"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. Please help me out.. than u..