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Show that the matrix, A=[[1, 0,-2],[-2,-...

Show that the matrix, `A=[[1, 0,-2],[-2,-1, 2],[ 3, 4, 1]]` satisfies the equation, `A^3-A^2-3A-I_3=O` . Hence, find `A^(-1)` .

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. Show that A=[(6, 5),( 7, 6)] satisfies the equation x^2-12 x+1=0 . Thu...

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

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

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

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

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

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

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

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

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

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

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  16. Find the adjoint of the matrix A=[(-1,-2,-2), (2 ,1...

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  17. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

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  18. Use elementary column operation C2 -> C2 -2C1 in the matrix equati...

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  19. Apply elementary transformation R2->R2-3R1 in the matrix equation ...

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  20. Using elementary transformations, find the inverse of the matrix[1 3 ...

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