A) 12
B) 24
C) -12
D) - 24
Correct Answer: B
Solution :
Trick: Put\[x=1\], then we have \[\left| \,\begin{matrix} 2 & 2 & -1 \\ 4 & 3 & 0 \\ 6 & 1 & 1 \\ \end{matrix}\, \right|=A-12\Rightarrow \left| \,\begin{matrix} 0 & 2 & -1 \\ 1 & 3 & 0 \\ 5 & 1 & 1 \\ \end{matrix}\, \right|=A-12\] {Apply\[{{C}_{1}}\to {{C}_{1}}-{{C}_{2}}\]} \[\Rightarrow \] \[-2+(-1)\,(-14)=A-12\Rightarrow A=24\].
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