Why is the "column space" on the vertical in a matrix? In my mind the column space is that space that the vectors in the matrix have created. I mean, for example take the equations:

```
3x + 4y = 5
2x + 8y = 6
```

Then the matrix will be:

\begin{pmatrix} 3 & 4 \\ 2 & 8 \end{pmatrix}

But why is the space defined by this matrix on the vertical?

Aren't the two vectors:

```
3i + 4j
```

and

```
2i + 8j
```

defining the space we're working in?