1.5.50 Systems of algebraic equations
Condition: Find a general solution to the system of linear equations using the Gauss method. \[ \left\{\begin{array}{l} x_{1}-x_{3}-2 x_{4}-2 x_{5}=2 \\ 2 x_{1}-x_{2}-x_{3}-2 x_{4}-3 x_{5}=2 \\ 2 x_{1}+x_{2}-3 x_{3}-6 x_{4}-5 x_{5}=6 \end{array}\right. \]
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.