Coordinate/matrix multiplication If I multiply a 3d coordinate (padded with a 1 to make it a 4x1 matrix) with a transformation matrix, I get a 1x4 matrix which contains my new (transformed) 3d coordinate.
Knowing that matrices must be multiplied in a single "direction", ie, AxB is not the same as BxA... and that the columns of the first matrix define the rows of the resulting matrix (and the rows of the second matrix define the columns of the resulting matrix), does this mean that the multiplication must always be this way around...
[X][Y][Z][1] * [.][.][.][.] = [new X]
               [.][.][.][.]   [new Y]
               [.][.][.][.]   [new Z]
               [.][.][.][.]   [.]

...and therefore you ALWAYS multiply a matrix by a coordinate and not a coordinate by a matrix?
...or is it...
[.][.][.][.] * [X] *  = [new X][new Y][new Z][.]
[.][.][.][.]   [Y]               
[.][.][.][.]   [Z]
[.][.][.][.]   [1]

Thanks
I hope my babblings make sense.

All the linear coordinate transformations I'm familiar with look like this:
$$
\left[\begin{array}{cccc}
a & b & c & d \\
e & f & g & h \\
i & j & k & l \\
0 & 0 & 0 & 1 \\
\end{array}\right]
\left[\begin{array}{c}
x \\ y \\ z \\ 1
\end{array}\right] = 
\left[\begin{array}{c}
\text{new } x \\ \text{new } y \\ \text{new } z \\ 1
\end{array}\right] 
$$
$\text{new }x = ax + by + cz + d$ and so on.
