Find a Singular Value Decomposition of the Matrix A $$A = \left[ \begin{array} { r r r } 4 & 0 & - 4 \\4 & 4 & 4\end{array} \right]$$

question 9

Multiple Choice

Find a singular value decomposition of the matrix A.
- $$A = \left[ \begin{array} { r r r } 4 & 0 & - 4 \\4 & 4 & 4\end{array} \right]$$

• A)
• \[A = \left[ \begin{array} { r r }
• 0 & - 1 \\
• 1 & 0
• \end{array} \right] \left[ \begin{array} { r r r }
• 48 & 0 & 0 \\
• 0 & 32 & 0
• \end{array} \right] \left[ \begin{array} { c c c }
• 1 / \sqrt { 3 } & 1 / \sqrt { 3 } & 1 / \sqrt { 3 } \\
• - 1 / \sqrt { 2 } & 0 & 1 / \sqrt { 2 } \\
• 1 / \sqrt { 6 } & - 2 / \sqrt { 6 } & 1 / \sqrt { 6 }
• \end{array} \right]\]
• B)
• \[A = \left[ \begin{array} { r r }
• 0 & - 1 \\
• 1 & 0
• \end{array} \right] \left[ \begin{array} { c c c }
• 4 \sqrt { 3 } & 0 & 0 \\
• 0 & 4 \sqrt { 2 } & 0
• \end{array} \right] \left[ \begin{array} { c c c }
• 1 / \sqrt { 3 } & 1 / \sqrt { 3 } & 1 / \sqrt { 3 } \\
• - 1 / \sqrt { 2 } & 0 & 1 / \sqrt { 2 } \\
• 1 / \sqrt { 6 } & - 2 / \sqrt { 6 } & 1 / \sqrt { 6 }
• \end{array} \right]\]
• C)
• \[A = \left[ \begin{array} { r r }
• 0 & - 1 \\
• 1 & 0
• \end{array} \right] \left[ \begin{array} { c c c }
• 4 \sqrt { 3 } & 0 & 0 \\
• 0 & 4 \sqrt { 2 } & 0
• \end{array} \right] \left[ \begin{array} { c c c }
• 1 / \sqrt { 3 } & - 1 / \sqrt { 2 } & 1 / \sqrt { 6 } \\
• 1 / \sqrt { 3 } & 0 & - 2 / \sqrt { 6 } \\
• 1 / \sqrt { 3 } & 1 / \sqrt { 2 } & 1 / \sqrt { 6 }
• \end{array} \right]\]
• D)
• \[A = \left[ \begin{array} { c c }
• 0 & - 1 \\
• 1 & 0
• \end{array} \right] \left[ \begin{array} { c c }
• 4 \sqrt { 3 } & 0 \\
• 0 & 4 \sqrt { 2 }
• \end{array} \right] \left[ \begin{array} { r r r }
• 1 & 1 & 1 \\
• - 1 & 0 & 1 \\
• 1 & - 2 & 1
• \end{array} \right]\]

---

Definitions:

Meissner Corpuscles

Nerve endings in the skin that are specialized to detect light touch sensitivity.

Pacinian Corpuscle

Named for Italian anatomist Filippo Pacini (1812–1883). See lamellated corpuscle.

Sensory Receptor

A specialized cell or nerve ending that responds to specific stimuli, such as light, sound, or touch, and converts it into neural signals.

Deep Pressure

A type of firm tactile sensory input that is often calming and is used therapeutically to reduce chronic stress and anxiety.