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If A=[(ab ,b^2) ,(-a^2 ,-ab)] , show tha...

If `A=[(ab ,b^2) ,(-a^2 ,-ab)]` , show that `A^2=O` .

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

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  2. If A=[(1,1),(0,1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3 ),(...

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  3. If A=[(ab ,b^2) ,(-a^2 ,-ab)] , show that A^2=O .

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  4. If A=[cos2thetasin2theta-sin2thetacos2theta] , find A^2 .

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  5. If A=[(2 ,-3, -5), (-1, 4, 5),( 1, -3 ,-4)] and B=[(-1, 3, 5), (1,-3, ...

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  6. If A=[[0 ,c,-b],[-c, 0, a],[ b, -a, 0]] and B=[[a^2, ab, ac],[ ab, ...

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  7. If A=[(2, -3, -5) , (-1, 4, 5), (1, -3, -4)] and B=[(2, -2, -4) , (-1,...

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  8. Let A=[(-1 ,1,-1),(3,-3 ,3),( 5, 5, 5)] and B=[(0 ,4 ,3 ),(1,-3,-3),(-...

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  9. For the following matrices verify the associativity of matrix multip...

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  10. For the following matrices verify the distributivity of matrix multi...

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  11. If A=[1 0-2 3-1 0-2 1 1] , B=[0 5-4-2 1 3-1 0 2] and C=[1 5 2-1 1 0 0-...

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  12. Compute the elements a(43) and a(22) of the matrix: A=[[0, 1, 0],[ 2, ...

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

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

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

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

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

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

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

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

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