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Math Help - Inverse of 2x1 matrix.

  1. #1
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    Inverse of 2x1 matrix.

    A=\left(\begin{array}{cc}a\\b\end{array}\right)

    What is the inverse of A?

    Thanks
    Last edited by mr fantastic; February 7th 2011 at 03:08 AM.
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  2. #2
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    Only square matrices have inverses...
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    Can I partition the matrix and then directly reverse a and b separately, although this seems odd?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by eulerian View Post
    Can I partition the matrix and then directly reverse a and b separately, although this seems odd?

    You can speak about the existence of right inverse R=(\alpha,\beta) satisfying

    \begin{pmatrix}{a}\\{b}\end{pmatrix} (\alpha,\beta)=\begin{pmatrix}{1}&{0}\\{0}&{1}\end  {pmatrix}

    and about the existence of left inverse L=(\lambda,\mu)^t satisfying

    (\lambda,\mu)\begin{pmatrix}{a}\\{b}\end{pmatrix}=  (1)


    Fernando Revilla
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    Quote Originally Posted by FernandoRevilla View Post
    You can speak about the existence of right inverse R=(\alpha,\beta) satisfying
    \begin{pmatrix}{a}\\{b}\end{pmatrix} (\alpha,\beta)=\begin{pmatrix}{1}&{0}\\{0}&{1}\end  {pmatrix}
    I don't think that a right inverse is possible. Consider the equations involved:

    a\alpha=1\not=0, which implies a\not=0 and \alpha\not=0. Also,

    b\beta=1\not=0, implying b\not=0 and \beta\not=0.

    However, a\beta=0, which implies that either a=0 or \beta=0, a contradiction.

    Therefore, a right inverse doesn't exist in this case.
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    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Ackbeet View Post
    Therefore, a right inverse doesn't exist in this case.
    I said, we can speak about the existence of right and left inverse (i.e. it has sense to define them). Of course left and/or right inverse could not exist.
    Choosing for example a=b=0 does not exist R and does not exist L.


    Fernando Revilla
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    Quote Originally Posted by FernandoRevilla View Post
    I said, we can speak about the existence of right and left inverse (i.e. it has sense to define them). Of course left and/or right inverse could not exist.


    Fernando Revilla
    Got it.
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