At what value of \[x,\]will \[\left| \,\begin{matrix} x+{{\omega }^{2}} & \omega & 1 \\ \omega & {{\omega }^{2}} & 1+x \\ 1 & x+\omega & {{\omega }^{2}} \\ \end{matrix}\, \right|=0\] [DCE 2000, 01]

At what value of \[x,\]will \[\left| \,\begin{matrix} x+{{\omega

1.	At what value of \[x,\]will \[\left\| \,\begin{matrix} x+{{\omega }^{2}} & \omega & 1 \\ \omega & {{\omega }^{2}} & 1+x \\ 1 & x+\omega & {{\omega }^{2}} \\ \end{matrix}\, \right\|=0\] [DCE 2000, 01]
A.	\[x=0\]
B.	\[x=1\]
C.	\[x=-1\]
D.	None of these
Answer» B. \[x=1\]

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At what value of \[x,\]will \[\left| \,\begin{matrix} x+{{\omega }^{2}} & \omega & 1 \\ \omega & {{\omega }^{2}} & 1+x \\ 1 & x+\omega & {{\omega }^{2}} \\ \end{matrix}\, \right|=0\] [DCE 2000, 01]

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