1.5.44 Systems of algebraic equations
condition: Given a system of linear equations \( \left\{\begin{array}{c}x_{1}+x_{3}-2 x_{4}=1 \\ 3 x_{1}-x_{2}-x_{3}+2 x_{4}=3 \\ 4 x_{1}-x_{2}=4\end{array}\right. \) a) find the rank of the extended matrix of the system and find out whether the system is uncertain; 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.