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If "Delta"r=|[2^(r-1),2. 3^(r-1),4. 5^(r...

If `"Delta"_r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, 5^n-1]|` Show that `sum_(r=1)^n"Delta"_r`= Constant

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,...

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  2. Let "T"r=|[r ,x,(n(n+1))/2], [2r-1,y, n^2],[ 3r-2,z,(n(3n-1))/2]| .whe...

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  3. If "Delta"r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, ...

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  4. If m is a positive integer and Dr=|(2r-1,\ ^m Cr,1),(m^2-1, 2^m ,m+1...

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  5. Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b,...

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  6. Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x...

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  7. Prove that: |(-2a , a+b, a+c),( b+a,-2b, b+c),( c+a , c+b,-2c)|=4(a+b...

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  8. Evaluate the following determinant: |[1 ,3, 5], [2 ,6, 10], [31, 11,...

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  9. Evaluate the following determinant: |[1, 4, 9], [4 ,9 ,16], [9, 16, ...

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  10. Without expanding, show that the value of each of the following dete...

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  11. Without expanding, show that the value of each of the following dete...

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  12. Without expanding, show that the value of the following determinant ...

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  13. Without expanding, show that the value of each of the following det...

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  14. Without expanding, show that the value of the following determinant...

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  15. Without expanding, show that the value of each of the following dete...

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  16. Evaluate the following: |[1,a, b c],[1,b, c a],[1,c, a b]|

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  17. Evaluate the following: |[0,x y^2,x z^2],[x^2y,0,y z^2],[x^2z, z y^2,...

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  18. If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"1=|(1, 1, 1),(...

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  19. Prove:\ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

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  20. Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^...

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