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If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1...

If `A=[[alpha,0],[1,1]]` and `B=[[1,0],[5,1]]`, show that for no values of `alpha, A^2=B`.

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SHARAM PUBLICATION-MATRICES-EXAMPLE
  1. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] then find the value of A^(2)-3A+2I

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  2. If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0.

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  3. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

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

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  5. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  6. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  7. [[1,-2],[3,2]][[x,2],[1,y]]=[[-3,4],[-1,4]]Find x and y.

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  8. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  9. Find the inverse of the matrix [{:(2,5),(1,3):}]

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  10. Find x, so that [{:(1,x,1):}][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(...

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  11. Can the inverse of the following matrix be found? [[0,0,2],[3,6,0],[2,...

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  12. Construct the matrix [a(ij)](2xx3) where a(ij)=|i-j|.

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

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

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

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

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

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

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

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

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