Let $$A = \left[ {\begin{matrix} {{a_1}} \\ {{a_2}} \\ \end{matrix} } \right]$$ and $$B = \left[ {\begin{matrix} {{b_1}} \\ {{b_2}} \\ \end{matrix} } \right]$$ be two 2 $\times$ 1 matrices with real entries such that A = XB, where $$X = {1 \over {\sqrt 3 }}\left[ {\begin{matrix} 1 & { - 1} \\ 1 & k \\ \end{matrix} } \right]$$, and k $\in$ R. If $a_1^2$+$a_2^2$=${2 \over 3}$(b $_1^2$ + b $_2^2$) and (k2 + 1) b $_2^2 e-$ 2b1b2, then the value of k is $\underline{\hspace{2cm}}$.