Is the lattice of subgroups of S3 distributive? Is it complemented? (See Figure 63.5.)

1 MATH 205 LINEAR ALGEBRA SUPPLEMENT STEVEN H. WEINTRAUB 1. Coordinates and Change of Basis Deﬁnition 1.1. Let B = {v ,v1,..2,v } bn a basis for the vector space V . Let v ∈ V so that v = c 1 1 c 2 +2▯▯▯ + c vn n for unique scalars 1 ,2 ,...,n . The scalars 1 2c ,...nc are called the coordinates of v in the basis B, and the vector c1 c2 [v]B= . . c