A) 6
B) 3
C) 0
D) None of these
Correct Answer: C
Solution :
\[\left| \begin{matrix} 3-x & -6 & 3 \\ -6 & 3-x & 3 \\ 3 & 3 & -6-x \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[\left| \begin{matrix} -x & -x & -x \\ -6 & 3-x & 3 \\ 3 & 3 & -6-x \\ \end{matrix} \right|\] \[[{{R}_{1}}\to {{R}_{2}}+{{R}_{3}}+{{R}_{1}}]\] \[\Rightarrow \] \[x\left| \begin{matrix} -1 & -1 & -1 \\ -6 & 3-x & 3 \\ 3 & 3 & {} \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[x=0\]or \[\left| \begin{matrix} -1 & -1 & -1 \\ -3 & 3-x & 3 \\ 3 & 3 & -6-x \\ \end{matrix} \right|=0\]
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