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Homework Help: Show that det(I-xy'T)= 1-y'T x

  1. Sep 4, 2006 #1
    Need Help Please!!!

    I am very much in need of your help. I have a question saying:

    Let x,y E R. Show that det(I-xy'T)= 1-y'T x

    y'T is transpose of y and I is identity matrix.

    Actually I dont know how to solve something like det( A-B). What am I going to do when there is addition or subtraction in the determinant.

    Thanks for your response.
  2. jcsd
  3. Sep 4, 2006 #2


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    Well for some square matrix M, you know how to calculate [itex]\det(M)[/itex], right? And for two nxn square matrices A and B, A-B is an nxn matrix C, true again? Then calculating [itex]\det(A-B)[/itex] is no different than calculating [itex]\det(C)[/itex].
  4. Sep 4, 2006 #3
    So is this so simple wov thank you very much I think I can handle the rest.
  5. Sep 5, 2006 #4


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    In future it might be a good idea not to say things like
    "Let x,y E R" and then assert that they are matrices!
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