\subsection{Problem 8}
Let
\begin{equation*}
    \matr{A} = 
    \begin{bmatrix}
        \phantom{-}1 & -1 & \phantom{-}0 & \phantom{-}0 \\
        -1 & \phantom{-}2 & -1 & \phantom{-}0 \\
        \phantom{-}0 & -1 & \phantom{-}2 & -1 \\
        \phantom{-}0 & \phantom{-}0 & -1 & \phantom{-}2
    \end{bmatrix}
\end{equation*}

Check whether the symmetric matrix $\mathbf{A}$ is positive-definite. If so, apply the Cholesky factorization. Then, compute its inverse.

\lstinputlisting[style=Matlab-editor]{problems/Problem8.m}