{"id":11005,"date":"2025-07-15T13:34:51","date_gmt":"2025-07-15T13:34:51","guid":{"rendered":"https:\/\/functiontranslator.com\/matriz-determ\/"},"modified":"2021-02-25T17:24:33","modified_gmt":"2021-02-25T17:24:33","slug":"mdeterm","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/pt-pt\/mdeterm\/","title":{"rendered":"MATRIZ.DETERM"},"content":{"rendered":"

O comando MATRIZ.DETERM no MS Excel e nas Google Tabelas \u00e9 uma ferramenta indispens\u00e1vel para calcular o determinante de uma matriz quadrada. O determinante \u00e9 um valor derivado dos elementos da matriz e tem aplica\u00e7\u00f5es cr\u00edticas em v\u00e1rias \u00e1reas da matem\u00e1tica, inclusive na resolu\u00e7\u00e3o de sistemas de equa\u00e7\u00f5es lineares.<\/p>\n

Vis\u00e3o geral da sintaxe<\/h2>\n

A sintaxe para utilizar a fun\u00e7\u00e3o MATRIZ.DETERM \u00e9 bastante direta:<\/p>\n

MATRIZ.DETERM(matriz)<\/code><\/pre>\n
    \n
  • matriz:<\/strong> Representa a matriz quadrada cujo determinante deseja-se calcular. Este par\u00e2metro pode ser tanto uma refer\u00eancia a um intervalo de c\u00e9lulas quanto uma matriz inserida diretamente na fun\u00e7\u00e3o.<\/li>\n<\/ul>\n
    Veja um exemplo pr\u00e1tico de aplica\u00e7\u00e3o:<\/p>\n
    =MATRIZ.DETERM(A1:C3)<\/code><\/pre>\n
    Neste caso, o determinante da matriz localizada no intervalo de A1 at\u00e9 C3 ser\u00e1 calculado.<\/p>\n
    Exemplos pr\u00e1ticos de uso<\/h2>\n
    1. Resolvendo sistemas de equa\u00e7\u00f5es lineares<\/h2>\n
    Considere o seguinte sistema de equa\u00e7\u00f5es lineares:<\/p>\n
      \n
    • 3x + 4y + 2z = 1<\/li>\n
    • 2x – y + 3z = -6<\/li>\n
    • x + 3y – 2z = 0<\/li>\n<\/ul>\n
      Para resolver esse sistema pela regra de Cramer, formamos a matriz dos coeficientes e calculamos seu determinante com a fun\u00e7\u00e3o MATRIZ.DETERM:<\/p>\n
      =MATRIZ.DETERM({3,4,2; 2,-1,3; 1,3,-2})<\/code><\/pre>\n
      Se o determinante obtido n\u00e3o for zero, o sistema possui uma solu\u00e7\u00e3o \u00fanica. Determinantes espec\u00edficos para cada vari\u00e1vel (x, y, z) podem ser calculados com a substitui\u00e7\u00e3o da coluna de coeficientes correspondente pela coluna de resultados e, posteriormente, recalculando o determinante.<\/p>\n
      2. An\u00e1lise de depend\u00eancia linear de vetores<\/h2>\n
      Suponha que voc\u00ea deseja verificar se tr\u00eas vetores em R\u00b3 s\u00e3o linearmente independentes. Os vetores s\u00e3o definidos como:<\/p>\n
        \n
      • V1 = (1, 4, 7)<\/li>\n
      • V2 = (2, 5, 8)<\/li>\n
      • V3 = (3, 6, 9)<\/li>\n<\/ul>\n
        Colocamos esses vetores como colunas de uma matriz e calculamos o determinante da seguinte maneira:<\/p>\n
        =MATRIZ.DETERM({1,2,3; 4,5,6; 7,8,9})<\/code><\/pre>\n
        Um determinante igual a zero sugere que os vetores s\u00e3o linearmente dependentes, indicando que pelo menos um deles pode ser representado como combina\u00e7\u00e3o linear dos outros.<\/p>\n
        Esses exemplos ilustram a utilidade da fun\u00e7\u00e3o MATRIZ.DETERM tanto no \u00e2mbito educacional quanto no profissional, facilitando a resolu\u00e7\u00e3o de problemas complexos com efic\u00e1cia.<\/p>\n","protected":false},"excerpt":{"rendered":"
        Devolve o determinante matricial de uma matriz<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[437],"tags":[],"class_list":["post-11005","post","type-post","status-publish","format-standard","hentry","category-matematica-e-trigonometria"],"acf":[],"yoast_head":"\nFun\u00e7\u00e3o MDETERM (MATRIZ.DETERM) no Excel \u2013 como funciona, exemplos e sintaxe<\/title>\n<meta name=\"description\" content=\"Breve descri\u00e7\u00e3o da fun\u00e7\u00e3o MDETERM (MATRIZ.DETERM) do Excel. 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