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

question 41

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) \(Q=\left[\begin{array}{rr} -4 & 6 \\ 2 & -18 \\ 0 & 6 \end{array}\right], R=\left[\begin{array}{ll} \frac{30}{\sqrt{5}} & 0 \\ \frac{36}{\sqrt{6}} & \frac{-10}{\sqrt{5}} \end{array}\right]\)

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