1.5.30 Systems of Algebraic Equations

Condition: to solve the system of linear algebraic equations, by the method of Gauss to find the rank of system and its general solution, to single out a private solution from the latter and all the fundamental solutions of the corresponding homogeneous system, to make an audit of everyone. \[ \left\{\begin{array}{l} x_{1}+x_{2}-3 x_{4}-x_{5}=0 \\ x_{1}-x_{2}+2 x_{3}-x_{4}=0 \\ 4 x_{1}-2 x_ {2} +6 x_ {3} +3 x_ {4} -4 x_ {5} = 0 \\ 2 x_ {1} +4 x_ {2} -2 x_ {3} +4 x_7 x_ {5} = 0 \ End {Array} \ Right. \]