1.5.53 Systems of algebraic equations
condition: Solve the system of equations using the Gauss method. Indicate a general and one particular solution. \[ \left\{\begin{array}{l} -3 x_{1}+2 x_{2}+5 x_{3}-2 x_{4}=-1 \\ -4 x_{1}+13 x_{3}+x_{4}=-10 \\ -2 x_{1}+3 x_{2}-3 x_{3}-4 x_{4}=6 \\ 2 x_{1}-4 x_{2}+3 x_{3}+5 x_{4}=-8 \end{array}\right. \]
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.