{"id":10532,"date":"2025-07-15T13:34:49","date_gmt":"2025-07-15T13:34:49","guid":{"rendered":"https:\/\/functiontranslator.com\/macierz-odw\/"},"modified":"2021-02-26T05:21:14","modified_gmt":"2021-02-26T05:21:14","slug":"minverse","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/pl\/minverse\/","title":{"rendered":"MACIERZ.ODW"},"content":{"rendered":"

Opis funkcji<\/h2>\n

Funkcja MINVERSE<\/code> w Microsoft Excel oraz MACIERZ.ODW<\/code> w Google Sheets s\u0105 u\u017cywane do obliczania macierzy odwrotnej dla kwadratowej macierzy podanej jako argument. Aby obliczy\u0107 macierz odwrotn\u0105, dane wej\u015bciowe musz\u0105 stanowi\u0107 macierz kwadratow\u0105, nieosobliw\u0105, co oznacza, \u017ce jej wyznacznik nie mo\u017ce by\u0107 r\u00f3wny zeru.<\/p>\n

Sk\u0142adnia funkcji<\/h2>\n

Sk\u0142adnia obu funkcji jest bardzo podobna:<\/p>\n

  Excel: MINVERSE(matryca) Google Sheets: MACIERZ.ODW(matryca) <\/code> <\/pre>\n
Argument:<\/p>\n
    \n
  • matryca<\/strong> – Dwuwymiarowa tablica lub zakres reprezentuj\u0105cy kwadratow\u0105 macierz, kt\u00f3rej macierz odwrotna ma zosta\u0107 obliczona.<\/li>\n<\/ul>\n
    Przyk\u0142ad u\u017cycia:<\/p>\n
      =MINVERSE(A1:C3) \/\/ Excel =MACIERZ.ODW(A1:C3) \/\/ Google Sheets <\/code> <\/pre>\n
    Praktyczne zastosowanie funkcji<\/h2>\n
    Przyjrzyjmy si\u0119 kilku praktycznym zastosowaniom funkcji MINVERSE<\/code> oraz MACIERZ.ODW<\/code>.<\/p>\n
    Przyk\u0142ad 1: Obliczanie macierzy odwrotnej<\/h2>\n
    Za\u0142\u00f3\u017cmy, \u017ce dysponujemy nast\u0119puj\u0105c\u0105 macierz\u0105 3×3 umieszczon\u0105 w kom\u00f3rkach od A1 do C3:<\/p>\n\n\n\n\n
    1<\/td>\n2<\/td>\n3<\/td>\n<\/tr>\n
    0<\/td>\n1<\/td>\n4<\/td>\n<\/tr>\n
    5<\/td>\n6<\/td>\n0<\/td>\n<\/tr>\n<\/table>\n
    Aby wyznaczy\u0107 macierz odwrotn\u0105, nale\u017cy zastosowa\u0107 funkcj\u0119 MINVERSE<\/code> w Excelu lub MACIERZ.ODW<\/code> w Google Sheets, wprowadzaj\u0105c formu\u0142\u0119:<\/p>\n
      =MINVERSE(A1:C3) \/\/ Excel =MACIERZ.ODW(A1:C3) \/\/ Google Sheets <\/code> <\/pre>\n
    Wstawienie tej formu\u0142y w odpowiedniej liczbie kom\u00f3rek pozwoli na wy\u015bwietlenie macierzy odwrotnej.<\/p>\n
    Przyk\u0142ad 2: Rozwi\u0105zywanie uk\u0142ad\u00f3w r\u00f3wna\u0144 liniowych<\/h2>\n
    Macierze odwrotne s\u0105 cz\u0119sto wykorzystywane do rozwi\u0105zywania uk\u0142ad\u00f3w r\u00f3wna\u0144 liniowych. Rozwa\u017cmy uk\u0142ad r\u00f3wna\u0144 definiowany przez macierz wsp\u00f3\u0142czynnik\u00f3w A i wektor sta\u0142ych b:<\/p>\n\n\n\n\n
    x<\/td>\n+<\/td>\n2y<\/td>\n+<\/td>\n3z<\/td>\n=<\/td>\n9<\/td>\n<\/tr>\n
    0x<\/td>\n+<\/td>\ny<\/td>\n+<\/td>\n4z<\/td>\n=<\/td>\n8<\/td>\n<\/tr>\n
    5x<\/td>\n+<\/td>\n6y<\/td>\n+<\/td>\n0z<\/td>\n=<\/td>\n23<\/td>\n<\/tr>\n<\/table>\n
    Wykonuj\u0105c nast\u0119puj\u0105ce obliczenia, mo\u017cna znale\u017a\u0107 warto\u015bci x, y, z:<\/p>\n
      Let A = [1 2 3; 0 1 4; 5 6 0] Let b = [9; 8; 23] \/\/ Obliczamy macierz odwrotn\u0105 A^-1 A_inv = MINVERSE(A) \/\/ Mno\u017cymy A^-1 przez b x = MMULT(A_inv, b) <\/code> <\/pre>\n
    Takie dzia\u0142anie zwraca rozwi\u0105zanie uk\u0142adu r\u00f3wna\u0144 w formie wektora warto\u015bci x, y, z.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Zwraca odwrotno\u015b\u0107 macierzy tablicy<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[423],"tags":[],"class_list":["post-10532","post","type-post","status-publish","format-standard","hentry","category-matematyczne-i-trygonometryczne"],"acf":[],"yoast_head":"\nFunkcja MINVERSE (MACIERZ.ODW) w Excelu \u2013 jak dzia\u0142a, przyk\u0142ady u\u017cycia i sk\u0142adnia<\/title>\n<meta name=\"description\" content=\"Opis funkcji MINVERSE (MACIERZ.ODW) w Excelu. 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