Isistimu yezibalo ze-algebraic zomugqa

Kulolu shicilelo, sizocubungula incazelo yohlelo lwezibalo ze-algebraic zomugqa (i-SLAE), ukuthi lubukeka kanjani, yiziphi izinhlobo ezikhona, kanye nendlela yokuluveza ngendlela ye-matrix, okuhlanganisa neluliwe.

Incazelo yesistimu yezibalo zomugqa

Isistimu yezibalo ze-algebraic zomugqa (noma “i-SLAU” ngamafuphi) isistimu evame ukubukeka kanje:

• m inombolo yezibalo;
• n inani lezinto eziguquguqukayo.
• x₁, x₂,…, x_n - akwaziwa;
• a₁₁,₁₂…, a_mn - ama-coefficients angaziwa;
• b₁,b₂,…, b_m - amalungu mahhala.

Izinkomba ze-Coefficient (a_ij) zakhiwe kanje:

• i inombolo yesibalo somugqa;
• j inombolo yokuguquguquka lapho i-coefficient ibhekisela khona.

Isixazululo se-SLAU – izinombolo ezinjalo c₁, C₂,…, c_n , esimweni lapho esikhundleni sokuthi x₁, x₂,…, x_n, zonke izibalo zesistimu zizophenduka zibe ubunikazi.

Izinhlobo ze-SLAU

1. Kuyafana - wonke amalungu amahhala ohlelo alingana noziro (b₁ =b₂ = b_m = 0).

   

2. Okungafani – uma isimo esingenhla singahlangatshezwana nayo.
3. Square - inani lezibalo lilingana nenani lokungaziwa, okungukuthi m = n.

   

4. Akunqunyelwe phansi - inani lokungaziwa likhulu kunenani lezibalo.

   

5. kukhishwe Kunezibalo eziningi kuneziguquguqukayo.

   

Ngokuya ngenani lezixazululo, i-SLAE ingaba:

1. Joint inesixazululo okungenani esisodwa. Ngaphezu kwalokho, uma ihlukile, uhlelo lubizwa ngokuthi oluqondile, uma kunezixazululo eziningana, lubizwa ngokuthi olungapheli.

   

   I-SLAE engenhla ihlangene, ngoba okungenani kunesixazululo esisodwa: x = i-2,y = 3.

2. akuhambisani Uhlelo alunazo izixazululo.

   

   Izinhlangothi ezingakwesokudla zezibalo ziyefana, kodwa ezingakwesokunxele azifani. Ngakho, azikho izixazululo.

I-matrix notation yesistimu

I-SLAE ingamelwa ngendlela ye-matrix:

I-AX = B

• A i-matrix eyakhiwe ama-coefficients wokungaziwa:

  

• X - ikholomu yokuguquguquka:

  

• B - ikholomu yamalungu amahhala:

  

Isibonelo

Simelela isistimu yezibalo ngezansi ngendlela ye-matrix:

Sisebenzisa amafomu angenhla, sihlanganisa i-matrix eyinhloko ngama-coefficients, amakholomu anamalungu angaziwa namahhala.

Irekhodi eliphelele lesistimu enikeziwe yezibalo ngefomu le-matrix:

I-SLAE Matrix enwetshiwe

Uma ku-matrix yesistimu A engeza ikholomu yamahhala yamalungu kwesokudla B, ukuhlukanisa idatha ngebha eqondile, uthola i-matrix enwetshiwe ye-SLAE.

Ngokwesibonelo esingenhla, kubonakala kanje:

- ukuqokwa kwe-matrix enwetshiwe.