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)
• \[A = \left[ \begin{array} { c c }
• 0 & - 1 \\
• 1 & 0
• \end{array} \right] \left[ \begin{array} { c c }
• 4 \sqrt { 3 } & 0 \\
• 0 & 4 \sqrt { 2 }
• \end{array} \right] \left[ \begin{array} { r r r }
• 1 & 1 & 1 \\
• - 1 & 0 & 1 \\
• 1 & - 2 & 1
• \end{array} \right]\]

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Definitions:

Short Run

The short run is a time period in economics during which at least one input is fixed, limiting the ability of the economy or firm to adjust its output levels.

Market Price

The price of a good or service as determined by supply and demand in the open market.

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A type of legume native to East Asia, widely grown for its edible bean used in a variety of foods and products.

Short-Run Profit

Profits earned by a firm in a period where at least one input is fixed, reflecting immediate financial performance.