\subsection{Problem 12}

Compute the QR factorization of the matrix:

\begin{equation*}
    \matr{A} = 
    \begin{bmatrix}
    0 & -1 & -3  \\
    0 & \phantom{-}0 & -2 \\
    0 & -2 & -1 
    \end{bmatrix}
\end{equation*}

How many flops (multiplications/divisions, additions/subtractions) are needed to perform the QR factorization with the Householder transformations and Givens rotations?