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Evaluate |(1,omega,omega^2),(omega,omeg...

Evaluate `|(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)|` where `omega` is cube root of unity.

A

0

B

1

C

3

D

2

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AAKASH INSTITUTE-DETERMINANTS -SECTION A
  1. Let A=[{:(costheta,sintheta),(-sintheta,costheta):}], then abs(2A) is ...

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  2. Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| ...

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  3. If A is a square matrix of order n , prove that |Aa d jA|=|A|^n

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  4. The value of the determinant |{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| is eq...

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  5. The value of the determinant |{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| is eq...

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  6. If A is 3xx3 matrix and |A|=4, then |A^(-1)| is equal to

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  7. If A is a square matrix of order 3 such that ||A =3, then find the val...

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  8. If A, B and C are three sqare matrices of the same order such that A ...

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  9. If delta =|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| then the value of |(2a1+3...

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  10. If the system of equations x + 4ay + az = 0 and x + 3by + bz = 0 and x...

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  11. Let ax^3+bx^2+cx+d=|{:(3x,x+1,x-1),(x-3,-2x,x+2),(x+3,x-4,5x):}| then ...

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  12. Let x + y + z = 6, 4x + lambday - lambdaz = 0,3x + 2y - 4z = -5. The v...

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  13. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

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  14. The value of theta lying between 0 and pi/2 and satisfying the equatio...

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  15. |[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]|=0

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  16. If |{:(4,-4,0),(a,b+4,c),(a,b,c+4):}|=0, then a+b+c is equal to

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  17. The equation |{:(x-2,3,1),(4x-2,10,4),(2x-1,5,1):}|=0 is satisfied by

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  18. |{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is eqaual to

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  19. |{:(a,b,c),(b,c,a),(c,a,b):}| is equal to

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

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