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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Definitions:

Tendon

A fibrous connective tissue that attaches muscle to bone, transmitting forces to produce movement at joints.

Upper Leg Muscle

Refers to the muscles located in the thigh region, such as the quadriceps and hamstrings.

Gemellus

A term referring to one of a pair of small muscles located in the buttocks, involved in the rotation of the thigh.

Hip Muscle

The hip muscle is part of a group of muscles around the hip joint that supports movement and stability of the hip, including flexors, extensors, abductors, and adductors.