MathProblemsBank

1.5.27 Systems of algebraic equations

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

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.

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