\/2 x det A<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">det B = &nbsp;1\/16 x 32 = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 A matriz C \u00e9 igual a matriz transposta de B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>PROPRIEDADE<\/strong>: <strong>O\ndeterminante da transposta \u00e9 igual ao determinante da matriz original.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Logo, det C = det BT (Transposta de B) &nbsp;= det B = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 A matriz D \u00e9 definida a partir da matriz C; a \u00fanica\ndiferen\u00e7a entre essas duas matrizes \u00e9 que a matriz D tem como primeira linha a\nprimeira linha de C multiplicada por 2.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>PROPRIEDADE<\/strong>:<strong> Quando multiplicamos uma\nfila (linha ou coluna) por uma constante, o determinante fica multiplicado por\nesta mesma constante.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u00fanica diferen\u00e7a entre as matrizes C e D \u00e9 que a\nmatriz D \u00e9 obtida multiplicando a primeira linha da matriz C por 2. Assim, det\nD = 2 x det C = 2 x 2 = 4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Resposta: det B + det C + det D = 2 + 2 + 4 = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>GABARITO: E<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aqui termina o nosso artigo de hoje.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Um abra\u00e7o!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Fiquem com DEUS e bons estudos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Carlos Vitor<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ol\u00e1, guerreiros e guerreiras! Tudo bem ? Meu nome \u00e9 Carlos Vitor e sou Coach aqui no Estrat\u00e9gia Concursos. Tamb\u00e9m sou Servidor P\u00fablico Federal e Professor de Matem\u00e1tica. No artigo de hoje comentarei uma quest\u00e3o de MATRIZES\/DETERMINANTES que foi cobrada no concurso de Auditor Fiscal da Receita Federal do Brasil (AFRFB), em 2012. QUEST\u00c3O (AFRFB [&hellip;]<\/p>\n","protected":false},"author":1224,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"post_tipo":"article","footnotes":""},"categories":[1],"tags":[],"tax_estado":[],"class_list":["post-388299","post","type-post","status-publish","format-standard","hentry","category-cursos-e-concursos"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.1 (Yoast SEO v28.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Quest\u00e3o resolvida 01 (AFRFB)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/questao-comentada-01-afrfb\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quest\u00e3o resolvida 01 (AFRFB)\" \/>\n<meta property=\"og:description\" content=\"Ol\u00e1, guerreiros e guerreiras! Tudo bem ? Meu nome \u00e9 Carlos Vitor e sou Coach aqui no Estrat\u00e9gia Concursos. Tamb\u00e9m sou Servidor P\u00fablico Federal e Professor de Matem\u00e1tica. No artigo de hoje comentarei uma quest\u00e3o de MATRIZES\/DETERMINANTES que foi cobrada no concurso de Auditor Fiscal da Receita Federal do Brasil (AFRFB), em 2012. 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