Ukuthola i-matrix ephambene

Kulolu shicilelo, sizocubungula ukuthi iyini i-matrix ephambene, futhi, sisebenzisa isibonelo esisebenzayo, sizohlaziya ukuthi ingatholakala kanjani kusetshenziswa ifomula ekhethekile kanye ne-algorithm yezenzo ezilandelanayo.

Incazelo ye-matrix ephambene

Okokuqala, ake sikhumbule ukuthi yiziphi i-reciprocals ku-mathematics. Ake sithi sinenombolo 7. Khona-ke inverse yayo izoba ngu-7^-1 or ¹/₇. Uma uphindaphinda lezi zinombolo, umphumela uzoba munye, okungukuthi 7 7^-1 = 1.

Kucishe kufane nomatikuletsheni. reverse I-matrix enjalo ibizwa ngokuthi, iphindaphinda ukuthi ngeyokuqala, sithola ubunikazi. Ubhalwe ngokuthi A^-1.

A · A^-1 =E

I-algorithm yokuthola i-matrix ephambene

Ukuze uthole i-matrix ephambene, udinga ukwazi ukubala ama-matrics, futhi ube namakhono okwenza izenzo ezithile nawo.

Kufanele kuqashelwe ngaso leso sikhathi ukuthi okuphambene kungatholakala kuphela ku-matrix yesikwele, futhi lokhu kwenziwa kusetshenziswa ifomula engezansi:

|A| - i-matrix determinant;

A^T_M i-matrix eguquliwe yezengezo ze-algebraic.

Qaphela: uma i-determinant inguziro, khona-ke i-matrix ephambene ayikho.

Isibonelo

Masitholele i-matrix A ngezansi kukhona okuphambene nakho.

Isixazululo

1. Okokuqala, ake sithole i-determinant ye-matrix enikeziwe.

2. Manje masenze imatrix enobukhulu obufanayo neyokuqala:

Sidinga ukuthola ukuthi yiziphi izinombolo okufanele zithathe indawo yezinkanyezi. Ake siqale nge-elementi ephezulu kwesokunxele ye-matrix. Okuncane kukho kutholakala ngokweqa umugqa nekholomu lapho itholakala khona, okungukuthi kuzo zombili izimo enombolweni yokuqala.

Inombolo esele ngemva kokudwetshwa yincane edingekayo, isb M₁₁ = 8.

Ngokufanayo, sithola izingane zezakhi ezisele ze-matrix futhi sithole umphumela olandelayo.

3. Sichaza i-matrix yezengezo ze-algebra. Indlela yokubala kubo nge-elementi ngayinye, sicabangele ngokwehlukana.

Isibonelo, nge-elementi a₁₁ Ukwengezwa kwe-algebraic kubhekwa njengokulandelayo:

A₁₁ = (-1)^{1 + 1} M₁₁ = 1 · 8 = 8

4. Yenza ukuguqulwa kwe-matrix engumphumela yezengezo ze-algebra (okungukuthi, shintshanisa amakholomu nemigqa).

5. Kusele kuphela ukusebenzisa ifomula engenhla ukuthola i-matrix ephambene.

Singashiya impendulo kuleli fomu, ngaphandle kokuhlukanisa izakhi ze-matrix ngenombolo engu-11, ngoba kulokhu sithola izinombolo ezimbi ze-fractional.

Ihlola umphumela

Ukuqinisekisa ukuthi sikutholile okuphambene ne-matrix yokuqala, singathola umkhiqizo wabo, okufanele ulingane ne-matrix yobunikazi.

Ngenxa yalokho, sithole i-matrix yobunikazi, okusho ukuthi senze konke ngendlela efanele.