1.5.22 Systems of algebraic equations
Condition: Solve the system of equations using Cramer's formulas: \[ \left\{\begin{array}{c} 11 x_{1}+7 x_{2}+3 x_{3}+5 x_{4}=-2 \\ 7 x_{1}+4 x_{2}+4 x_{3}+3 x_{4}=4 \\ 12 x_{1}+6 x_{2}+11 x_{3}+7 x_{4}=15 \\ 9 x_{1}+5 x_{2}+6 x_{3}+5 x_{4}=6 \end{array}\right. \]
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.