{"id":56633,"date":"2016-02-09T02:33:02","date_gmt":"2016-02-09T04:33:02","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=56633"},"modified":"2023-03-31T20:21:45","modified_gmt":"2023-03-31T23:21:45","slug":"problema-de-gincana-determine-um-determinante","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-de-gincana-determine-um-determinante\/","title":{"rendered":".Problema de Gincana:   Determine um determinante"},"content":{"rendered":"<p style=\"margin:20px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nSeja [tex]A[\/tex] uma matriz [tex]3 \\,\\times \\, 3[\/tex] tal que  [tex]det(A) = 5[\/tex].<br \/>\nEnt\u00e3o o valor de [tex]det(2A)[\/tex] pertence ao intervalo<\/p>\n<p>[tex](a)\\,[1 , 10].\\,\\,\\,\\,\\,\\,\\\\  \\,  \\\\(b)\\, ]10 , 20].\\,\\,\\,\\,\\,\\,\\\\ \\,  \\\\(c)\\, ]20, 30].\\,\\,\\,\\,\\,\\,\\\\ \\, \\\\(d)\\,]30, 40].\\,\\,\\,\\,\\,\\,\\\\ \\, \\\\(e)\\,N.R.A.[\/tex]<\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:27px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nSe [tex]m[\/tex] \u00e9 um inteiro positivo e [tex]A[\/tex] uma matriz quadrada de ordem [tex]n[\/tex], ent\u00e3o<br \/>\n [tex]\\qquad det(mA) = m^n \\cdot det(A)[\/tex].<br \/>\nNo problema, temos <\/p>\n<ul>\n<li>[tex]det(A)=5[\/tex],<\/li>\n<\/ul>\n<ul>\n<li>[tex]\\,n =3\\,[\/tex] e<\/li>\n<\/ul>\n<ul>\n<li> [tex]m=2[\/tex],<\/li>\n<\/ul>\n<p> logo:<br \/>\n[tex]\\qquad det(2A) = 2^3 \\cdot 5 = 40[\/tex] e[tex] \\,  \\, \\boxed{40\\in  \\, ]30, 40] \\, }[\/tex].<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">\nSolu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"gg\">\nSegunda Gincana de 2015 &#8211; Clubes de Matem\u00e1tica da OBMEP<br \/>\nN\u00edvel C &#8211; Quest\u00e3o F\u00e1cil<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema Seja [tex]A[\/tex] uma matriz [tex]3 \\,\\times \\, 3[\/tex] tal que [tex]det(A) = 5[\/tex]. Ent\u00e3o o valor de [tex]det(2A)[\/tex] pertence ao intervalo [tex](a)\\,[1 , 10].\\,\\,\\,\\,\\,\\,\\\\ \\, \\\\(b)\\, ]10 , 20].\\,\\,\\,\\,\\,\\,\\\\ \\, \\\\(c)\\, ]20, 30].\\,\\,\\,\\,\\,\\,\\\\ \\, \\\\(d)\\,]30, 40].\\,\\,\\,\\,\\,\\,\\\\ \\, \\\\(e)\\,N.R.A.[\/tex] Solu\u00e7\u00e3o Se [tex]m[\/tex] \u00e9 um inteiro positivo e [tex]A[\/tex] uma matriz quadrada de ordem [tex]n[\/tex], ent\u00e3o &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-de-gincana-determine-um-determinante\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-56633","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/56633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=56633"}],"version-history":[{"count":12,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/56633\/revisions"}],"predecessor-version":[{"id":185942,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/56633\/revisions\/185942"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=56633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}