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Math Help - Finding inverse of a matrix (A^-1)

  1. #1
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    Finding inverse of a matrix (A^-1)

    find the inverse of

    1 2 -3
    3 2 -1
    2 1 3

    if there is
    Last edited by swiftshift; May 12th 2010 at 11:25 PM.
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  2. #2
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    how to find the inverse

    The inverse can be found by setting this matrix equal to the identity matrix and row reducing so that the identity matrix is on the other side of equal sign (the inverse matrix will be where the identity matrix is originally).
    So
    1 2 -3 | 1 0 0
    3 2 -1 | 0 1 0
    2 1 3 | 0 0 1

    Does that help?
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  3. #3
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    Quote Originally Posted by swiftshift View Post
    find the inverse of

    1 2 -3
    3 2 -1
    2 1 3

    if there is
    Dear swiftshift,

    \left(\begin{array}{ccc}1&2&-3\\3&2&-1\\2&1&3\end{array}\right)\times\left(\begin{array  }{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right)=\left(  \begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\r  ight)

    By matrix multiplication you could obtain nine equations and solve for the unknowns.
    Last edited by Sudharaka; May 13th 2010 at 06:32 AM. Reason: Mistake about the number of equations.
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  4. #4
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    Quote Originally Posted by kaelbu View Post
    The inverse can be found by setting this matrix equal to the identity matrix and row reducing so that the identity matrix is on the other side of equal sign (the inverse matrix will be where the identity matrix is originally).
    So
    1 2 -3 | 1 0 0
    3 2 -1 | 0 1 0
    2 1 3 | 0 0 1

    Does that help?
    thanks mate
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  5. #5
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    Quote Originally Posted by Sudharaka View Post
    Dear swiftshift,

    \left(\begin{array}{ccc}1&2&-3\\3&2&-1\\2&1&3\end{array}\right)\times\left(\begin{array  }{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right)=\left(  \begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\r  ight)

    By matrix multiplication you could obtain six equations and solve for the unknowns.
    Actually, you get nine equations for the nine unknowns. Probably not the best way to find an inverse!
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