If I had a set of matrices a,b, and c, and I knew a*b=c, how would I find matrix a?
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
Are you guaranteed that 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?