1.5.5 Systems of algebraic equations

Problem: Solve the matrix equation using the Gauss method: \( A X=B \), where \[ A=\left(\begin{array}{ccccc} 2 & 0 & -3 & 15 & 14 \\ -2 & 3 & -2 & 4 & 1 \\ -2 & 2 & -4 & 16 & 18 \\ -4 & 2 & -2 & 5 & 10 \\ 3 & -1 & 3 & -13 & -19 \end{array}\right), B=\left(\begin{array}{c} 19 \\ 17 \\ 16 \\ 0 \\ -1 \end{array}\right) \text {. } \]