1.5.31 Systems of algebraic equations
condition: Solve a system of linear algebraic equations using Cramer and Gauss methods, find a unique solution, and check. \[ \left\{\begin{array}{l} x_{1}+2 x_{2}+3 x_{3}=3 \\ 2 x_{1}+6 x_{2}+4 x_{3}=6 \\ 3 x_{1}+10 x_{2}+8 x_{3}=21\end{array}\right. \]
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.