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A and Bare square matrices of order n.Th...

A and Bare square matrices of order n.Their product is commutative:Prove that`A^2B = BA^2`.

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SHARAM PUBLICATION-MATRICES-EXAMPLE
  1. Construct the matrix [a(ij)](2xx3) where a(ij)=|i-j|.

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  2. If A=[[1,1],[2,2]] and B=[[2,1],[2,1]]find AB andBA.

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  3. A and Bare square matrices of order n.Their product is commutative:Pro...

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  4. Find x,y if[[3,2],[7,x]][[5,-2],[-7,y]]=[[1,0],[0,1]].

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  5. If [[4x,x-2u],[2u+v,3v-2w]]=[[8,6],[3,5]] find x,u,v,w.

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  6. Construct a matrix [a(ij)] of order 2xx2where a(ij)=i+2j.

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  7. Find the adjoint of the matrix [[1,1,2],[0,1,2],[1,2,1]].

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  8. Find the matrix which when added to [[2,-3],[-4,7]] gives [[4,-1],[3,2...

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  9. IF [[x1,x2],[y1,y2]]-[[2,3],[0,1]]=[[3,5],[1,2]] then determine x1,x2,...

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  10. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  11. Using elementary transformation find the inverse of the matrix [[1,3],...

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  12. Using elementary operation,find the inverse of [[4,5],[3,4]].

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  13. If A=[[1,-2,1],[0,-1,1],[2,0,-3]]then find A^(-1) and hence solve the ...

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  14. Find the value of x,y, and z if A=[[0,2y,z],[x,y,-z],[x,-y,z]] satisfi...

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  15. Find the matrix A such that [[2,-1],[1,0],[-3,4]]A = [[-1,-8,-10],[...

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  16. Suppose A=[{:(2,2,-4),(-4,2,-4),(2,-1,5):}] and B=[{:(1,-1,0),(2,3,4),...

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  17. Findthe inverse ofthe matrix[[1,1,2],[0,1,2],[1,2,1]].

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  18. Matrices X and Y are such that 3X + 4Y = I and X-2Y = 2I where I deno...

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  19. Find the inverse of the matrix[[1,2,3],[2,1,4],[1,0,2]].

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  20. Find x,y if[[3,2],[7,x]][[5,-2],[-7,y]]=[[1,0],[0,1]].

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