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If A= [(1,-1,1),(2,-1,0),(1,0,0)] and B ...

If `A= [(1,-1,1),(2,-1,0),(1,0,0)]` and B = `[(1,3,2),(1,1,1),(2,-3,-1)]`, verify that `(AB)^-1 = B^-1 A^-1`

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. If A = 1/9 [(-8,1,4),(4,4,7),(1,-8,4)], show that A^-1 = A'

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

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  3. If A= [(1,-1,1),(2,-1,0),(1,0,0)] and B = [(1,3,2),(1,1,1),(2,-3,-1)],...

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

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  5. Show that [(1, - tantheta/2),(tantheta/2, 1)][(1, tantheta/2),(-tanthe...

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

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  7. For the matrix A=[{:(3,2),(1,1):}], find the numbers a and b such that...

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  8. If A=[(2,-3),(-4,7)] compute A^(-1) and show that 2A^(-1) + A-9I =0

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  9. Find A^(-1) if A=[(0,1,1),(1,0,1),(1,1,0)] and show that A^(-1)=(A^2-3...

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  10. Show that A = [(-8,5),(2,4)] satsfies the equation x^2 + 4x - 42= 0. H...

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  11. If A = [(2,3,3),(3,2,3),(3,3,2)], then show that A^2 - 7A - 8I = O

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  12. Find the matrix X satisfying X [(5,3),(-1,-2)]=[(14,7),(7,7)]

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  13. Find the matrix X satisfying. [(3,2),(7,5)] X [(-1,1),(-2,1)] = [(2,...

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  14. Find the matrix X satisfying. [(2,1),(5,3)] X [(5,3),(3,2)] = [(1,0)...

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  15. Find the matrix X satisfying. [(2,1),(3,2) X [(-3,2),(5,-3)] = [(1,0...

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  16. If A = [(6,-7, 8),(1,-3,1),(2,1,-4)], compute det (adj A).

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  17. If A = [(3,2,2),(2,3,2),(2,2,3)], find adj (Adj A)

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  18. If A = [(1,0,2),(0,2,1),(2,0,3)], find A (adj A)

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  19. Prove that |(bc-a^2, ca-b^2, ab-c^2),(ca-b^2, ab-c^2, bc-a^2),(ab-c^2,...

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  20. Using matrix method solve the following systems of equations: (3x + ...

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