1.5.35 Systems of algebraic equations
Condition: Given a system of linear equations \( \left\{\begin{array}{l}2 x_{1}+4 x_{2}+x_{3}-x_{4}=6 \\ 2 x_{1}+3 x_{2}-x_{3}-x_{4}=3 \\ x_{1}+4 x_{2}+2 x_{3}-x_{4}=6\end{array}\right. \) a) find the ranks of: the system matrix and the extended system matrix; b) show that the system is consistent; 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.