Relationship between nullspace and column space

Question

As column space is Combination of solution for $Ax=b$

And nullspace is Combination of solution for $Ax=0$

Does this mean that nullspace is a subspace of column space?

Answer 1

In the expression $Ax=b$ the columns of $A$ are combinated by the vector $x$ to obtain $b$ thus $b$ needs to belong to the column space of $A$ but $x$ in general is not related to column space of $A$.

Let consider for example to an $A_{n\times m}$ matrix, in this case $b\in R^n$ but $x\in R^m$.