1.5.15 Systems of algebraic equations
condition: Solve the system using Cramer's formulas, matrix method, Gauss method. \[ \left\{\begin{array}{c} x_{1}+2 x_{2}+3 x_{3}=7 \\ 5 x_{1}+x_{2}-2 x_{3}=-7 \\ 3 x_{1}+x_{2}+x_{3}=2 \end{array}\right. \]
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.