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Homework Help: Ax=b, if matrix A is unknown?

  1. Sep 29, 2012 #1
    1. The problem statement, all variables and given/known data

    I am trying to solve for the A matrix (3 x 3). I know matrix x is (3 x 1) and matrix b is (3 x 1), how do I go about solving for matrix A?

    3. The attempt at a solution

    I have not attempted this as I don't know the rules to initiate this problem.

    Please offer me some hints or rules I should know on how to solve this problem


  2. jcsd
  3. Sep 29, 2012 #2


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    Well you could re-arrange it with matrix algebra:




    Note the last step is allowed because [itex]xx^{T}[/itex] is a scalar.(You can't divide matrices by matrices)

    Familiarise yourself with the transpose of a matrix (in this case, a column vector) and matrix multiplication, and perhaps rules of matrix algebra and that should be all you need to understand the above.

    This link may be helpful http://people.hofstra.edu/stefan_waner/RealWorld/Summary3.html [Broken], though it may go into much more depth than you need.

    Last edited by a moderator: May 6, 2017
  4. Sep 29, 2012 #3


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    Gold Member

    Other than what K29 has suggested, here are some methods commonly used to solve systems of linear equations (matrix equations). You can do a little research, or refer in your book/s:

    1. Cramer's rule.
    2. Gauss elimination method (reduce to row echelon form)
    3. LU-factorisation method
    4. Using matrix inversion.

    Personally, i prefer the Gauss elimination method which is quicker.
  5. Sep 29, 2012 #4

    Ray Vickson

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    This is incorrect. Since x and b are column vectors, the objects xxT and bxT are 3×3 matrices, not scalars.

    Anyway, if x and b are known but A is unknown, the equations Ax = b give 3 equations in the 9 unknowns aij, so the system is underdetermined. Additional information or some type of optimization criterion would need to be incorporated in order to obtain a unique solution.

    Last edited by a moderator: May 6, 2017
  6. Sep 29, 2012 #5

    D H

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    The last step is disallowed because [itex]xx^{T}[/itex] is a 3x3 matrix. What you might be able to do is post-multiply by the inverse of [itex]xx^{T}[/itex], but that too is disallowed because [itex]xx^{T}[/itex] is singular.

    So let's go back to the start.

    You can't. Ax=b comprises three equations. However, you have nine unknowns, the nine elements of A. That's an underdetermined system. There are either no solutions or there are an infinite number of solutions.

    I now see that Ray Vickson beat me to it.
  7. Sep 29, 2012 #6


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    My mistake. I was working too quickly. Apologies to OP
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