A) 6
B) 3
C) 0
D) None of these
Correct Answer: C
Solution :
Applying\[{{C}_{1}}\to {{C}_{1}}+{{C}_{2}}+{{C}_{3}}\], we obtain \[-x\,\left| \,\begin{matrix} 1 & -6 & 3 \\ 1 & 3-x & 3 \\ 1 & 3 & -6-x \\ \end{matrix}\, \right|\] = 0 \[\Rightarrow \]\[-x\,\left| \,\begin{matrix} 1 & -6 & 3 \\ 0 & 9-x & 0 \\ 0 & 9 & -9-x \\ \end{matrix}\, \right|=0\] \[\Rightarrow \] \[-x(9-x)\,(-9-x)=0\Rightarrow x=0,\,9,\,-9\]. Trick: Check by assuming the values of x from the given options.
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