1.5.10 Systems of algebraic equations

Problem: Solve the homogeneous system of equations \[ \left\{\begin{array}{l} x_{1}+2 x_{2}+x_{3}+4 x_{4}+x_{5}=0 \\ 2 x_{1}+x_{2}+3 x_{3}+x_{4}-5 x_{5}=0 . \\ x_{1}+3 x_{2}-3 x_{3}+6 x_{4}-x_{5}=0 \end{array}\right. \]