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If omega is a complex cube root of uni...

If `omega` is a complex cube root of unity, show that `([[1,omega,omega^2],[omega,omega^2, 1],[omega^2, 1,omega]]+[[omega,omega^2, 1],[omega^2 ,1,omega],[omega,omega^2, 1]])[[1,omega,omega^2]]=[[0, 0 ,0]]`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Compute the elements a(43) and a(22) of the matrix: A=[[0, 1, 0],[ 2, ...

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  2. If A =[{:(0,1,0),(0,0,1),(p,q,r):}], show that ltbargt A^(3)= pI+qA+rA...

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  3. If omega is a complex cube root of unity, show that ([[1,omega,omega...

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  4. If A=[[1,-2,3],[0, 2 ,-1],[ -4,5-,2]] , find A (adj A) .

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  5. If A=[[4,-1,-4],[ 3, 0,-4],[ 3,-1,-3]] , show that A^2=I3dot

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  6. If [1\ \ 1\ \ x][[1, 0, 2],[ 0 ,2, 1],[ 2, 1, 0]][[1],[ 1],[ 1]]=0 , f...

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  7. If [2 3 5 7][1-3-2 4]=[-4 6-9x] , find xdot

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  8. If [x\ \ 4\ \ 1][[2, 1 ,2],[ 1, 0 ,2],[ 0 ,2,-4]][[x],[4],[-1]]=0 , fi...

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  9. If [1\ -1\ \ x][[0, 1,-1 ],[2 ,1 ,3],[ 1, 1, 1]][[0 ],[1],[ 1]]=0 , fi...

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  10. If A=[ (3,-2),( 4 ,-2) ] and I=[(1,0),(0,1)] , then prove that A^2-A+2...

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  11. If A=[[3 ,1],[-1 ,2]] and I=[[1, 0],[ 0, 1]] , then find lambda so tha...

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  12. If A=[[3 ,1],[-1, 2]] , show that A^2-5A+7I^2=O .

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  13. If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I^2=O .

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  14. Show that the matrix A=[(2, 3), (1, 2)] satisfies the equation A^3-4A...

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  15. Show that the matrix A=[(5, 3), (12 ,7)] then show A^2-12 A-I=O .

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  16. If A=[(3,-5),(-4, 2)] , find A^2-5A-14 Idot

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  17. If A=[[3, 1],[-1 ,2]] , show that A^2-5A+7I=O . Use this to find A^4

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  18. If A=[(3,-2) ,(4,-2)] , find k such that A^2-k A-2I^2=O .

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  19. If A=[(1, 0),(-1 ,7)] , find k such that A^2-8A+k I=O .

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  20. If A=[(1 ,2 ),(2, 1)] and f(x)=x^2-2x-3 , show that f(A)=O .

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