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Using the properties of determinants, prove that following `|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3`

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Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Without expanding, show that the value of each of the determinants is ...

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

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  3. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  4. Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+...

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  5. For any triangleABC, the value of determinant |[sin^2A,cotA,1],[sin^2B...

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

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  7. If x , y in R , then the determinant =|(cos x , -sin x,1),(sin x, cos...

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  8. The maximum value of Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)...

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

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

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

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

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

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

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

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

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

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  20. 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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