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Math Help - Matrix Inverses.

  1. #1
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    Matrix Inverses.

    Suppose that CA=I where C is m*n and A is n*m. Consider the system A.X=B of n equations in m variables.
    Show that this system has a unique solution CB if it is consistent.
    (Problem 11 a, page 60. "Linear Algebra with applications"-5th edition W. Keith
    Nicholson)

    Please help me!
    Last edited by mr fantastic; January 10th 2010 at 02:32 AM. Reason: Edited post title
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  2. #2
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    Quote Originally Posted by Bugati View Post
    Suppose that CA=I where C is m*n and A is n*m. Consider the system A.X=B of n equations in m variables.
    Show that this system has a unique solution CB if it is consistent.
    (Problem 11 a, page 60. "Linear Algebra with applications"-5th edition W. Keith
    Nicholson)

    Please help me!

    Well, the definition of consistency in that book is precisely that the associated linear system has at least one solution. In our case, with the info we have, we get:

    AX=B\,\,\,consistent\,\Longrightarrow\,CAX=CB\Long  rightarrow I_mX=X=CB and since the system is consistent then X is uniquely determined by the product CB and is thus unique.

    Tonio
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  3. #3
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    I'm sorry. I confused this issue by split 3 case: n=m, n<m,n>m . Thanks alot.
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