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If A = [(costheta,-sintheta,0),(sintheta...

If A = `[(costheta,-sintheta,0),(sintheta,costheta,0),(0,0,1)]` verify that A(adj A) =1

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Verify A(adj A) = (adj A).A = |A|.I :[[2,3],[-4,-6]]

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

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  3. If A = [(costheta,-sintheta,0),(sintheta,costheta,0),(0,0,1)] verify t...

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  4. Find the inverse of each of the following matrices: {:[(-1,5),(-3,2)...

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  5. Find the inverse of each of the following matrices: {:[(2,-2),(4,3)]

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

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  7. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

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  8. Consider the matrix A = {:[(2,3),(4,5)] Show that A^2-7A-2I=O

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  9. Consider the matrix A = {:[(2,3),(4,5)] Hence , find A^-1

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  10. If A = [ {:(2,3),(5,-2):} ] , write A^(-1) in terms of A.

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  11. Verify that (AB)^(-1) = B^(-1)A^(-1) for the matrices A and B where ...

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  12. Verify (AB)^-1 = B^(-1)A^(-1) for the matrices A and B. Where : A = ...

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  13. Verify that (AB)^(-1) = B^(-1)A^(-1) for the matrices A and B where ...

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  14. Verify (AB)^-1 = B^(-1)A^(-1) for the matrices A and B. Where : A = ...

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  15. Show that the matrix A = [[2,3],[1,2]satisfies the equation A^2-4A+I =...

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  16. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

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  17. For the matrix A = [[3,2],[1,1]], find the numbers a and b such that A...

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

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  19. If A= {:[(6,7),(8,9)] and B = {:[(3,2),(7,5)], find (AB)^-1

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  20. Find the inverse of each of the following: {:[(1,-1,2),(0,2,-3),(3,-...

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