A) 0
B) 1
C) \[i\]
D) \[\omega \]
Correct Answer: A
Solution :
Let \[\Delta =\left| \begin{matrix} 1 & 1+i+{{\omega }^{2}} & {{\omega }^{2}} \\ 1-i & -1 & {{\omega }^{2}}-1 \\ -i & -1+\omega -i & -1 \\ \end{matrix} \right|\]. Applying \[({{R}_{1}}\to {{R}_{1}}+{{R}_{3}})\] \[=\left| \begin{matrix} 1-i & -1 & {{\omega }^{2}}-1 \\ 1-i & -1 & {{\omega }^{2}}-1 \\ -i & -1+\omega -i & -1 \\ \end{matrix} \right|=0\] (\[\because \] two rows are identical \[\therefore \omega +{{\omega }^{2}}=1\])
You need to login to perform this action.
You will be redirected in
3 sec
