Zomwe zimayambitsa matrix ndi zizindikiro zake

Zida za matrices - funso limene ambiri angayambitse mavuto. Choncho, ndi bwino kuiganizira mwatsatanetsatane.

Matrix ndi tebulo la mawonekedwe ang'onoting'ono, kuphatikizapo manambala ndi zinthu. Imeneyi ndi mndandanda wa ziwerengero ndi zigawo zina za maonekedwe omwe amalembedwa ngati tebulo laling'ono lokhala ndi mizere yambiri ndi mizere. Gome ngatilo liyenera kulowetsedwa pakati pa ana. Izi zikhoza kukhala mabwalo oyandikana , mabakiteriya apakati, kapena mabilikiti awiri a mtundu wowongoka. Ziwerengero zonse zomwe zimapezeka m "matrix zimatchedwa chinthu choyambirira, ndipo zimakhalanso ndi zolemba zawo m'munda wa tebulo. Matrix amasonyezedwa ndi kalata yaikulu ya chilembo cha Chilatini.

Zida za matrices kapena masamu zamatauni zikuphatikizapo mbali zingapo. Kuwonjezera ndi kuchotsa matrices ndizofunikira kwambiri. Kuwonjezeka ndi kugawidwa kwa iwo kumapitirira mopitirira malire osadziwika. Kuti tipeze matrix imodzi ndi wina, tifunikira kukumbukira zambiri zokhudzana ndi zojambulazo za vector imodzi.

C = (a, b) = 1 b 1 + 2 b 2 + ... + a N b N

Zomwe zimakhala ndi kuchuluka kwa masrix zimakhala ndi maonekedwe osiyanasiyana. Zopangidwa kuchokera kumtundu umodzi ndi wina sizosintha, ndiko, (a, b) sizili zofanana ndi (a, b).

Zinthu zazikuluzikulu za matrices zimaphatikizapo chinthu ngati chiyeso. Ulemuwo umaonedwa kuti ndiyeso ya ma tebulo oterowo. Chodziwika ndi ntchito inayake ya zinthu zingapo za mzere wa masentimita kulowa mu dongosolo n. M'mawu ena, determinant amatchedwa determinant. Mu tebulo ndi yachiwiri, determinant ndi ofanana kusiyana kusiyana kwa malonda a manambala kapena zigawo za awiri diagonals a matrix A11A22-A12A21. Chidziwitso cha chiwerengero chokwanira ndi chapamwamba chimasonyezedwa ndi ziganizo zazitsulo zake.

Kuti mumvetse momwe matrix amavutitsira, lingaliro lofanana ndi udindo wa matrix linayambika. Chiwerengero ndi chiwerengero chazitsulo zokhazikika ndi mizera ya tebulo lopatsidwa. Matrix akhoza kukhala osasunthika kokha ngati malo ake atsirizidwa, ndiko kuti, udindo (A) ndi wofanana ndi N.

Zomwe zimayambitsa matrix zimaphatikizapo:

1. Kwa chiwerengero chokwanira, chosankha sichimasintha pamene chimasinthidwa. Izi zikutanthauza kuti chidziwitso cha chiwerengero ichi chidzakhala chofanana ndi tebulo ili mu mawonekedwe osinthidwa.

2. Ngati mzere uliwonse kapena mzere uli ndi zero imodzi yokha, ndiye kuti chiwerengero cha matrix chomwecho chidzakhala chofanana ndi zero.

3. Ngati muli ndi zipilala ziwiri kapena mizere iwiri yosinthidwa, chizindikiro cha chiganizo cha tebulo chotero chidzasintha mtengo wake.

4. Ngati mzere uliwonse kapena mzere uliwonse wa chiwerengerocho umachulukitsidwa ndi chiwerengero, ndiye kuti chiwerengero chake chikuchulukitsidwa ndi nambala yomweyo.

5. Ngati mu chilembo chilichonse cholembedwa chimakhala chiwerengero cha zigawo ziŵiri kapena zikuluzikulu, ndiye kuti tebulo lotereli lidalembedwa ngati chiwerengero cha zifukwa zingapo. Chiwerengero cha ndalama zonsezi ndi chiwerengero cha masanjidwe, omwe m'malo mwa zilembo zimayimilidwa ndi chiwerengerocho, chimodzi mwazigawo za mndandandawu ndizolembedwa molingana ndi dongosolo la determinant.

6. Ngati mu mzere uliwonse muli mizere iwiri yokhala ndi zinthu zomwezo kapena zipilala ziwiri zofanana, ndiye kuti chigamulo cha tebuloyi chikufanana ndi zero.

7. Komanso, determinant ndi ofanana zero kwa matrix, momwe mizere iwiri kapena mizere iŵiri ndi yofanana wina ndi mzake.

8. Ngati zinthu za mzere kapena ndime zikuwonjezeka ndi chiwerengero, ndiyeno zinawonjezeredwa ndi zigawo mu mzere wina kapena mzere umodzi wa matrix womwewo, motero, ndiye kuti determinant ya tebulo ili sidasintha.

Kawirikawiri, tinganene kuti matrices amaimira zovuta, koma panthawi imodzimodzi, kudziwa kofunika kwambiri za masamu. Zonse zomwe zimakhala ndi matrix zimadalira mwazigawo zake ndi zigawo zake.