Dongosolo la linear algebraic equations

M'bukuli, tiwona tanthauzo la dongosolo la linear algebraic equation (SLAE), momwe likuwonekera, mitundu yomwe ilipo, komanso momwe mungawonetsere mu mawonekedwe a matrix, kuphatikizapo yowonjezera.

Tanthauzo la dongosolo la ma equation a mzere

Dongosolo la linear algebraic equations (kapena "SLAU" mwachidule) ndi dongosolo lomwe nthawi zambiri limawoneka motere:

• m ndi chiwerengero cha equations;
• n ndi chiwerengero cha zosinthika.
• x₁,x₂,…, x_n - osadziwika;
• a₁₁,₁₂…, a_mn - coefficients kwa osadziwika;
• b₁,b₂,…, b_m - mamembala aulere.

Coefficient indices (a_ij) amapangidwa motere:

• i ndi nambala ya equation ya mzere;
• j ndi nambala ya kusintha komwe coefficient imatanthawuza.

SLAU yankho - nambala zotere c₁, C₂,…, c_n , m'malo mwake x₁,x₂,…, x_n, ma equation onse a dongosolo adzasandulika kukhala ma identity.

Mitundu ya SLAU

1. Ofanana - mamembala onse aulere a dongosololi ndi ofanana ndi ziro (b₁ =b₂ =…= b_m = 0).

   

2. Zosasintha - ngati zomwe zili pamwambapa sizikukwaniritsidwa.
3. Square - chiwerengero cha equations ndi chofanana ndi chiwerengero cha osadziwika, mwachitsanzo m = n.

   

4. Osatsimikiza - chiwerengero cha osadziwika ndi chachikulu kuposa chiwerengero cha equations.

   

5. cholephereka Pali ma equation ambiri kuposa ma variable.

   

Kutengera kuchuluka kwa mayankho, SLAE ikhoza kukhala:

1. olowa ali ndi njira imodzi yokha. Komanso, ngati ili yapadera, dongosololi limatchedwa lotsimikizika, ngati pali mayankho angapo, limatchedwa losatha.

   

   SLAE pamwambapa ndi yolumikizana, chifukwa pali yankho limodzi: x = 2,y = 3.

2. zosagwirizana Dongosolo ilibe njira zothetsera.

   

   Mbali zakumanja za equation ndizofanana, koma zamanzere sizili choncho. Choncho, palibe njira zothetsera.

Matrix notation ya system

SLAE ikhoza kuyimiridwa mu mawonekedwe a matrix:

AX = B

• A ndi matrix opangidwa ndi ma coefficients a osadziwika:

  

• X - magawo osiyanasiyana:

  

• B - gawo la mamembala aulere:

  

Mwachitsanzo

Timayimira dongosolo la equation pansipa mu mawonekedwe a matrix:

Pogwiritsa ntchito mafomu omwe ali pamwambapa, timapanga matrix akuluakulu ndi ma coefficients, mizati yokhala ndi mamembala osadziwika komanso aulere.

Malizitsani mbiri ya dongosolo lomwe laperekedwa la ma equation mu mawonekedwe a matrix:

Zowonjezera SLAE Matrix

Ngati ku matrix a dongosolo A onjezani gawo la mamembala aulere kumanja B, kulekanitsa deta ndi bar yowongoka, mumapeza matrix owonjezera a SLAE.

Kwa chitsanzo pamwambapa, zikuwoneka motere:

- kutchulidwa kwa matrix owonjezera.