3 equations, 3 unknowns x,y,z can be represented by Row Matrix below:

1 2 3x10

4 5 6y=11

7 8 9z12

This can be represented by column vectors:

1x4y5etc

7

I am troubled by this idea. The row vectors make sense, but as the columns represent coefficients of the same axis (on 3d coordinate graph) how can these columns be vectors which can themselves be represented on the same style graph. Dr Strang cannot be wrong so there is something I have ommited to understand. Can anyone explain and put me out of my misery?