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If A=[(4 ,3 ),(2 ,5)] , find x and y suc...

If `A=[(4 ,3 ),(2 ,5)]` , find `x` and `y` such that `A^2-x A+y I=O` .

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. Show that A=[(-8, 5),( 2, 4)] satisfies the equation A^2+4A-42 I=O . H...

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  2. If A=[(3, 1),(-1 ,2)] , show that A^2-5A+7I=O . Hence, find A^(-1) .

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  3. If A=[(4 ,3 ),(2 ,5)] , find x and y such that A^2-x A+y I=O .

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  4. If A=[(3,-2),( 4,-2)] , find the value of lambda so that A^2=lambdaA-2...

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  5. Show that A=[(5, 3),(-1,-2)] satisfies the equation x^2-3x-7=0 . Thus,...

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  6. Show that A=[(6, 5),( 7, 6)] satisfies the equation x^2-12 x+1=0 . Thu...

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  7. For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I3=O ...

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  8. Show that the matrix, A=[[1, 0,-2],[-2,-1, 2],[ 3, 4, 1]] satisfies th...

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  9. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

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  10. If A=1/9[-8 1 4 4 4 7 1-8 4] , prove that A^(-1)=A^T .

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  11. If A=[3-3 4 2-3 4 0-1 1] , show that A^(-1)=A^3 .

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  12. If A=[-1 2 0-1 1 1 0 1 0] , show that A^2=A^(-1) .

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  13. Solve the matrix equation [[5 ,4] ,[1 ,1]]X=[[1,-2],[ 1 ,3]] , where...

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  14. Find the matrix X satisfying the matrix equation: X[[5, 3],[-1,-2]]=...

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  15. Find the matrix X for which: [(3, 2), (7, 5)]X[(-1, 1),(-2, 1)]=[(2,-...

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  16. Find the matrix X satisfying the equation: [[2, 1 ],[5, 3]]X[[5, 3],...

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  17. If A=[1 2 2 2 1 2 2 2 1] , find A^(-1) and prove that A^2-4A-5I=O .

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  18. If A is a square matrix of order n , prove that |A\ a d j\ A|=|A|^n...

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  19. If A^(-1)=[3-1 1-15 6-5 5-2 2]and B=[1 2-2-1 3 0 0-2 1], find (A B)^(-...

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  20. If A=[[1, -230] ,[-14, -221]] , find (A^ T) .

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