Math 4326 Linear Algebra
Major Theorems for Midterm Exam
One of these three theorems will appear on the midterm exam for you to give the proof of:
[Note: These statements are just quick, imprecise summaries of each result.]
- 1.45: A sum of subspaces is a direct sum iff 0 is uniquely represented.
- 2.23/2.35: The length of a linearly independent list is less than or equal to the length of a spanning list;
then use this to prove that any two bases of a finite-dimensional vector space have the same length.
- 3.22: dim V = dim null T + dim range T