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Using properties of determinants prove t...

Using properties of determinants prove the
following.
`abs[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2`

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Solve the system of equations x-y+z=4,2x+y-3z=0,x+y+z=2 Using matr...

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

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

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

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

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

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

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

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

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

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  12. Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

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  13. Check the consistency of the following equations, 2x+3y+z=6,x+2y-z...

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  14. If abs[[x,3],[5,2]]=5,then x=…..

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  15. By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],...

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  16. Solve the following system of linear Equations,using matrix method, ...

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  17. Find values of x if i) |[2 , 4],[ 5, 1]|=|[2 x, 4], [6, x]| ii) ...

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  18. Find the values of x, if |(2,3),(4,5)|=|(x,3),(2x,5)|

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

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  20. Find the adjoint of B=[[1,-1,2],[2,3,5],[-2,0,1]]

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