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

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