1.5.56 Systems of algebraic equations
Condition: Given a system of three linear equations with three unknowns. It is required to write the system in matrix form and solve it using matrix calculus. Check the correctness of the inverse matrix calculation using multiplication. \[ \left\{\begin{array}{c} -2 x_{2}-5 x_{3}=-12 \\ -2 x_{1}-x_{2}+3 x_{3}=7 \\ -x_{1}+x_{2}+x_{3}=4 \end{array}\right. \]
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.