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Without expanding, show that the value o...

Without expanding, show that the value of each of the determinants is zero: `|1/a a^2 bc 1/b b^2 ac 1/c c^2 ab|`

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Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

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Prove that the value of each the following determinants is zero: |[(a^x+a^(-x))^2,(a^x-a^(-x))^2 ,1],[(b^y+b^(-y))^2,(b^y-b^(-y))^2 ,1],[(c^z+c^(-z))^2,(c^z-c^(-z))^2, 1]|

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. The maximum value of Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)...

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

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  3. Without expanding, show that the value of each of the determinants is ...

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  4. If m is a positive integer and Dr=|2r-1\ ^m Cr1m^2-1 2^m m+1s in^2(...

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  5. Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y...

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

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  7. If Deltar=|[2^(r-1) , 2.3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 ,...

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  8. Find a quadratic polynomial phi(x) whose zeros are the maximum and mi...

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  9. Let f(x)=|[secx,cosx,sec^2x+cotxcosecx],[cos^2x,cos^2x,cosec^2x],[1,co...

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  10. Show that: |[a,b-c,c+b],[a+c,b,c-a],[a-b,b+a,c]|=(a+b+c)(a^2+b^2+c^2).

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  11. If a , b , c are real numbers, prove that |[a,b,c],[b,c,a],[c,a,b]|=-(...

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  12. Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0

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  13. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

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  14. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

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  15. Solve : |[x-2,2x-3,3x], [-4x-4,2x-9,3x-16], [x-8,2x-27,3x-64]| = 0

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  16. If x+y+z=0 , prove that |[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y ...

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  17. If a , b , c are all positive and are pth ,qth and rth terms of a G.P....

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  18. Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-...

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  19. |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|...

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  20. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

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