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Prove that |a x-b y-c z a y+b x c x+a z...

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

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CENGAGE-DETERMINANTS-All Questions
  1. For all values of A,B,C and P,Q,R show that |{:(cos(A-P),,cos(A-Q)...

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  2. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

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  3. Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c...

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  4. If (x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x| show...

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  5. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

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  6. If p+q+r=0=a+b+c =0, then the value of the determnalnt |p a q b r c q ...

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  7. Let =|2a1b1a1b2+a2b1a1b3+a3b1a1b2+a2b1 2a2b2a2b3+a3b2a1b3+a3b1a3b2+a2b...

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  8. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

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  9. Evaluate |^x C1^x C2^x C3^y C1^y C2^y C3^z C1^z C2^z C3|

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  10. Using factor theorem, show that |(-2a,a+b,c+a),(a+b,-2a,b+c),(c+a,c+b,...

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  11. If a determinant of order 3xx3 is formed by using the numbers 1 or -1 ...

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  12. If z=|-5 3+4i5-7i3-4i6 8+7i5+7i8-7i9|,t h e nz is purely real purely ...

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  13. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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  14. If omega = cis (2pi)/(3), then number of distinct roots of |(z+1,omega...

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  15. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

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  16. Consider the determinant "Delta"=|a1+b1x^2a1x^2+b1c1a2+b2x^2a2x^2+b2c2...

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  17. Evaluate : int dx/(2x^2+x+3)

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  18. If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...

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  19. If A , B ,a n dC are the angles of triangle, show that the system o...

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  20. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

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