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If omega = (-1+sqrt3i)/2 , find the valu...

If `omega = (-1+sqrt3i)/2` , find the value of `|(1, omega, omega^2),(omega, omega^2, 1),(omega^2, 1 , omega)|`

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. If A of order n xx n and det A = k, then find det (adj A).

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  2. The value of |[[1,a,b+c],[1,b,c+a],[1,c,a+b]]| is

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  3. If omega = (-1+sqrt3i)/2 , find the value of |(1, omega, omega^2),(ome...

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  4. Compute |(2,a,3),(4,b,6),(6,c,9)|

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  5. Find the area of the triangle whose vertices are (0,0),(a,0) and (0,b)

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  6. For what x, are the points (1,x), (2,2x), (3,3x) collinear?

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  7. Write down the adjoint of the matrix [(2,-1),(4,3)]

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  8. If A^-1 = [(0,1),(1,0)] and B^-1 = [(1,0),(0,1)], find (AB)^-1

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  9. Is the following system of equations consistent? 2x - 3y = 4, 3x + 2 y...

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  10. Find the number of solutions of the system of equations. 3x + 2y = 5, ...

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  11. If A is a scalar matrix of order 3xx3 such that a22 = 5, then find det...

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  12. If A is of order 5xx5 and det A = 1, find det (-A)

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  13. Find A^-1 if A = [(2,0),(0,3)]

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  14. If A = [(a,b),(c,d)], find adj (adj A)

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  15. If |A| = -5, find A (adj A).

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  16. Write the value of the determinant |(0,a-b,a-c), (b-a, 0, b-c),(c-a, c...

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  17. Find x if |(2x, 5),(3,x)| = |(16,5),(3,2)|

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  18. Without expanding, show that : Delta = {:|(cosec^2theta,cot^2theta,1...

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  19. Evaluate the following determinants: {:|(x^2-x+1,x-1),(x+1,x+1)|

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  20. True or False statements : If and B are invertible matrices such tha...

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