Learning Outcomes
After completing this chapter, students should be able to do the following.
- Interpret a matrix as a linear transformation from to .
- Produce a matrix representation of a linear transformation given its action on the standard unit vectors.
- Identify some basic geometric transformations of the plane.
- Discuss the kernel and image of the transformation geometrically and in terms of nullity and rank of the matrix.
- Give examples of linear transformations that are invertible or not invertible.
- Interpret a matrix product as a composition of linear transformations.