For the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 5&3 \\ 1&3 \end{array}} \right],\]   ONE of the normalized eigen vectors is given as

A. \[\left( {\begin{array}{*{20}{c}} {\frac{1}{2}} \\ {\frac{{\sqrt 3 }}{2}} \end{array}} \right)\]

B. \[\left( {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}} \\ {\frac{{ - 1}}{{\sqrt 2 }}} \end{array}} \right)\]

C. \[\left( {\begin{array}{*{20}{c}} {\frac{3}{{\sqrt {10} }}} \\ {\frac{{ - 1}}{{\sqrt {10} }}} \end{array}} \right)\]

D. \[\left( {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 5 }}} \\ {\frac{2}{{\sqrt 5 }}} \end{array}} \right)\]

Answer: Option B