Linear space, linear subspace and linear span

Description
Applicability of additive rules such as commutativity, associativity, existence of zero and existence of negatives for a n tuple space are discussed. The properties of scalar multiplication namely associativity, distributivity and multiplication by identity holds or not in a n tuple space, is discussed here. Linear space, linear subspace and linear span are defined. Example sums are solved on this topic.
Prof. James McKernan, Maths, 18.024. Calculus with Theory II, Spring 2003: Linear Space: Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed October19, 2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc