1.5.55 Systems of algebraic equations
Condition: Solve a homogeneous system of equations. Indicate the general solution and the fundamental system of solutions. \[ \left\{\begin{array}{l} 3 x_{1}+2 x_{2}+2 x_{3}+x_{4}=0 \\ -3 x_{1}+x_{2}-x_{3}+4 x_{4}=0 \\ 9 x_{1}+3 x_{2}+3 x_{3}-2 x_{4}=0 \\ -9 x_{1}-4 x_{3}+7 x_{4}=0 \end{array}\right. \]
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.