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If A={:[(1,2,2),(2,1,2),(2,2,1)], prove ...

If `A={:[(1,2,2),(2,1,2),(2,2,1)]`, prove thst `A^2-4A-5I = O ` and hence, obtain `A^-1`.

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. If P = {:[(1,2,-2),(-1,3,0),(0,-2,1)], find P^-1. Verify that PP^-1= I...

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

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  3. If A={:[(1,2,2),(2,1,2),(2,2,1)], prove thst A^2-4A-5I = O and hence,...

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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...

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

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  6. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

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  7. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that (A^-1)^-1 = A

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  8. Find |A|: A = {:[(1,-2,2),(2,3,5),(-2,0,1)]

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  9. Verify A(adj A) = (adj A).A = |A|.I : [[1,-1,2],[3,0,-2],[1,0,3]]

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  10. Find |A|: A = {:[(2,1,5),(3,-2,-4),(-3,1,-2)]

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  11. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)].

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  12. Find the determinant of the matrix : A = {:[(a,b),(c,bc)]

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  13. Find the determinant of the matrix : A = {:[(a,b),(c,(1+bc)/a)]

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  14. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)].

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  15. Find the inverse of the matrix : A = [(costheta,sintheta),(-sintheta,c...

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  16. Find the transpose of the matrix : A = {:[(a,b),(c,(1+bc)/a)]

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  17. Find the inverse of the matrix : {:[(2//13,-5//3),(3//13,-1//13)]

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  18. Find the inverse of the matrix : {:[(3/14,1/7),(-2/7,1/7)]

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  19. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)] and show t...

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  20. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)] and show t...

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