
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.
\[
A=\left(\begin{array}{cccc}
-2 & 3 & -1 & 0 \\
2 & 0 & -2 & 0 \\
-6 & -3 & 3 & 0 \\
0 & 0 & 0 & -2
\end{array}\right), B=\left(\begin{array}{cc}
1 & -2 \\
-3 & 0 \\
2 & -1 \\
1 & -1
\end{array}\right), A X=B .
\]