Indlela yokwenza ekutholeni determinant we matrix?

Ukuthola determinant we matrix kubaluleke kabi, hhayi nje ngobe kutawutfutfukisa isinyathelo algebra eqondile: isibonelo, umnotho ngokusebenzisa le ukubala uhlelo ixazululwe of zibalo lwento nge angaziwa amaningi kabanzi izinkinga zomnotho.

Umqondo determinant

determinant determinant noma matrix ibizwa ngokuthi inani elilingana ivolumu parallelepiped ukwakhiwa phezu irowu yayo zithwala noma amakholomu. Bala kwaleli nani kuphela matrix square lapho inani lemigqa, nezinsika efanayo. Uma amalungu-matrix - inombolo, inani kuyoba futhi etintfweni.

Ukubalwa etintfweni

Khumbula ukuthi kukhona abanye imithetho esingenza lula kakhulu izibalo ezinjengalezi.

Njengoba determinant we matrix ehlanganisa ilungu elilodwa, kuba isici esisodwa. Bala determinant ye-oda yesibili akunzima, kwanele umkhiqizo amalungu idayagonali thatha umkhiqizo izakhi ngokufanele kwi idayagonali yesibili.

Kubalwa determinant 3 mayelana indlela elula ukuba afeze ku kokubusa unxantathu. Ukuze wenze lokhu, wenze izinyathelo ezilandelayo:

1. Sithola umkhiqizo matrices ezintathu amalungu esisogwini main yayo idayagonali.
2. Phindaphinda ngamalungu amathathu abasendleleni onxantathu, lezisekelo zazo yilezi kuhambisana idayagonali main.
3. Phinda kuqala futhi isenzo yesibili diagonal yesibili.
4. Thola isamba amagugu okuholela izibalo langaphambilini, izinombolo etholwe isigaba sesithathu, sithatha value ezimbi.

Ukuchitha kalula ekutholeni determinant oda 4 nobungako ephakeme, kubalulekile ukuba sicabangele izakhiwo emimoya zonke etintfweni:

1. Inani determinant engashintshwa emva transposition we matrix.
2. Kushintshaniswa irowu emibili elandelanayo noma ikholomu kuholela ushintsho uphawu determinant.
3. Uma matrix has imigqa emibili alinganayo noma amakholomu, noma zonke izici kwekholomu (imigqa) zero, determinant salo zero.
4. Ukubuyabuyelela of matrix kunoma iyiphi inombolo kuholela kukhuliswe determinant yayo inani elifanayo izikhathi.

Ukusebenzisa izakhiwo ngenhla kwenza kube lula ukuba afeze ukuzimisela determinant we matrix oda kokubonisana nomkayo. Ngokwesibonelo, usebenzisa umyalelo ukunciphisa indlela lapho yokubola irowu determinant isici (ikholomu) siphindwe cofactor.

Enye indlela kube lula ukuthola determinant matrix, iwukwenza yona ifomu elingunxantathu, lapho zonke izinto ngaphansi idayagonali eziyinhloko zero. Kulokhu, determinant ibalwa njengoba umkhiqizo izinombolo kahle kule idayagonali.

Futhi ekugcineni Ngithanda wazi ukuthi ukubala etintfweni, nakuba liqukethe a izibalo obonakala ulula zezibalo, Nokho, kudinga ukunakekelwa eside nokubekezela.