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If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|...

If `|(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+c)`
where a, b, c are all different, then the determinant
`|(1,1,1),((x-a)^(2),(x -b)^(2),(x -c)^(2)),((x -b) (x -c),(x -c) (x -a),(x -a) (x -b))|` vanishes when

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MODERN PUBLICATION-DETERMINANTS-Revision Exercise
  1. Prove that Delta=[a+b x c+dx p+q x a x+b c x+d p x+q u v w]=(1-x^2)|a ...

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  2. Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,co...

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  3. If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+...

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  4. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

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  5. If a,b,c are in A.P. find the value of: ||2y+4, 5y+7, 8y+a],[3y+5, 6y+...

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  6. If ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+n)(l'x+m'y+n'), then prove tha...

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

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  8. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

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  9. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  10. If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

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  11. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}], then show that A^(3)=A^(-1).

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  12. If A=[1tanx-tanx1] , show that A^T\ A^(-1)=[cos2x-sin2xsin2xcos2x] .

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  13. If A=[(2,-3),(4,6)] " verify that " (adj A)^(-1)=(adj A^(-1)).

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  14. Prove that : adj. I(n)=I(n)

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  15. Prove that : adj.O=O

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  16. Prove that : I(n)^(-1)=I(n)

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  17. Find the inverse of each of the matrices given below : Let D= "dia...

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  18. Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}...

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  19. Find the inverse of each of the matrices given below : Obtain the in...

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  20. Use product [1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2] to solve th...

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