1.5.41 Systems of algebraic equations
Condition: Given a system of linear equations \( \left\{\begin{array}{l}2 x_{1}+x_{2}-x_{3}=1 \\ x_{1}+3 x_{2}+x_{3}-2 x_{4}=2 \\ 3 x_{1}+4 x_{2}-2 x_{4}=3\end{array}\right. \) a) show that the system is consistent; b) find out whether the system is certain or uncertain; c) solve the system: write down the general solution, find a particular solution 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.