1.5.14 Systems of algebraic equations

Problem: Given a system of three linear equations with three unknowns. Required: 1) to find its solution using Cramer's formulas; 2) to solve by the Gauss method; 3) to write the system in matrix form and solve it using matrix calculus. Check the correctness of the calculation of the inverse matrix using matrix multiplication. \[ \left\{\begin{array}{c} 2 x_{1}+4 x_{2}-3 x_{3}=-10 \\ -x_{1}+5 x_{2}-2 x_{3}=5 \\ 3 x_{1}-2 x_{2}+4 x_{3}=3 \end{array}\right. \]