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using properties of determinants, prove that `abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)`.

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  2. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  3. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

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  4. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Find A^-1

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  5. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Using it solve the system of equat...

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  6. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  7. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] Prov...

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  8. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] ...

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  9. If A=[[a,1],[1,0]] is such that A^2=I then a equals

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  10. Solve the system of equations x-y+z=4,2x+y-3z=0,x+y+z=2 Using matr...

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  11. The value of abs((x,x-1) , (x+1,x):} is a)1 b)x c)x^2d)0

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  12. Using properties of determinants prove the following. abs[[1,x,x^2...

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  13. Prove that |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y).

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  14. Prove that abs[[1!,2!,3!],[2!,3!,4!],[3!,4!,5!]]=4!

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  15. Solve the system of Linear equations x+2y+z=8,2x+y-z=1,x-y+z=2

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  16. Inverse of the matrix [[0,1,2],[0,1,1],[1,0,2]]

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  17. Find the values of x in which abs[[3,x],[x,1]]=abs[[3,2],[4,1]]

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  18. Using the property of determinants,show that the points A(a,b+c),B(b...

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  19. Examine the consistency of system of following equations: 5x-6y+4z...

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  20. Let B is a square matrix of order 5, then abs[kB] is equal to….

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