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Math Help - Matrix (I think) question

  1. #1
    Senior Member Paze's Avatar
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    Matrix (I think) question

    I'm reading and learning through a finals exam for what I will be learning next year (I'm usually a year ahead) and there's a question:

    A). Find the transpose of the matrix A



    B). Show that A^{-1}\cdot A=A\cdot A^{-1}=I

    I think this is related to matrices but I'm not sure what the question begs at all. I'm not sure if that's a I or l on the end of the equation either. No values seem to be given for this I/l.
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  2. #2
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    Re: Matrix (I think) question

    Do you know the definitions of transpose and inverse matrices? These are just simple operations, for the transpose you just interchange rows and columns.

    If A=\left[\begin{array}{ c c }a & b \\c & d \end{array} \right] then you can find the inverse using the formula:

    A^{-1}=\frac{1}{detA}\left[\begin{array}{ c c }d &- b \\-c & a \end{array} \right]

    where,

    det(A)=ad-bc

    So once you use that plug-and-go formula you just multiply the two matrices... AA^{-1} if you multiply in opposite order A^{-1}A it will be the same, which will be I= \left[\begin{array}{ c c }1& 0 \\0 & 1 \end{array} \right] which is what they're asking you to demonstrate.
    Last edited by adkinsjr; July 21st 2013 at 12:48 PM.
    Thanks from topsquark and Paze
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    Senior Member Paze's Avatar
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    Re: Matrix (I think) question

    Quote Originally Posted by adkinsjr View Post
    Do you know the definitions of transpose and inverse matrices? These are just simple operations, for the transpose you just interchange rows and columns.

    If A=\left[\begin{array}{ c c }a & b \\c & d \end{array} \right] then you can find the inverse using the formula:

    A^{-1}=\frac{1}{detA}\left[\begin{array}{ c c }d &- b \\-c & a \end{array} \right]

    where,

    det(A)=ad-bc

    So once you use that plug-and-go formula you just multiply the two matrices... AA^{-1} if you multiply in opposite order A^{-1}A it will be the same, which will be I= \left[\begin{array}{ c c }1& 0 \\0 & 1 \end{array} \right] which is what they're asking you to demonstrate.
    Great! Thanks!
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