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If x,y,z are positive and are the pth, q...

If x,y,z are positive and are the pth, qth and rth terms of a G.P. then prove that
`|[logx,p,1],[logy,q,1],[logz,r,1]|=0`

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SHARAM PUBLICATION-DETERMINANT-EXAMPLE
  1. if a, b,c are in A.P. then what is the value of: |[x+1,x+2,x+a],[x+2,x...

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  2. If p+q+r=0=a+b+c, then write the value of the determinant |[pa,qb,rc],...

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  3. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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  4. Answer the following: What are the values of x and y if [[x,y],[1,...

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  5. Write the value of k, if |{:(aa1,aa2,aa3),(ab1,ab2,ab3),(ac1,ac2,ac3...

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  6. Answer the following: What is the value of [[1/a,1,bc],[1/b,1,ca],[1...

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  7. Answer the following: In which inverval does the determinant A =[[1...

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  8. Evaluate the following determinants: [[1,0,-5863],[-7361,2,7361],[1,...

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  9. what is value of: |[cosec^2theta,cot^2theta,1],[cot^2theta,cosec^2thet...

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  10. Evaluate the following determinants. [[1,x,y],[0,sinx,siny],[0,cosx,c...

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  11. Evaluate the following determinants: [[a-b,b-c,c-a],[b-c,c-a,a-b],[c...

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  12. Write the value of |[2,3,4],[5,6,8],[6x,9x,12x]|

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  13. What is the value of : |[4,a,b+c ],[4,b,c+a],[4,c,a+b]|

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  14. What is the value of the determinant |[102,18,36],[1,3,4],[17,3,6]|?

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  15. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  16. Solve the following : [[0,x-a,x-b],[x+a,0,x-c],[x+b,x+c,0]]=0

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  17. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  18. Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^...

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  19. Factorise the determinant |[x^3-a^3,x^2,x],[b^2-a^3,b^2,b],[c^3-a^3,c^...

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  20. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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