given matrix A and solution b solving Ax=b you get the solution space which is the column space of A so the solution space is spanned by by what of A?????

Question

given matrix A and solution b solving Ax=b you get the solution space which is  the column space of A so the solution space is spanned by by what of A?????

anonymous · Answer

solving AX=b gives you all possible solutions x for b if solutions exist .... the column space of A meanwhile is all possible x(all possible combinations of A) .. solution space of B is not a subspace and is contained in C(A) (assuming b exists in column space of A)

anonymous · Answer

Solving Ax=b does NOT give you the column space (you solve for x).  The column space is spanned by the columns of A, and b is within it.  The solution space (all solutions for x) is not a subspace and hence is not spanned, but it is equal to any solution plus the nullspace, which is spanned by the special solutions.  I think the nullspace is orthogonal to the rowspace but not sure.