The Invertible Matrix Theorem ties together just about all the concepts we’ve covered in the course so far. Here are some resources to supplement the textbook and our discussion in class:
- Extended statements of the IMT here and within the Invertible Matrix entry on Wikipedia (i.e., they include a bunch of additional equivalent conditions, which deal with concepts we will cover later in the course, like the column and null spaces, determinants, and eigenvalues.
- A detailed proof of the IMT, written up by another CityTech faculty member who has taught this course: “Using pivot positions to prove the Invertible Matrix Theorem in Lay’s Linear Algebra“
- A set of slides that go along with the treatment of the IMT in the the textbook