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Find the inverse of the matrix A=[(a, ...

Find the inverse of the matrix `A=[(a, b),( c,(1+b c)/a)]` and show that `a A^(-1)=(a^2+b c+1)I-a A` .

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. Given =[(2,-3),(-4, 7)] , compute A^(-1) and show that 2A^(-1)=9I-A .

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  2. If A=[(4, 5),( 2 ,1)] , then show that A-3I=2(I+3A^(-1))

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  3. Find the inverse of the matrix A=[(a, b),( c,(1+b c)/a)] and show th...

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  4. Given A=[(5, 0, 4),( 2, 3, 2),( 1, 2, 1)] , B^(-1)=[(1, 3, 3),( 1, 4, ...

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  5. Let F(alpha)=[cosalpha-sinalpha0sinalphacosalpha0 0 0 1] and G(beta)=[...

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  6. If A=[(2, 3),( 1, 2)] , verify that A^2-4A+I=O , where I=[(1, 0),( 0, ...

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  7. Show that A=[(-8, 5),( 2, 4)] satisfies the equation A^2+4A-42 I=O . H...

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

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

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

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

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

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

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

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

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

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

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

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