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Math Help - [SOLVED] Matrices

  1. #1
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    [SOLVED] Matrices

    A is a 2x2 matrix, a12=a21=0, a11 does not equal 0, a22 does not equal 0.

    Show that A is regular and find inverse of A
    Last edited by NewtoMath; March 21st 2010 at 06:09 AM.
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  2. #2
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    matrices

    Hi NewtoMath,

    To find the inverse of a (2x2) matrix, interchange the elements in the leading diagonal, change the signs of the elements in the other diagonal and divide by the determinant of the matrix.

    We have  A = \left( \begin{array}{cc} a_{11} & 0 \\ 0 & a_{22} \end{array} \right)

    A^{-1} = \frac{1}{det A} \left( \begin{array}{cc} a_{22} & 0 \\ 0 & a_{11} \end{array}  \right)

    det A = \frac{1}{a{11}a_{22}}

    So, A^{-1} = \left( \begin{array}{cc} \frac{1}{a_{11}} & 0 \\ 0 & \frac{1}{a_{22}} \end{array}   \right)

    clearly AA^{-1} = I I tried to find out what a regular matrix was. There are various definitions to do with stochastic matrices. The most suitable was that a regular matrix is one for which AB = BA, which is true in this case.
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  3. #3
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    Hey thanks ingram! can't believe I didn't figure what "a12=a21=0" meant

    In my book it means to be a regular square matrix when there is an existing inverse or determinent, like when it doesn't equal zero in which case it's a singular.

    Thanks again.
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