MathProblemsBank

1.5.8 Systems of algebraic equations

Problem: For the given matrix equation a) solve it by the Gauss method, b) make a substitution check, c) solving (by the Gauss method) the equation \( A X=E \), find \( A^{-1} \), d) check the correctness of the answer by calculation \( A^{-1} A \), e) solve the given equation again using \( A^{-1} \), compare the results. \[ A=\left(\begin{array}{cccc} -2 & 3 & -1 & 0 \\ 2 & 0 & -2 & 0 \\ -6 & -3 & 3 & 0 \\ 0 & 0 & 0 & -2 \end{array}\right), B=\left(\begin{array}{cc} 1 & -2 \\ -3 & 0 \\ 2 & -1 \\ 1 & -1 \end{array}\right), A X=B . \]