Generally speaking, Ax=b considers more about the rows of A while Ax=0 more about the columns. Existence: 1. Ax=b is consistent: (there are no all-zero rows) rank of matrix = rank of augmented matrix 2. Ax=0 is consistent: always (x=0) Uniqueness: 1. Ax=b  2. Ax=0 has a infinity of solutions: it has at least one free variable Subspace: If A is m by n, [a1, ... ,an] are the columns of A 1. Col A       All the linear combinations of columns of A (i.e. b where Ax=b)       In fact it is Span={a1, ... ,an}       It is a subspace of Rm 2. Null A       The solutions of Ax=0       It is a subspace of Rn

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