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If (x)=|(alpha+x,theta+x,lambda+x),(beta...

If `(x)=|(alpha+x,theta+x,lambda+x),(beta+x,varphi+x,mu+x),(gamma+x,psi+x, v+x)|` show that `"Delta^"(x)=0a n d"Delta"(0)+S x ,w h e r eS` denotes he sum of all the cofactors of all elements in `"Delta"(0)a n d` dash denotes the derivative with respect of `xdot`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

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  2. 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...

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  3. If (x)=|(alpha+x,theta+x,lambda+x),(beta+x,varphi+x,mu+x),(gamma+x,psi...

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

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  5. If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],...

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  6. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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  7. 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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  8. Find the value of lambda for which |{:(2a1+b1 , 2a2+b2 , 2a3+b3),(2b1+...

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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. if a determinant of order 3xx 3 is formed by using the numbers 1 ...

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  11. If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) p...

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

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  13. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

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

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  15. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

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  16. 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 ^...

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

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

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  19. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

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  20. If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​is ...

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