1.5.29 Systems of algebraic equations
condition: Investigate a system of linear algebraic equations (prove compatibility, write down the fundamental system of solutions, find and check the general solution): \[ \left\{\begin{array}{l} -2 x_{1}+7 x_{2}+9 x_{3}-11 x_{4}=0 \\ -3 x_{1}+5 x_{2}+8 x_{3}-11 x_{4}=0 \end{array}\right. \]
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.