Week 7 -- Sections 4.5, 5.1

Short-term objectives

1. Find the change in the matrix representation of a linear function induced by a change of basis in the domain or codomain (or both) (Sec. 4.5)
2. Test whether a given subset of a vector space is a subspace. (Sec. 5.1)
3. Test whether a given subset of a vector space is an affine subspace. (Sec. 5.1)
4. Relate the dimension of the sum of two subspaces to the dimension of their intersection. (Sec. 5.1)

Long-term objectives

1. Distinguish between the definitions of "subspace" and of "linear function" and understand why they are superficially similar. (Sec. 5.1)
2. Understand the differences among the concepts of union, sum, and direct sum. (Sec. 5.1)