# Thread: solving a matrix problem

1. ## 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

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

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

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

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

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

3. 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?

4. Originally Posted by Ackbeet
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?
Serves me right for not reading the question fully...

5. 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!