8-§. Sízíqlí teńlemeler sistemasí

8-§. Sízíqlí teńlemeler sistemasí
Endi biz sízíqlí algebralíq teńlemeler sistemasín tekseriw máselesi menen shuǵíllanamíz. Meyli bizge \[n\] belgisizli \[m\] teńlemeler sistemasí (ulíwma jaǵdayda, \[m\ne n\] bolíwí da múmkin) berilgen bolsín.
\[\left\{ \begin{align}
& {{a}_{11}}{{x}_{1}}+{{a}_{12}}{{x}_{2}}+...+{{a}_{1n}}{{x}_{n}}={{b}_{1}}, \\
& {{a}_{21}}{{x}_{1}}+{{a}_{22}}{{x}_{2}}+...+{{a}_{2n}}{{x}_{n}}={{b}_{2}}, \\
& .\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,.\,\,\,\,.\,\,\,.\,\,\, \\
& {{a}_{m1}}{{x}_{1}}+{{a}_{m2}}{{x}_{2}}+...+{{a}_{mn}}{{x}_{n}}={{b}_{n}} \\
\end{align} \right.\] (8.1)
Egerde (8.1) sistemada \[{{x}_{i}}\,(i=\overline{1,n})\] belgisizlerdiń \[{{x}_{1}}={{\alpha }_{1}},...,\,{{x}_{n}}={{\alpha }_{n}}\] san mánislerin tabíw múmkin bolsa hám de ol (8.1) sistemaníń barlíq teńlemelerin qanaatlandírsa, onda (8.1) sistema birgelikli delinedi. Bunda \[{{\alpha }_{i}}(i=\overline{1,n})\] mánisler kópligi sistemaníń sheshimi delinedi.
Egerde sízíqlí teńlemelerdiń birgelikli sheshimi bir ǵana sheshimge iye bolsa, oní aníq sistema, eger sheksiz kóp sheshimge iye bolsa, onda aníq emes sistema delinedi.
Berilgen (8.1) sistemadaǵí belgisizlerdiń aldíndaǵí koeffitsientlerden dúzilgen matritsaní \[A\] arqalí, al \[B\] arqalí bolsa saltań aǵzalardan ibarat baǵananí \[A\] matritsaǵa qosímsha baǵana etip kirgiziwden payda bolǵan matritsaní belgileyik:
\[A=\left( \begin{align}
& {{a}_{11}}\,\,{{a}_{12}}\,\,\,...\,\,\,{{a}_{1n}} \\
& {{a}_{21}}\,\,{{a}_{22}}\,\,\,...\,\,\,{{a}_{2n}} \\
& .\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,. \\
& {{a}_{m1}}\,\,{{a}_{m2}}\,\,\,...\,\,\,{{a}_{mn}} \\
\end{align} \right)\,,\,\,\,\,\,\,\,\,\,\,\,\,B=\left( \begin{align}
& {{a}_{11}}\,\,{{a}_{12}}\,\,\,...\,\,\,\,{{a}_{1n}}\,\,\,\,{{b}_{1}} \\
& {{a}_{21}}\,\,{{a}_{22}}\,\,\,...\,\,\,\,{{a}_{2n}}\,\,\,\,{{b}_{2}} \\
& .\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,.\,\,\,\,\,. \\
& {{a}_{m1}}\,\,{{a}_{m2}}\,\,\,...\,\,\,{{a}_{mn}}\,\,\,{{b}_{m}} \\
\end{align} \right)\]
\[B\] matritsaní keńeytirilgen matritsa dep ataymíz.