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Math Help - solving a matrix problem

  1. #1
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    solving a matrix problem

    If I had a set of matrices a,b, and c, and I knew a*b=c, how would I find matrix a?
    assuming;
    matrix a= a 3x4 matrix, values unknown
    matrix b= a 4x1 matrix, values = M1 M2 M3 M4
    matrix c= a 3x1 matrix, values = 0 0 0
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  2. #2
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    \displaystyle \mathbf{A}\mathbf{B} = \mathbf{C}

    \displaystyle \mathbf{A}\mathbf{B}\mathbf{B}^T = \mathbf{C}\mathbf{B}^{T}

    \displaystyle \mathbf{A}\mathbf{B}\mathbf{B}^T(\mathbf{B}\mathbf  {B}^T)^{-1} = \mathbf{C}\mathbf{B}^T(\mathbf{B}\mathbf{B}^T)^{-1}

    \displaystyle \mathbf{A}\mathbf{I} = \mathbf{C}\mathbf{B}^T(\mathbf{B}\mathbf{B}^T)^{-1}

    \displaystyle \mathbf{A} = \mathbf{C}\mathbf{B}^T(\mathbf{B}\mathbf{B}^T)^{-1}.
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  3. #3
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    Are you guaranteed that BB^{T} is invertible? In fact, given that you're generating a whole matrix out of one column vector, I can't help but wonder if you aren't guaranteed that it doesn't have an inverse! Is there another way to do this, do you think, Prove It?
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  4. #4
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    Quote Originally Posted by Ackbeet View Post
    Are you guaranteed that BB^{T} is invertible? In fact, given that you're generating a whole matrix out of one column vector, I can't help but wonder if you aren't guaranteed that it doesn't have an inverse! Is there another way to do this, do you think, Prove It?
    Serves me right for not reading the question fully...
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  5. #5
    A Plied Mathematician
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    With 3 equations and 12 unknowns, I don't think there's enough information to find a. You might be able to find a 9-parameter family of solutions. That's a lot of guessing!
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