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Math Help - Solve A in Ax = b

  1. #1
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    Solve A in Ax = b

    If I have to vectors x and b, how can I solve matrix A in Ax = b? Or is this not possible?

    Eg:

    Code:
    Ax = b
    [a0, a1, a2, a3][x] = [x']
    [b0, b1, b2, b3][y]   [y']
    x, y, x' and y' are known. Is it possible to get a0-a3 and b0-b3?

    Thanks
    Last edited by goocreations; June 26th 2011 at 11:48 PM. Reason: Update
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  2. #2
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    Re: Solve A in Ax = b

    \displaystyle \begin{align*}\mathbf{Ax} &= \mathbf{b} \\ \mathbf{A}^T\mathbf{Ax} &= \mathbf{A}^T\mathbf{b} \\ (\mathbf{A}^T\mathbf{A})^{-1}\mathbf{A}^T\mathbf{Ax} &= (\mathbf{A}^T\mathbf{A})^{-1}\mathbf{A}^T\mathbf{b} \\ \mathbf{x}&= (\mathbf{A}^T\mathbf{A})^{-1}\mathbf{A}^T\mathbf{b}\end{align*}
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  3. #3
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    Re: Solve A in Ax = b

    Thank you. I'll try that.
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  4. #4
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    Re: Solve A in Ax = b

    I have also realised that your matrix equation as written makes no sense, as the dimensions of the matrices \displaystyle A and \displaystyle x don't allow multiplication. Are you sure the equation wasn't

    \displaystyle \left[\begin{matrix}a_0 & b_0 \\ a_1 & b_1 \\ a_2 & b_2 \\ a_3 & b_3\end{matrix}\right]\left[\begin{matrix}x \\ y\end{matrix}\right] = \left[\begin{matrix}c_0 \\ c_1 \\ c_2\\ c_3\end{matrix}\right]

    because that WILL work...
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  5. #5
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    Re: Solve A in Ax = b

    Thought I did something wrong. Thanks man
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  6. #6
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    Re: Solve A in Ax = b

    I've now managed to compute x. Is there any way of getting A when I have x and b available?
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  7. #7
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    Re: Solve A in Ax = b

    Use a similar method - postmultiply both sides by \displaystyle \mathbf{x}^T in order to create a square matrix, then postmultiply both sides by \displaystyle (\mathbf{xx}^T)^{-1} in order to get rid of the \displaystyle x terms.
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  8. #8
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    Re: Solve A in Ax = b

    Oh, that simple. Thank you very much
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