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.