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The value of the determinant |a^2a1cosn ...

The value of the determinant `|a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n+1)xsin(n+2)x|` is independent of n (b) a (c) x (d) none of these

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

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  2. If Delta1=|(1, 1 ,1),(a, b, c ),(a^2,b^2,c^2)|,Delta2=|(1,b c, a),(1,c...

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  3. The value of the determinant |a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n...

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  4. Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,si...

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  5. Evaluate: (i) |(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)|

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  6. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by expanding it along th...

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  7. Evaluate the determinant D=|[2 ,3,-2],[ 1, 2 ,3],[-2, 1,-3]| by expa...

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  8. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]|

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  9. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by method.

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  10. For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singul...

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  11. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

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  12. If A=[1 3 2 1] , find the determinant of the matrix A^2-2A .

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  13. If A=[1 2 4 2] , then show that |2A|=4|A| .

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  14. If |[x-2 ,-3], [3x, 2x]|=3 , find the values of x

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  15. Let |[3,y],[x,1]|=|[3,2],[4,1]| Find possible values of x and y if x,y...

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  16. Evaluate the determinant =|((log)3 512,(log)4 3),((log)3 8,(log)4 9)...

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  17. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

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  18. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

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  19. If [ ] denotes the greatest integer less than or equal to the real nu...

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  20. Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),...

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