# Ax=b; every vector b is exactly from one vector x (from row space of A) <more>?

1. Mar 18, 2012

### kthurst

"Ax=b; every vector b is exactly from one vector x (from row space of A)".. <more>?

Hi,
I m refering 'Linear Algebra and its applications by Gilbert Starng".

I read (ch.3.1)"Matrix transforms every vector from its row space to its column space". Or
if given Ax=b; every vector b is exactly from one vector x (from row space of A).
Just want to know What if we multiply A with some vector x which is not in row space?
(can we do it !?)...
Not able to figure it out. may be i have missed some basic concept or misunderstood it.