Find a QR Factorization of the Matrix A $$A = \left[ \begin{array} { r r } - 4 & 6 \\2 & - 18 \\0 & 6\end{array} \right]$$

Multiple Choice

Find a QR factorization of the matrix A.
- $$A = \left[ \begin{array} { r r } - 4 & 6 \\2 & - 18 \\0 & 6\end{array} \right]$$

A)
$$Q = \left[ \begin{array} { r r } - 4 & - 6 \\2 & - 12 \\0 & 6\end{array} \right] , R = \left[ \begin{array} { c c } \frac { - 10 } { \sqrt { 5 } } & \frac { 30 } { \sqrt { 5 } } \\0 & \frac { 36 } { \sqrt { 6 } }\end{array} \right]$$
B)
$$Q = \left[ \begin{array} { c c } \frac { 2 } { \sqrt { 5 } } & - \frac { 1 } { \sqrt { 6 } } \\- \frac { 1 } { \sqrt { 5 } } & - \frac { 2 } { \sqrt { 6 } } \\0 & \frac { 1 } { \sqrt { 6 } }\end{array} \right] , R = \left[ \begin{array} { c c } \frac { - 10 } { \sqrt { 5 } } & \frac { 30 } { \sqrt { 5 } } \\0 & \frac { 36 } { \sqrt { 6 } }\end{array} \right]$$
C)
$Q=\left[\begin{array}{rr}-4 & 6 \\2 & -18 \\0 & 6\end{array}\right], R=\left[\begin{array}{ll}\frac{30}{\sqrt{5}} & 0 \\\frac{36}{\sqrt{6}} & \frac{-10}{\sqrt{5}}\end{array}\right]$

D)