Sistimu yemutsara algebraic equations

Muchinyorwa chino, isu tichatarisa tsananguro yeiyo mutsara algebraic equations (SLAE), kuti inotaridzika sei, ndeapi marudzi aripo, uye zvakare maitiro ekuiburitsa mune matrix fomu, kusanganisira yakawedzerwa.

Tsanangudzo yehurongwa hwemitsetse equation

Sistimu yemutsara algebraic equations (kana kuti "SLAU" kwenguva pfupi) ihurongwa hunowanzo taridzika seizvi:

• m nhamba ye equations;
• n ndiyo nhamba yezvinoshanduka.
• x₁,x₂,…, x_n - kusazivikanwa;
• a₁₁,₁₂…, a_mn - coefficients kune zvisingazivikanwe;
• b₁,b₂,…, b_m – nhengo dzakasununguka.

Coefficient indices (a_ij) inogadzirwa nenzira inotevera:

• i inhamba yemutsara equation;
• j inhamba yemutsara unoreva iyo coefficient.

SLAU mhinduro - nhamba dzakadaro c₁, C₂,…, c_n , mumamiriro ezvinhu ayo pane x₁,x₂,…, x_n, ese maequation ehurongwa anozoshanduka kuita zvitupa.

Mhando dzeSLAU

1. Homogeneous - nhengo dzese dzemahara dzesystem dzakaenzana ne zero (b₁ =b₂ = ... = b_m = 0).

   

2. Heterogeneous - kana mamiriro ari pamusoro asina kusangana.
3. sikweya - nhamba ye equations yakaenzana nenhamba yezvisingazivikanwi, kureva m = n.

   

4. Underdetermined - nhamba yezvisingazivikanwi yakakura kudarika nhamba ye equations.

   

5. overridden Kune akawanda equations pane akasiyana.

   

Zvichienderana nehuwandu hwemhinduro, SLAE inogona kuva:

1. Joint ine kana mhinduro imwe chete. Uyezve, kana iri yakasarudzika, iyo sisitimu inonzi yakasarudzika, kana paine akati wandei mhinduro, inonzi isingaperi.

   

   Iyo SLAE iri pamusoro yakabatana, nekuti pane imwechete mhinduro: x = 2,y = 3.

2. hazvienderani Iyo system haina mhinduro.

   

   Mativi ekurudyi eequation akafanana, asi kuruboshwe haana. Nokudaro, hapana mhinduro.

Matrix notation yehurongwa

SLAE inogona kumiririrwa mune matrix fomu:

AX = B

• A ndiyo matrix inoumbwa ne coefficients yezvisingazivikanwi:

  

• X - column yezvakasiyana:

  

• B - column yenhengo dzemahara:

  

muenzaniso

Isu tinomiririra iyo system ye equations pazasi mune matrix fomu:

Tichishandisa mafomu ari pamusoro, tinonyora matrix makuru ane coefficients, makoramu ane nhengo dzisingazivikanwi uye dzakasununguka.

Zadzisa rekodhi yeyakapihwa system ye equations mune matrix fomu:

Yakawedzerwa SLAE Matrix

Kana kune matrix yehurongwa A wedzera nhengo dzemahara column kurudyi B, kuparadzanisa data nebhari yakasimudzika, unowana matrix akawedzerwa eSLAE.

Kune muenzaniso uri pamusoro, zvinotaridzika seizvi:

- kusarudzwa kwematrix akawedzerwa.