1.5.51 Systems of algebraic equations
Condition: Solve a system of linear equations using Cramer's rule. \[ \left\{\begin{array}{l} 5 x_{1}-3 x_{2}+7 x_{3}=43 \\ 8 x_{1}+x_{2}+4 x_{3}=24 \\ 3 x_{1}-2 x_{2}+x_{3}=17 \end{array}\right. \]
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.