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

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Definitions:

Cell Membrane

The semipermeable membrane surrounding the cytoplasm of a cell, which controls the entry and exit of substances.

Phospholipids

A type of fat molecule that forms the main structural component of cell membranes.

Cholesterol

A type of lipid molecule that is crucial for the formation of cell membranes and serves as a precursor for the synthesis of certain hormones and vitamins.

Steroid

A type of organic molecule with a characteristic structure consisting of four fused rings, playing various roles in the body including as components of cell membranes and as signaling molecules.