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Without expanding or evaluating show that `|(0,b-a, c-a),( a-b,0,c-b),( a-c ,b-c,0)|=0` .

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If A is a skew-symmetric matrix of odd order n , then |A|=O .

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  2. Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

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  3. Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b)...

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  4. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

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  5. Prove that: |-a^2 ab ac ba -b^2 bc ...

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  6. Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

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  7. Evaluate: |(1,a ,a^2), (1,b,b^2) ,(1,c,c^2)| .

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  8. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

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  9. Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,g...

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  10. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

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  11. In a A B C ,if|1 1 1 1+cosA 1+cosB 1+cosC cos^2A+A cos^2B+cosB cos^2...

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  12. Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,...

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  13. If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove th...

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  14. For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z...

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  15. Using properties of determinants, show that |1 a a^2 -b c 1 b ...

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  16. Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

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  17. Let a ,\ b and c denote the sides B C ,\ C A and A B respectively of ...

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  18. If f(x)=|[a-1, 0,a] , [x,a-1,a], [x^2a, x, a]| , using properties of ...

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  19. Show that: x p q p x q q q xx-p)(x^2+p x-2q^2) .

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  20. If m in N and mgeq2 prove that: |1 1 1\ ^m C1\ ^(m+1)C1\ ^(m+2)C1\ ^m...

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