Kupeza inverse matrix

M'bukuli, tiwona kuti matrix osinthika ndi chiyani, komanso, pogwiritsa ntchito chitsanzo chothandiza, tidzasanthula momwe angapezeke pogwiritsa ntchito fomula yapadera komanso algorithm pazotsatira motsatizana.

Tanthauzo la inverse matrix

Choyamba, tiyeni tikumbukire zomwe reciprocals ali mu masamu. Tiyerekeze kuti tili ndi nambala 7. Kenako kusintha kwake kudzakhala 7^-1 or ¹/₇. Mukachulukitsa manambala awa, zotsatira zake zimakhala chimodzi, mwachitsanzo 7 7^-1 = 1.

Pafupifupi chimodzimodzi ndi matrices. n'zosiyana matrix oterowo amatchedwa, kuchulukitsa komwe ndi choyambirira, timapeza chizindikiritso. Amalembedwa ngati A^-1.

A · A^-1 =E

Algorithm kuti mupeze inverse matrix

Kuti mupeze matrix osinthika, muyenera kuwerengera matrices, komanso kukhala ndi luso lochita nawo zinthu zina.

Ziyenera kuzindikirika nthawi yomweyo kuti chosiyanacho chikhoza kupezeka pa matrix a square, ndipo izi zimachitika pogwiritsa ntchito njira ili pansipa:

|A| | - chizindikiro cha matrix;

A^T_M ndiye matrix osinthika a zowonjezera za algebra.

Zindikirani: ngati determinant ndi zero, ndiye kuti inverse matrix palibe.

Mwachitsanzo

Tiyeni tipeze matrix A m'munsimu ndi m'mbuyo mwake.

Anakonza

1. Choyamba, tiyeni tipeze chizindikiritso cha matrix operekedwa.

2. Tsopano tiyeni tipange matrix omwe ali ndi miyeso yofanana ndi yoyambayo:

Tiyenera kudziwa manambala omwe angalowe m'malo mwa nyenyezi. Tiyeni tiyambe ndi gawo lakumanzere la matrix. Zing'onozing'ono kwa izo zimapezeka podutsa mzere ndi mzati momwe zilili, mwachitsanzo, muzochitika zonsezo pa nambala wani.

Nambala yomwe imatsalira pambuyo pa kugunda ndi yaying'ono yofunikira, mwachitsanzo M₁₁ = 8.

Mofananamo, timapeza ang'onoang'ono pazinthu zotsalira za matrix ndikupeza zotsatira zotsatirazi.

3. Timatanthauzira matrix a zowonjezera za algebraic. Momwe tingawerengere pa chinthu chilichonse, tidakambirana padera.

Mwachitsanzo, kwa chinthu a₁₁ Kuwonjezera kwa algebraic kumaganiziridwa motere:

A₁₁ = (-1)^{1 + 1} M₁₁ = 1 · 8 = 8

4. Pangani masinthidwe a matrix otsatila a zilembo za algebra (ie, sinthanani mizati ndi mizere).

5. Zimangotsala pang'ono kugwiritsa ntchito njira yomwe ili pamwambapa kuti mupeze matrix osinthika.

Tikhoza kusiya yankho mu mawonekedwe awa, popanda kugawa zinthu za matrix ndi nambala 11, chifukwa pamenepa timapeza manambala oyipa.

Kuyang'ana zotsatira

Kuti tiwonetsetse kuti tili ndi zotsutsana ndi matrix oyambilira, titha kupeza zomwe zidapangidwa, zomwe ziyenera kufanana ndi matrix.

Zotsatira zake, tapeza matrix odziwika, zomwe zikutanthauza kuti tachita zonse moyenera.