# Math 4326 Linear Algebra

Major Theorems for Midterm Exam

## Spring 2015

One of these three theorems will appear on the midterm exam for you to give the proof of:
**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*

[Note: These statements are just quick, imprecise summaries of each result.]