solving a matrix problem

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• Feb 1st 2011, 10:36 PM
sheeper
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
• Feb 1st 2011, 11:11 PM
Prove It
$\displaystyle \mathbf{A}\mathbf{B} = \mathbf{C}$

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

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

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

$\displaystyle \mathbf{A} = \mathbf{C}\mathbf{B}^T(\mathbf{B}\mathbf{B}^T)^{-1}$.
• Feb 2nd 2011, 03:26 AM
Ackbeet
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?
• Feb 2nd 2011, 03:38 AM
Prove It
Quote:

Originally Posted by Ackbeet
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...
• Feb 2nd 2011, 03:45 AM
Ackbeet
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!