1.5.59 Systems of algebraic equations
Condition: Find the general solution of the system of equations using the Gaussian method: \[ \left\{\begin{array}{c} x_{1}-2 x_{2}-2 x_{3}+x_{4}=1 \\ 2 x_{1}+26 x_{2}-x_{3}+x_{4}=1 \\ x_{1}-x_{3}+x_{3}-2 x_{4}=26 \end{array}\right. \]
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.