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Math Help - Matrices

  1. #1
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    Matrices

    The matrix ( 1 2) maps Q(1,2) to R(5,7).
    (1 3)

    Find the 2 x 2 matrix which maps R back to Q.

    Help please.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Crystal09 View Post
    The matrix ( 1 2) maps Q(1,2) to R(5,7).
    (1 3)
    I will guess that you meant to say the following:

    Code:
    The matrix [ 1 2 ]
               [ 1 3 ] maps Q(1, 2) to R(5, 7)]
    Find the 2 x 2 matrix which maps R back to Q.
    If so, then note that, for Ax = b, you have A^(-1)Ax = A^(-1)b = x. So you need only find the matrix inverse.
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  3. #3
    Senior Member Twig's Avatar
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    hi

     \left[\begin{matrix} 1 & 2 \\ 1 & 3 \end{matrix}\right] \left[\begin{matrix} 1 \\ 2 \end{matrix}\right] = \left[\begin{matrix} 5 \\ 7 \end{matrix}\right]

    That is, a linear transformation described by the matrix A.

     A\vec{x}=\vec{b} \Rightarrow x=A^{-1}\vec{b}

     A^{-1} = \left[\begin{matrix} 3 & -2 \\-1 & 1 \end{matrix}\right]

     \left[\begin{matrix} 3 & -2 \\ -1 & 1 \end{matrix}\right] \left[\begin{matrix} 5 \\ 7 \end{matrix}\right] = \left[\begin{matrix} 1 \\ 2 \end{matrix}\right]
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