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Thread: Matrix Inverse

  1. May 12th 2008, 10:54 PM #1
    ah-bee
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    Matrix Inverse

    How can i show that the matrix inverse exists for A^2 - 3A + I = 0
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  2. May 12th 2008, 11:41 PM #2
    Dr Zoidburg
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    assuming that A is invertible rearrange the equation to make I the subject:
    I = 3A - A^2
    multiply by A^{-1}
    A^{-1} = 3I - A
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  3. May 12th 2008, 11:54 PM #3
    ah-bee
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    umm.. show that it exists.. not find what it is if it exists
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  4. May 13th 2008, 01:44 AM #4
    Isomorphism
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    Quote Originally Posted by ah-bee View Post
    How can i show that the matrix inverse exists for A^2 - 3A + I = 0
    A^2 - 3A + I = 0

    A^2 - 3A = -I

    det(A^2 - 3A) = det(-I) \neq 0

    det(A) . det(A - 3I) = det(-I) \neq 0

    Thus det(A) \neq 0
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