### Week 7 -- Sections 4.5, 5.1

#### Short-term objectives

- 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)
- Test whether a given subset of a vector space is a subspace.
(Sec. 5.1)
- Test whether a given subset of a vector space is an affine subspace.
(Sec. 5.1)
- Relate the dimension of the sum of two subspaces to the dimension
of their intersection. (Sec. 5.1)

#### Long-term objectives

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