1.5.26 Systems of algebraic equations
condition: Solve the system of equations: \[ \left\{\begin{array}{l} 2 x_{1}+x_{2}-x_{3}=5 \\ x_{1}-2 x_{2}+3 x_{3}=-3 \\ 7 x_{1}+x_{2}-x_{3}=10 \end{array}\right. \]
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.