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Prove that |x^2x^2-(y-z)^2y z y^2y^2-(...

Prove that `|x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-y)(y-z)(z-x)(x+y+z)(x^2+y^2+z^2)dot`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  2. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  3. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(...

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  4. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  5. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  6. Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)...

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  7. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

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

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  9. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[log a...

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  10. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

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  11. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

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  12. The number of distinct roots of abs((sinx, cosx, cosx),(cosx, sinx, co...

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  13. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

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  14. If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, the...

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  15. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

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  16. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

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  17. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

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  18. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

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  19. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

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  20. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, a) There are ex...

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