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Prove that: {:|(a+b+nc,na-a,nb-b),(nc-...

Prove that:
`{:|(a+b+nc,na-a,nb-b),(nc-c,b+c+na,nb-b),(nc-c,na-a,c+a+nb)| = n(a+b+c)^3`

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. If A=[(3,1),(7,5)] , find x and y so that A^2 + xI-yA=0. Hence find A^...

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  2. Without expanding, show that the following determinants vanish: {:|(...

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  3. Prove that: {:|(a+b+nc,na-a,nb-b),(nc-c,b+c+na,nb-b),(nc-c,na-a,c+a+...

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  4. Prove that triangle = |[a+bx,c+dx,p+qx],[ax+b,cx+d,px+q],[u,v,w]| = (1...

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  5. If |[[x,2],[18,x]]|=|[[6,2],[18,6]]|, then x is equal to:

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  6. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  7. Which of the following is correct

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  8. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

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  9. Let A be a non-singular matrix of order 3 xx 3. Then I adj. A I is equ...

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  10. Select the Correct Option If A is an invertible matrix of order 2, the...

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  11. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  12. Let A = [[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], wher...

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  13. If |(2x,5),(8,x)|=|(6,-2),(7,3)| , write the value of x.

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  14. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

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  15. If A,B and C are angles of a triangle, then the determinant: {:|(-1,...

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  16. If determinant A is of order 2xx2 and |A|=3, then the value of |2A| is

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  17. Write the value {:|(x,x+1),(x-1,x)|

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  18. If matric A = {:|(3-2x,x+1),(2,4)| is singular, then x is equal to

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  19. The value of x from the equation {:|(x,2,3),(4,x,1),(x,2,5)|=0 is

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  20. If A is a square matrix of order 3 such that |adjA|=16, then |A| is

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