Show how to find the inverse of the matrix \(C= \left[\begin{array}{cccc} 1 & 2 & 4 & -7 \\ -1 & -1 & -2 & 2 \\ -1 & -2 & -3 & 2 \\ -1 & -1 & -3 & 8 \end{array}\right] \).
Answer:
\[C^{-1}= \left[\begin{array}{cccc} -4 & 1 & -3 & -3 \\ -6 & 6 & -7 & -5 \\ 6 & -5 & 6 & 5 \\ 1 & -1 & 1 & 1 \end{array}\right] \]