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Show that abs(((a-x)^2,(a-y)^2,(a-z)^2...

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`abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) , ((c-x)^2,(c-y)^2, (c-z)^2)) = 2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Prove that |[a1alpha1+b1beta1, a1alpha2+b1beta2, a1alpha3+b1beta3], [a...

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  2. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value o...

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  3. Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) ...

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  4. If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value ...

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  5. If |[x^n, x^(n+2), x^(n+3)], [y^n, y^(n+2), y^(n+3)], [z^n, z^(n+2), z...

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  6. Solve the system of the equations: a x+b y+c z=d, a^2x+b^2y+c^2z=d^2,...

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  7. If |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=0 , then the line a x+b y+c=0...

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  8. If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solutio...

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  9. If [] denotes the greatest integer less than or equal to the real numb...

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  10. If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation...

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  11. If x ,y \ a n d \ z are not all zero and connected by the equations ...

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  12. Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-...

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  13. If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2...

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  14. For what values of k , the following system of equations possesses a...

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  15. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

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  16. Solve for x by Cramers rule x+y+z=6, x-y+z=2 3x+2y-4z=-5

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  17. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

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  18. Find the value of a \ a n d \ b if the system of equation a^2x-b y=a...

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  19. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

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  20. f(x)=|[cosx,x,1],[2sinx,x^2,2x],[tanx,x,1]| . Then value of lim(x->0)(...

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