Tsarin daidaitattun algebraic na layi

A cikin wannan ɗaba'ar, za mu yi la'akari da ma'anar tsarin daidaitattun algebraic (SLAE), yadda yake kama, wane nau'i ne, da kuma yadda za a gabatar da shi a cikin sigar matrix, gami da mai tsawo.

Ma'anar tsarin ma'auni na layi

Tsarin daidaitattun algebraic na layi (ko "SLAU" a takaice) tsari ne wanda gaba daya yayi kama da haka:

• m shine adadin ma'auni;
• n shine adadin masu canji.
• x₁, x₂,…, x_n - wanda ba a sani ba;
• a₁₁,₁₂…, a_mn - coefficients ga wadanda ba a sani ba;
• b₁,b₂,…, b_m – free members.

Ma'aunin ƙididdiga (a_ij) an kafa su kamar haka:

• i shine adadin ma'aunin mizani;
• j shine adadin ma'auni wanda ƙididdiga ke nuni zuwa gare shi.

Maganin SLAU - irin waɗannan lambobi c₁, C₂,..., c_n , a cikin saitin wanda maimakon x₁, x₂,…, x_n, duk ma'auni na tsarin zasu juya zuwa ga ganewa.

Nau'in SLAU

1. Madigo - duk membobin tsarin kyauta daidai suke da sifili (b₁ =b₂ = b. = b_m = 0).

   

2. Tsammani - idan yanayin da ke sama bai cika ba.
3. square – adadin ma'auni yayi daidai da adadin waɗanda ba a san su ba, watau m = n.

   

4. Ba a yanke hukunci ba - adadin abubuwan da ba a sani ba ya fi yawan adadin ma'auni.

   

5. wuce gona da iri Akwai ƙarin daidaito fiye da masu canji.

   

Dangane da adadin mafita, SLAE na iya zama:

1. hadin gwiwa yana da aƙalla mafita ɗaya. Bugu da ƙari, idan ya kasance na musamman, ana kiran tsarin tabbatacce, idan akwai mafita da yawa, ana kiran shi marar iyaka.

   

   SLAE da ke sama haɗin gwiwa ne, saboda akwai aƙalla mafita ɗaya: x = 2y = 3.

2. m Tsarin ba shi da mafita.

   

   Bangaren dama na lissafin daidai suke, amma na hagu ba. Don haka, babu mafita.

Matrix bayanin kula na tsarin

SLAE za a iya wakilta a cikin matrix form:

AX = B

• A shine matrix da aka kafa ta hanyar ƙididdiga na abubuwan da ba a sani ba:

  

• X - shafi na masu canji:

  

• B - ginshiƙin membobin kyauta:

  

Example

Muna wakiltar tsarin daidaitawa a ƙasa a cikin sigar matrix:

Yin amfani da siffofin da ke sama, muna tsara babban matrix tare da ƙididdiga, ginshiƙai tare da membobin da ba a sani ba da kyauta.

Cikakken rikodin tsarin da aka bayar a cikin sigar matrix:

Ƙarfafa SLAE Matrix

Idan zuwa matrix na tsarin A ƙara ginshiƙin membobin kyauta zuwa dama B, Rarraba bayanan tare da sandar tsaye, kuna samun matrix mai tsayi na SLAE.

Ga misalin da ke sama, yayi kama da haka:

– nadi na Extended matrix.