Linear algebra

Final Exam Study Guide (Concepts and Formulas)

1. You have to know when a matrix A is invertible.

2. You have to know the definitions and how to find:

a. Col A, b. Nul A, c. Row A, d. Rank A, e . dim Nul A.

3. You have to know how to diagonalize a matrix.

4. You have to know the Rank theorem.

5. You have to know how the properties and definition of linear transformations.

6. You have to know the definition of a subspace.

7. You have to know the definition of orthogonal/orthonormal basis.

8. You have to know the definition and properties of an orthogonal projection.

9. You have to know how to find the distance between a vector and its orthogonal projection.

10. You have to know how to solve a system (inconsistent, with many solutions, with a unique solution.)

11. You have to know when a mapping is onto.

12. You have to know the definition and how to find a kernel

13. You have to know when the inverse transformation exists

14. You have to know the definition of an orthogonal matrix.

15. You have to know the inverse matrix theorem. (all different forms)

16. You have to know the definition of linear independent/dependent vectors.