14.4.1 Sweep method

Problem: Solve the system of linear algebraic equations by the sweep method: \[ \left\{\begin{array}{c} -4 X_{1}+X_{2}=-5 \\ 2 X_{1}+5 X_{2}-X_{3}=-1 \\ 4 X_{2}-8 X_{3}+3 X_{4}=21 \\ -6 X_{3}-7 X_{4}=-9 \end{array}\right. \]