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Let omega=-1/2+i(sqrt(3))/2dot Then the ...

Let `omega=-1/2+i(sqrt(3))/2dot` Then the value of the determinant `|1 1 1 1-1-omega^2omega^2 1omega^2omega^4|` is `3omega` b. `3omega(omega-1)` c. `3omega^2` d. `3omega(1-omega)`

A

`3 omega`

B

`3 omega (omega -1)`

C

`3 omega^(2)`

D

`3 omega (1 - omega)`

Text Solution

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The correct Answer is:
D
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Let omega=-1/2+i(sqrt(3))/2 . Then the value of the determinant |(1,1,1),(1,-1-omega^2,omega^2),(1,omega^2,omega^4)| is (A) 3omega (B) 3omega(omega-1) (C) 3omega^2 (D) 3omega(1-omega)

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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. Using properties of determinants, show that |{:(x, p, q), ( p, x, q)...

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  2. The factors of |(x,a,b),(a,x,b),(a,b,x)|, are

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  3. Let omega=-1/2+i(sqrt(3))/2dot Then the value of the determinant |1 1 ...

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  4. If a+b+c=0, one root of |a-x c b c b-x a b a c-x|=0 is x=1 b. x=2 c. ...

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  5. suppose D= |{:(a(1),,b(1),,c(1)),(a(2),,b(2),,c(2)),(a(3),,b(3),,c(3...

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  6. A and B are two non-zero square matrices such that AB = O. Then,

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  7. The roots of the equation |{:(x-1,1,1),(1,x-1,1),(1,1,x-1):}|=0 are

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  8. From the matrix equation AB=AC, we conclude B=C provided.

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  9. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

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  10. The value of |(11,12,13),(12,13,14),(13,14,15)|, is

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  11. |{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is equal to:

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  12. If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|, then

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  13. Let a ,b , c be the real numbers. The following system of equations in...

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  14. A ,\ B are two matrices such that A B and A+B are both defined; sho...

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  15. If omega is an imaginary cube root of unity, then the value of |(a,b o...

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  16. If alpha, beta are non - real numbers satifying x^3-1=0 then the value...

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  17. The value of the determinant |(-1,1,1),(1,-1,1),(1,1,-1)| is equal to

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  18. In a third order determinant, each element of the first column consist...

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  19. A root of the equation |[3-x,-6,3],[-6,3-x,3],[3,3,-6-x]|=0

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  20. For positive numbers x, y and z, the numerical value of the determinan...

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