{"product_id":"atividade1-geometria-analitica-e-algebra-linear-51-2026","title":"ATIVIDADE1 - GEOMETRIA ANALÍTICA E ÁLGEBRA LINEAR 51_2026","description":"\u003cbr\u003e\u003ca href=\"https:\/\/wa.me\/5518981218965?text=Ol%C3%A1!%20Quero%20saber%20mais%20sobre%20esta%20atividade:%20%0A%0A*ATIVIDADE1%20-%20GEOMETRIA%20ANAL%C3%8DTICA%20E%20%C3%81LGEBRA%20LINEAR*\" target=\"_blank\" style=\"display: inline-block; background: #25D366; color: #fff; padding: 12px 20px; border-radius: 5px; text-decoration: none; font-weight: bold; margin-top: 15px;width:100%;text-align:center\"\u003eClique Aqui e Compre pelo Whatsapp\u003c\/a\u003e\u003cbr\u003e\u003cbr\u003e\u003cdiv style=\"text-align:justify\"\u003ePrezado (a) aluno(a).\u003cbr\u003e\r\nÁlgebra Linear é um ramo da matemática que estuda espaços vetoriais, transformações lineares e sistemas de equações lineares. Muitas situações problemas, seja na química, física, engenharia, ciência da computação e estatística, podem ser representadas por meio de uma tabela numérica denominada de Matriz. Essa ferramenta matemática, possui dois conceitos de extrema importância nos estudos das matrizes, o primeiro conceito é o determinante associado a uma matriz quadrada que corresponde a um número real, e quando é diferente de zero, garante a existência da matriz inversa. O outro conceito, na verdade, consiste em técnicas para se obter a matriz inversa, que pode ser obtida por meio de determinantes ou por um número finito de operações elementares sobre uma matriz que admite inversa.\u003cbr\u003e\r\nPara essa Atividade de Estudos vamos utilizar os três últimos algarismos \u003cem\u003e\u003cstrong\u003ea\u003c\/strong\u003e\u003c\/em\u003e, \u003cem\u003e\u003cstrong\u003eb\u003c\/strong\u003e\u003c\/em\u003e e \u003cem\u003e\u003cstrong\u003ec\u003c\/strong\u003e\u003c\/em\u003e do seu R.A. (registro acadêmico), algarismos esses que irão compor a terceira linha da seguinte matriz.\u003cbr\u003e\r\n\u003cbr\u003e\r\n\u003cimg alt=\"\" src=\"http:\/\/sistemasead.unicesumar.edu.br\/flex\/amfphp\/services\/Portal\/ImagemQuestionario2\/QUE_301869_663605_1.png\" style=\"height:78px; margin-bottom:0px; margin-left:0px; margin-right:0px; margin-top:0px; width:452px\"\u003e\n\u003c\/div\u003e\r\n\r\n\u003cdiv style=\"text-align:center\"\u003e \u003c\/div\u003e\r\n\r\n\u003cdiv style=\"text-align:justify\"\u003ePor exemplo, suponhamos que o aluno tenha o RA = 1816054-5, neste caso, utilizaríamos os algarismos 5, 4 e 5, na qual a sua matriz ficaria\u003cbr\u003e\r\n\u003cimg alt=\"\" src=\"http:\/\/sistemasead.unicesumar.edu.br\/flex\/amfphp\/services\/Portal\/ImagemQuestionario2\/QUE_301869_663605_2.png\" style=\"height:83px; margin-bottom:0px; margin-left:0px; margin-right:0px; margin-top:0px; width:451px\"\u003e\n\u003c\/div\u003e\r\n\r\n\u003cdiv style=\"text-align:justify\"\u003eDesse modo, tome nota dos \u003cstrong\u003etrês últimos algarismos do seu RA\u003c\/strong\u003e, isto é, \u003cstrong\u003e\u003cem\u003ea = _____\u003c\/em\u003e\u003c\/strong\u003e, \u003cem\u003e\u003cstrong\u003eb = _____\u003c\/strong\u003e\u003c\/em\u003e, \u003cem\u003e\u003cstrong\u003ec =\u003c\/strong\u003e\u003c\/em\u003e _____ e monte sua matriz \u003cstrong\u003e\u003cem\u003eM\u003c\/em\u003e\u003c\/strong\u003e. Essa matriz será utilizada para resolver os itens (1) e (2).\u003cbr\u003e\r\n\u003cimg alt=\"\" src=\"http:\/\/sistemasead.unicesumar.edu.br\/flex\/amfphp\/services\/Portal\/ImagemQuestionario2\/QUE_301869_663605_3.png\" style=\"height:77px; margin-bottom:0px; margin-left:0px; margin-right:0px; margin-top:0px; width:452px\"\u003e\n\u003c\/div\u003e\r\n\r\n\u003cdiv style=\"text-align:justify\"\u003e\n\u003cbr\u003e\r\n1) Atribua um valor inteiro para \u003cem\u003e\u003cstrong\u003ek\u003c\/strong\u003e\u003c\/em\u003e de maneira que seu determinante seja \u003cstrong\u003ediferente de zero\u003c\/strong\u003e.\u003cbr\u003e\r\n\u003cimg alt=\"\" src=\"http:\/\/sistemasead.unicesumar.edu.br\/flex\/amfphp\/services\/Portal\/ImagemQuestionario2\/QUE_301869_663605_4.png\" style=\"height:75px; margin-bottom:0px; margin-left:0px; margin-right:0px; margin-top:0px; width:451px\"\u003e\n\u003c\/div\u003e\r\n\r\n\u003cdiv style=\"text-align:center\"\u003e \u003c\/div\u003e\r\n\r\n\u003cdiv style=\"text-align:justify\"\u003eCalcule o valor do determinante da matriz \u003cem\u003e\u003cstrong\u003eM\u003c\/strong\u003e\u003c\/em\u003e utilizando o Desenvolvimento de Laplace ou Regra de Sarrus ( Link vídeo: https:\/\/youtu.be\/uWDMHbwbUN8 ). (Apresente todos os cálculos).\u003cbr\u003e\r\n\u003cbr\u003e\r\n2) Utilize os mesmos valores \u003cstrong\u003e\u003cem\u003ea = _____\u003c\/em\u003e\u003c\/strong\u003e, \u003cem\u003e\u003cstrong\u003eb = _____\u003c\/strong\u003e\u003c\/em\u003e, \u003cem\u003e\u003cstrong\u003ec =\u003c\/strong\u003e\u003c\/em\u003e _____ e \u003cem\u003e\u003cstrong\u003ek =\u003c\/strong\u003e\u003c\/em\u003e _____ do item anterior e obtenha a matriz inversa \u003cem\u003e\u003cstrong\u003eM\u003csup\u003e-1\u003c\/sup\u003e\u003c\/strong\u003e\u003c\/em\u003e, use a técnica da Matriz Adjunta ou por meio das Operações Elementares ( Link vídeo: https:\/\/youtu.be\/gux1jZgHtho  ). (Apresente os cálculos).\u003cbr\u003e\r\n\u003cbr\u003e\r\n3) Mostre que o produto das matrizes \u003c!--[if gte msEquation 12]\u003e\u003cm:omath\u003e\u003ci style=\"mso-bidi-font-style:normal\"\u003e\u003cspan style='font-size:11.0pt;line-height:\n 107%;font-family:\"Cambria Math\",serif;mso-fareast-font-family:\"Times New Roman\";\n mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:\"Times New Roman\";\n mso-bidi-theme-font:minor-bidi;mso-ansi-language:PT-BR;mso-fareast-language:\n EN-US;mso-bidi-language:AR-SA'\u003e\u003cm:r\u003eM\u003c\/m:r\u003e\u003cm:r\u003e.\u003c\/m:r\u003e\u003c\/span\u003e\u003c\/i\u003e\u003cm:ssup\u003e\u003cm:ssuppr\u003e\u003cspan style='font-family:\"Cambria Math\",serif;mso-ascii-font-family:\"Cambria Math\";\n   mso-fareast-font-family:\"Times New Roman\";mso-fareast-theme-font:minor-fareast;\n   mso-hansi-font-family:\"Cambria Math\";font-style:italic;mso-bidi-font-style:\n   normal'\u003e\u003cm:ctrlpr\u003e\u003c\/m:ctrlpr\u003e\u003c\/span\u003e\u003c\/m:ssuppr\u003e\u003cm:e\u003e\u003ci style=\"mso-bidi-font-style:\n   normal\"\u003e\u003cspan style='font-size:11.0pt;line-height:107%;font-family:\"Cambria Math\",serif;\n   mso-fareast-font-family:\"Times New Roman\";mso-fareast-theme-font:minor-fareast;\n   mso-bidi-font-family:\"Times New Roman\";mso-bidi-theme-font:minor-bidi;\n   mso-ansi-language:PT-BR;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'\u003e\u003cm:r\u003eM\u003c\/m:r\u003e\u003c\/span\u003e\u003c\/i\u003e\u003c\/m:e\u003e\u003cm:sup\u003e\u003ci style=\"mso-bidi-font-style:normal\"\u003e\u003cspan style='font-size:11.0pt;line-height:\n   107%;font-family:\"Cambria Math\",serif;mso-fareast-font-family:\"Times New Roman\";\n   mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:\"Times New Roman\";\n   mso-bidi-theme-font:minor-bidi;mso-ansi-language:PT-BR;mso-fareast-language:\n   EN-US;mso-bidi-language:AR-SA'\u003e\u003cm:r\u003e-\u003c\/m:r\u003e\u003cm:r\u003e1\u003c\/m:r\u003e\u003c\/span\u003e\u003c\/i\u003e\u003c\/m:sup\u003e\u003c\/m:ssup\u003e\u003c\/m:omath\u003e\u003c![endif]--\u003e\u003c!--[if !msEquation]--\u003e\u003c!--[if gte vml 1]\u003e\u003cv:shapetype id=\"_x0000_t75\" coordsize=\"21600,21600\" path=\"m@4@5l@4@11@9@11@9@5xe\" filled=\"f\" stroked=\"f\" o:spt=\"75\" o:preferrelative=\"t\"\u003e\r\n \u003cv:stroke joinstyle=\"miter\"\u003e\u003c\/v:stroke\u003e\r\n \u003cv:formulas\u003e\r\n  \u003cv:f eqn=\"if lineDrawn pixelLineWidth 0\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"sum @0 1 0\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"sum 0 0 @1\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"prod @2 1 2\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"prod @3 21600 pixelWidth\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"prod @3 21600 pixelHeight\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"sum @0 0 1\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"prod @6 1 2\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"prod @7 21600 pixelWidth\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"sum @8 21600 0\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"prod @7 21600 pixelHeight\"\u003e\u003c\/v:f\u003e\r\n  \u003cv:f eqn=\"sum @10 21600 0\"\u003e\u003c\/v:f\u003e\r\n \u003c\/v:formulas\u003e\r\n \u003cv:path o:extrusionok=\"f\" gradientshapeok=\"t\" o:connecttype=\"rect\"\u003e\u003c\/v:path\u003e\r\n \u003co:lock v:ext=\"edit\" aspectratio=\"t\"\u003e\u003c\/o:lock\u003e\r\n\u003c\/v:shapetype\u003e\u003cv:shape id=\"_x0000_i1025\" type=\"#_x0000_t75\" style=\"width:34.5pt;\n height:14.25pt\"\u003e\r\n \u003cv:imagedata src=\"http:\/\/sistemasead.unicesumar.edu.br\/flex\/amfphp\/services\/Portal\/ImagemQuestionario2\/QUE_301869_663605_5.Users\/ALEXAN~1\/AppData\/Local\/Temp\/msohtmlclip1\/01\/clip_i\" o:title=\"\" chromakey=\"white\"\u003e\u003c\/v:imagedata\u003e\r\n\u003c\/v:shape\u003e\u003c![endif]--\u003e\u003c!--[if !vml]--\u003e\u003c!--[endif]--\u003e\u003c!--[endif]--\u003e\u003cem\u003e\u003cstrong\u003eM.M\u003csup\u003e-1\u003c\/sup\u003e\u003c\/strong\u003e\u003c\/em\u003e é igual a matriz identidade.\u003cbr\u003e\r\n\u003cbr\u003e\r\nA seguir, link de apoio para realizar essa Atividade de Estudos.\u003cbr\u003e\r\nDeterminante (GeoGebra): https:\/\/www.geogebra.org\/calculator\/tqbkwynh\u003cbr\u003e\r\nMatriz Inversa (GeoGebra): https:\/\/www.geogebra.org\/calculator\/pw737f5p\u003c\/div\u003e\u003cbr\u003e\u003cbr\u003e\u003ca href=\"https:\/\/wa.me\/5518981218965?text=Ol%C3%A1!%20Quero%20saber%20mais%20sobre%20esta%20atividade:%20%0A%0A*ATIVIDADE1%20-%20GEOMETRIA%20ANAL%C3%8DTICA%20E%20%C3%81LGEBRA%20LINEAR*\" target=\"_blank\" style=\"display: inline-block; background: #25D366; color: #fff; padding: 12px 20px; border-radius: 5px; text-decoration: none; font-weight: bold; margin-top: 15px;width:100%;text-align:center\"\u003eClique Aqui e Compre pelo Whatsapp\u003c\/a\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e","brand":"Loja Papiron","offers":[{"title":"Default Title","offer_id":48582237585631,"sku":"fjipeY4zZfy2JEwafcc2Wv","price":24.9,"currency_code":"BRL","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0747\/5891\/4271\/files\/Logo_Unicesumar.png?v=1742757379","url":"https:\/\/www.lojapapiron.com.br\/products\/atividade1-geometria-analitica-e-algebra-linear-51-2026","provider":"Loja Papiron","version":"1.0","type":"link"}