1.5.38 Systems of algebraic equations
Condition: Given a system of linear equations \( \left\{\begin{array}{l}2 x_{1}+x_{2}-10 x_{3}+x_{4}=6 \\ 3 x_{1}+x_{2}-x_{3}+x_{4}=3 \\ 5 x_{1}+2 x_{2}-11 x_{3}+2 x_{4}=9\end{array}\right. \) a) find the rank of the extended matrix of the system and find out whether the system is defined; b) solve the system: write down the general solution; c) find a particular solution of the system and check it.
Solving systems of algebraic equations by the methods of Gauss, Jordan-Gauss, Cramer and using the inverse matrix. Homogeneous and non-homogeneous systems of equations.