@sanya I just wrote here something for you please see mathb.in/78537, may be that can answer your question because I can't render latex here :(

I would suggest you to watch 3Blue1Brown's playlist "Essence of Linear Algebra".

@sanya "Does it represent the linearly transformed unit vectors but in this case it has all been squished into one dimension?" As far as I can think, you're right here or just thing row matrix as a transpose of column matrix.