If {\a}_{ {\i}}, {\b}_{ {\i}}, {\c}_{ {\i}} \in \mathbb{R}( {\i}=1,2,3) and x \in \mathbb{R} and \left|\begin{array}{c}{\a\end{array}_1+b_1 x , a_1 x+b_1 , c_1 ; {\a}_2+b_2 x , a_2 x+b_2 , c_2 ; {\a}_3+b_3 x , a_3 x+b_3 , c_3|}=0, then

\left|\begin{array}{ccc}a_1 & b_1 & c_1 \ a_2 & b_2 & c_2 \ a_3 & b_3 & c_3|\end{array}=0