A) 5
B) 25
C) \[-1\]
D) 1
E) 125
Correct Answer: D
Solution :
\[\because \] \[a=\left[ \begin{matrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \\ \end{matrix} \right]\] \[\therefore \] \[B=adjA=\left[ \begin{matrix} 3 & 1 & 1 \\ -6 & -2 & 3 \\ -4 & -3 & 2 \\ \end{matrix} \right]\] Therefore adj \[B=\left[ \begin{matrix} 5 & -5 & 5 \\ 0 & 10 & -15 \\ 10 & 5 & 0 \\ \end{matrix} \right]\] Now\[|adj\,B|=\left| \begin{matrix} 5 & -5 & 5 \\ 0 & 10 & -15 \\ 10 & 5 & 0 \\ \end{matrix} \right|=625\] and| \[|C|=125|A|=125\left| \begin{matrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \\ \end{matrix} \right|=625\] \[\therefore \] \[\frac{|adj\,B|}{|C|}=\frac{625}{625}=1\]You need to login to perform this action.
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