The function $f(x) = \left[ {\begin{array}{*{20}{c}} {\left| {x\, - \,3} \right|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}&{,\,\,\,\,x\, \geqslant \,1} \\ {\left( {\tfrac{{{x^2}}}{4}} \right)\, - \,\left( {\tfrac{{3\,x}}{2}} \right)\, + \,\left( {\tfrac{{13}}{4}} \right)}&{,\,\,\,\,x\, < \,1} \end{array}} \right.$ is :
→If $\Delta = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ and ${A_1},{B_1},{C_1}$denote the co-factors of ${a_1},{b_1},{c_1}$ respectively, then the value of the determinant $\left| {\begin{array}{*{20}{c}}{{A_1}}&{{B_1}}&{{C_1}}\\{{A_2}}&{{B_2}}&{{C_2}}\\{{A_3}}&{{B_3}}&{{C_3}}\end{array}} \right|$ is
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