행렬 $A= \left (\begin{matrix*}[r] 1 & 1 & -1 \\ 1 & 1 & -1 \end{matrix*} \right)$ 의 특이값 분해(singular value decomposition)가

$\displaystyle A= \left (\begin{matrix*}[r] u _ {11} & u _ {12} \\ u _ {21} & - \frac{1} {\sqrt {2}} \end{matrix*} \right) \left (\begin{matrix*}[r] \sqrt {6} & \sigma _ {12} & \sigma _ {13} \\ \sigma _ {21} & 0 & \sigma _ {23} \end{matrix*} \right) \left (\begin{matrix*}[r] \frac{1} {\sqrt {3}} & v _ {12} & v _ {13} \\ v _ {21} & - \frac{1} {\sqrt {2}} & v _ {23} \\ v _ {31} & 0 & \frac{2} {\sqrt {6}} \end{matrix*} \right) ^ {T}$

일 때, $u_ {11} ^ {2} + \left (\sigma _ {12} ^ {2} + \sigma _ {13} ^ {2} + \sigma _ {21} ^ {2} + \sigma _ {23} ^ {2} \right) + \left (v_ {12} ^ {2} +v_ {23} ^ {2} +v_ {31} ^ {2} \right)$ 의 값은?

• ①$\displaystyle \frac{7} {6}$
• ②$\displaystyle \frac{4} {3}$
• ③$\displaystyle \frac{3} {2}$
• ④$\displaystyle \frac{5} {3}$
• ⑤$\displaystyle \frac{11} {6}$