1.5.39 Systems of algebraic equations
Condition: Given a homogeneous system of linear equations \( \left\{\begin{array}{l}2 x_{1}+2 x_{2}-4 x_{3}=0 \\ x_{1}-2 x_{2}+x_{3}=0 \\ x_{1}-x_{3}=0\end{array}\right. \) a) find out whether the system has a non-trivial solution; b) find the general solution of the system; c) find a non-trivial particular solution (if it exists) and test 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.