Consider the nearlinear space depicted in Figure 2 Find a ba

Consider the near-linear space depicted in Figure 2. Find a basis for the space. What is the dimension of the space? Prove your answer. Find all of its subspaces (up to isomorphism).

Solution

1. From definition of basis, we should look at independent lines . One basis is { {1,3}, {1, 5}, {3, 5}, {2,4} , {4, 6}, {2, 6}, {2, 7}, {4, 7}}.

2. From 1) as that is a minimal basis , dimension = 7.

3. consider 1 triangle and the rectangle.