Clearly the goal of a first course in linear algebra is not mathematical maturity. If you don't set up the notation consistently from the start, once you start introducing change of bases formulae or proving row rank = column rank, etc., some students will get confused. See all the questions from confused students on Maths Stack Exchange about this point. The way this particular author has handled the issue is perverse: first he writes vectors as row vectors, then he introduces a mapping M(v) which maps the vector v to its representation as a column vector. Also, as I tangentially noted, he misses out the brackets for a function writing T(0,1) instead of T((0,1)), which is just incompetent. The book should be titled "Algebra Done Shite" not "Algebra Done Right" ;)