### Chapter 1

- Echelon Form definition
- Pivot Position and Pivot Column definition
- Matrix-Vector Product definition
- Thm 3 - Matrix equation equivalences
- Thm 4 - Solution existence equivalences
- Vector properties and Matrix-Vector Product properties
- Theorem - Nontrivial solutions
- Thm 6 - Matrix equation solution set
- Linear Independence definition
- Theorem - Linearly independent columns of A
- Thm 8 - Linearly dependent if more than n vectors
- Thm 7 - Characterization of Linearly Dependent Sets
- Thm 9 - Sets with the zero vector are dependent
- Linear Transformation definition
- Thm 10 - Standard matrix for a linear transformation
- Onto and One-to-One definitions
- Thm 11 - One-to-one transformation equivalence
- Thm 12 - Onto and one-to-one transformation equivalences