Find the $Q R$ factorization of the following matrices: (a) $\left(\begin{array}{rr}1 & -3 \\ 2 & 1\end{array}\right)$,
(b) $\left(\begin{array}{ll}4 & 3 \\ 3 & 2\end{array}\right)$,
(c) $\left(\begin{array}{rrr}2 & 1 & -1 \\ 0 & 1 & 3 \\ -1 & -1 & 1\end{array}\right)$,
(d) $\left(\begin{array}{rrr}0 & 1 & 2 \\ -1 & 1 & 1 \\ -1 & 1 & 3\end{array}\right)$,
(e) $\left(\begin{array}{rrr}0 & 0 & 2 \\ 0 & 4 & 1 \\ -1 & 0 & 1\end{array}\right)$,
(f) $\left(\begin{array}{llll}1 & 1 & 1 & 1 \\ 1 & 2 & 1 & 0 \\ 1 & 1 & 2 & 1 \\ 1 & 0 & 1 & 1\end{array}\right)$.