solving a matrix problem

**sheeper** · February 1st 2011, 10:36 PM

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

**Prove It** · February 1st 2011, 11:11 PM

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

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

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

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

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

**Ackbeet** · February 2nd 2011, 03:26 AM

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?

**Prove It** · February 2nd 2011, 03:38 AM

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...

**Ackbeet** · February 2nd 2011, 03:45 AM

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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