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What is the value of |(1-i,omega^(2),-om...

What is the value of `|(1-i,omega^(2),-omega),(omega^(2)+i,omega,-i),(1-2i-omega^(2),omega^(2)-omega,i-omega)|` where `omega` is the rube root of unity ?

A

-1

B

1

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
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If omega is a cube root of unity, then |(1-i,omega^2, -omega),(omega^2+i, omega, -i),(1-2i-omega^2, omega^2-omega,i-omega)|= (A) -1 (B) i (C) omega (D) 0

PUNEET DOGRA-DETERMINANTS -PREV YEAR QUESTIONS
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  15. The system of equation 2x + y - 3z = 5 3x - 2y + 2z = 5 5x - 3y ...

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  16. The value of the determinants |("cos"^(2)(theta)/(2),"sin"^(2)(theta)/...

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  17. The system of equation kx + y + z = 1, x + ky + z = k and x + y + kz =...

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  18. If p + q + r = a + b + c = 0, then the determinant |(pa,qb,rc),(qc,ra,...

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  21. What is the value of the determinant ? |(1,1,1),(1,1+xyz,1),(1,1,1+x...

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