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Prove the following: [[a,b,c],[b,c,a],...

Prove the following:
`[[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3`

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MBD PUBLICATION-DETERMINATES-QUESTION BANK
  1. For what value of lamda the system of equations x+y+z=6, 4x+lamda y-...

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  2. If A is a 3xx3 matrix and absA=2, then which matrix is represented by ...

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  3. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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  4. Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+...

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  5. Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a...

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  6. Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

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  7. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  8. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

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  9. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  10. Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] =a^3+b^...

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  11. Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =...

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  12. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

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  13. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  14. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  15. Without expanding show that the following determinant is equal to Ax+B...

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  16. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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  17. If a1, a2,........,an are in G.P. and ai gt 0 for every i, then find t...

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  18. If f(x)=[[1+sin^2x,cos^2x,4sin2x],[sin^2x,1+cos^2x,4sin2x],[sin^2x,cos...

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  19. If fr(x),gr(x),hr(x),r=1, 2, 3 are polynomials in x such that fr(a)=...

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  20. If f(x)=[[cosx,sinx,cosx],[cos2x,sin2x,2cos2x],[cos3x,sin3x,3cos3x]] ...

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