If one of the cube roots of 1 be ω , then | 1 1+ω^2 ω^2 1-i -1 ω^2-1 -i -1+ω -1 |=

Correct answer: (D) 0. Hints: C_2 arrow C_2-C_3 C_3 arrow C_3+C_2 C_3 arrow C_3+ω C_1 C_2 arrow C_2-C_1

Q80 / 160 · WBJEE 2011 · Mathematics

If one of the cube roots of 1 be \(\omega\), then \(\left|\begin{array}{ccc}1 & 1+\omega^2 & \omega^2 \\ 1-i & -1 & \omega^2-1 \\ -i & -1+\omega & -1\end{array}\right|=\)

A
\(\omega\)
B
1
C
1
Correct answer
D
0

Solution

Hints: \(\mathrm{C}_2 \rightarrow \mathrm{C}_2-\mathrm{C}_3\) \(\begin{aligned} & \mathrm{C}_3 \rightarrow \mathrm{C}_3+\mathrm{C}_2 \\ & \mathrm{C}_3 \rightarrow \mathrm{C}_3+\omega \mathrm{C}_1 \\ & \mathrm{C}_2 \rightarrow \mathrm{C}_2-\mathrm{C}_1 \end{aligned}\)

Hence, the correct answer is option: 'D'.

If one of the cube roots of 1 be \(\omega\), then \(\left|\begin{array}{ccc}1 & 1+\omega^2 & \omega^2 \\ 1-i & -1 & \omega^2-1 \\ -i & -1+\omega & -1\end{array}\right|=\)

Solution

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