1.5.42 Systems of algebraic equations
Condition: Given a system of linear equations \( \left\{\begin{array}{l}2 x_{1}+x_{2}-5 x_{3}-x_{4}=2 \\ x_{1}+3 x_{2}+2 x_{3}=1 \\ 3 x_{1}+4 x_{2}-3 x_{3}-x_{4}=3\end{array}\right. \) a) find the rank of the extended matrix of the system; b) solve the system: write down the general solution; c) find two particular solutions of the system and check one of them.
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.