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

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