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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- Feb 1st 2011, 10:36 PMsheepersolving 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 - Feb 1st 2011, 11:11 PMProve It
$\displaystyle \displaystyle \mathbf{A}\mathbf{B} = \mathbf{C}$

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

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

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

$\displaystyle \displaystyle \mathbf{A} = \mathbf{C}\mathbf{B}^T(\mathbf{B}\mathbf{B}^T)^{-1}$. - Feb 2nd 2011, 03:26 AMAckbeet
Are you guaranteed that $\displaystyle BB^{T}$ 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? - Feb 2nd 2011, 03:38 AMProve It
- Feb 2nd 2011, 03:45 AMAckbeet
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!