Mmene angathetsere dongosolo la maikwezhoni liniya a mtundu

Chifukwa ankamvetsa bwino mmene angathetsere dongosolo la maikwezhoni, m'pofunika kuganizira zimene imaimira. Monga momwe tikuonera bwino liwu lokha "dongosolo" - magulu maikwezhoni angapo amagwirizana ndi mzake. Pali kachitidwe wa algebraic ndi maikwezhoni masiyanidwe. M'nkhaniyi tiona adzamvetsera mmene angathetsere dongosolo la maikwezhoni a mtundu woyamba.
Ndi tanthauzo, ndi aone kuti pali algebraic akutchedwa, mmene zosintha pamwamba zimachitika yosavuta yekha ntchito masamu, i.e. Komanso, magawano, wochotsera, chulutsa, exponentiation , ndi kupeza muzu. An aligorivimu kwa pothetsa aone kuti pali mtundu yafupika kusintha yake mu izo kupeza ndalama zokwana koma chosavuta yomanga.
Dongosolo la maikwezhoni algebraic anawagawa liniya ndi osalunjika.
Dongosolo la maikwezhoni liniya (chidule SLAE komanso chimagwiritsidwa ntchito) ndi osiyana ndi dongosolo la maikwezhoni osalunjika kuti pali zosintha osadziwika mu mlingo woyamba. General view SLAE mu mawonekedwe masanjidwewo zikuwoneka ngati: nkhwangwa = b, komwe ndi - zosiyanasiyana zinthu amadziwika × - zosintha, b - zosiyanasiyana kudziwika mamembala ufulu.

Pali njira zambiri pa mmene angathetsere dongosolo la maikwezhoni wa mtundu uwu, iwo ogaŵikana njira mwachindunji ndi iterative. njira Direct kulola ife kuti mupeze mfundo za zosintha chifukwa nambala inayake ya kusinthika masamu ndi iterative aligorivimu ntchito motsatizana chiyerekezo ndi kuukonza.

Tiyeni tione chitsanzo cha mmene angathetsere dongosolo la maikwezhoni liniya ntchito njira mwachindunji kupeza mfundo ya zosintha lapansi. The njira mwachindunji monga njira Gauss, Jordan-Gauss, Kramer, zikulilima ndi ena. Mmodzi wa zophweka kwambiri angatchedwe njira ya Cramer, nthawi zambiri anali naye ankadziwa masanjidwewo umayamba sukulu. njira lakonzedwa kuti kuthetsa machitidwe liniya quadratic, mwachitsanzo madongosolo otero imene chiwerengero cha maikwezhoni ndi wofanana ndi chiwerengero cha zosintha osadziwika mu chingwe. Komanso, kuti kuthetsa dongosolo la maikwezhoni ndi Cramer, muyenera kuonetsetsa kuti mawu mfulu - osati ziro (chofunika).

Aligorivimu yankho ili: 1 mu bokosi wopangidwa mwa zinthu zodziwika ndi machitidwe ndi determinant waukulu wa Δh. determinant chimapezeka mwa Kuchotsera mankhwala ya sekondale zinthu opendekera wa zinthu mankhwala chachikulu.

Komanso analemba 2 masanjidwewo kumene ndime yoyamba ya makhalidwe wogwirizira zilipo zinthu b, chimodzimodzi chitsanzo loyamba determinant Δh _1.

Ife kupanga masanjidwewo 3, mfundo ya koefishienti kupezeka m'malo mwa ndime yachiwiri, ife tikupeza kuti determinant ya masanjidwewo Δh _2. Ndipo kotero mpaka, mpaka inu kuwerengera determinant a masanjidwewo, kumene koefishienti b ali mu ndime yomaliza.

Kupeza phindu la variable makamaka, muyenera kumasula munthu koefishienti akamagwira m'malo qualifiers kugawidwa mu determinant chachikulu, mwachitsanzo ₁ = × Δh ₁ / Δh, ₂ × ₂ = Δh / Δh etc.
Ngati muli ndi mafunso okhudza mmene angathetsere dongosolo la maikwezhoni m'njira zina tikukulimbikitsani kuti Buku ndi zipangizo Sukuluyi, imene zofunikila njira zonse zoyambirira.