So here is a direct passage from the book we are learning from.

> 
> Every vector $\boldsymbol x$ in the nullspace is perpendicular to every row of $A$, because $A\boldsymbol x=\boldsymbol 0$. ***The nullspace $N(A)$ and the row space $C(A^{\rm T})$ are orthogonal subspaces of $\,{\bf R}^n$.***  
>    
>  To see why $\boldsymbol x$ is perpendicular to the rows, look at $A\boldsymbol x=\boldsymbol 0$. Each row multiplies $\boldsymbol x$:
> 
> 
> 
> > 
> > $$A\boldsymbol x=\begin{bmatrix}\text{row }1\\\vdots\\\ \quad\!\text{row n}\quad \end{bmatrix}\begin{bmatrix}\\ \boldsymbol x \\ \,\,\end{bmatrix}=\begin{bmatrix}0\\\vdots\\0\end{bmatrix}\quad\matrix{\longleftarrow&\; \text{(row 1)}\cdot\boldsymbol x\text{ is zero}\\ \\ \longleftarrow&\; \text{(row $m$)}\cdot\boldsymbol x\text{ is zero} }
> > \tag1$$
> > 
> > 
> > 
> 
> 
> 

Now the image I get in my mind is that A belongs to column space, A(transpose) belongs to row space and that x belongs to null space/left nullspace depending on we are calculating column or row space. This is the books best description of what represents what. I am trying to get an image of my head how things are related.

The image below is what I'm trying to figure out, x is in nullspace/left nullspace and the vectors a1 and a2 that belong to Matrix A is in rowspace and columnspace. Is this an accurate thinking of how the vectors are represented when x is nullspace/left nullspace if trying to visualize them?

![enter image description here](https://i.stack.imgur.com/CCcI8.jpg)