A) \[-1\]
B) \[-2\]
C) \[-3\]
D) \[4\]
Correct Answer: C
Solution :
\[\left| \begin{matrix} -12 & 0 & \lambda \\ 0 & 2 & -1 \\ 2 & 1 & 15 \\ \end{matrix} \right|=-360\] \[\Rightarrow \] \[-12\left| \begin{matrix} 2 & -1 \\ 1 & 15 \\ \end{matrix} \right|+\lambda \left| \begin{matrix} 0 & 2 \\ 2 & 1 \\ \end{matrix} \right|=-360\] \[\Rightarrow \] \[-12(30+1)-4\lambda =-360\] \[\Rightarrow \] \[-372+360=4\lambda \] \[\Rightarrow \] \[\lambda =-\frac{12}{4}=-3\]
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