Find a Singular Value Decomposition of the Matrix A $$A = \left[ \begin{array} { r r } 4 & - 1 \\- 1 & 4\end{array} \right]$$

question 13

Multiple Choice

Find a singular value decomposition of the matrix A.
- $$A = \left[ \begin{array} { r r } 4 & - 1 \\- 1 & 4\end{array} \right]$$

• A) \(A = \left[ \begin{array} { r r } - 1 / \sqrt { 2 } & 1 / \sqrt { 2 } \\ 1 / \sqrt { 2 } & 1 / \sqrt { 2 } \end{array} \right] \left[ \begin{array} { l l } 9 & 0 \\ 0 & 9 \end{array} \right] \left[ \begin{array} { r r } - 1 / \sqrt { 2 } & 1 / \sqrt { 2 } \\ 1 / \sqrt { 2 } & 1 / \sqrt { 2 } \end{array} \right]\)
• B)
• \[A = \left[ \begin{array} { r r }
• - 1 & 1 \\
• 1 & 1
• \end{array} \right] \left[ \begin{array} { r r }
• 4 & - 1 \\
• - 1 & 4
• \end{array} \right] \left[ \begin{array} { r r }
• - 1 & 1 \\
• 1 & 1
• \end{array} \right]\]
• C)
• \[A = \left[ \begin{array} { r r }
• - 1 & 1 \\
• 1 & 1
• \end{array} \right] \left[ \begin{array} { l l }
• 5 & 0 \\
• 0 & 3
• \end{array} \right] \left[ \begin{array} { r r }
• - 1 & 1 \\
• 1 & 1
• \end{array} \right]\]
• D)
• \[\mathrm { A } = \left[ \begin{array} { r r }
• - 1 / \sqrt { 2 } & 1 / \sqrt { 2 } \\
• 1 / \sqrt { 2 } & 1 / \sqrt { 2 }
• \end{array} \right] \left[ \begin{array} { l l }
• 5 & 0 \\
• 0 & 3
• \end{array} \right] \left[ \begin{array} { r r }
• - 1 / \sqrt { 2 } & 1 / \sqrt { 2 } \\
• 1 / \sqrt { 2 } & 1 / \sqrt { 2 }
• \end{array} \right]\]

---

Definitions:

Simple Thinking

The process of reasoning or problem-solving in a straightforward, uncomplicated manner, often involving direct observation and practicality.

Availability Heuristic

A mental shortcut that relies on immediate examples that come to a person's mind when evaluating a specific topic, concept, method, or decision.

Representativeness Heuristic

Judging the likelihood of things in terms of how well they seem to represent, or match, particular prototypes; may lead us to ignore other relevant information.

Algorithm

A fixed, step-by-step procedure or set of rules for solving a problem or accomplishing a task.