1.5.54 Systems of algebraic equations
Condition: Solve the system using the inverse matrix and Cramer formulas. \[ \left\{\begin{array}{c} 3 x_{1}+x_{2}-x_{3}=10 \\ -3 x_{1}+3 x_{2}+2 x_{3}=8 \\ 5 x_{1}+2 x_{2}+8 x_{3}=-1 \end{array}\right. \]
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.