- Review: rank may decrease when you pre/post compose by a linear transformation. If the linear transformation is either sirujective or injective, sometimes it stays the same.
- Inverses work out nicely.
- Ax=b corresponds to a linear system.
- general solutions and particular solutions.
- Relationships among the columns detected in the null space.
- We can determine column space
- We can determine null space.
- The row space is the perpindular complement of the null space. Since the null space doesn’t change, neither does the row space.
- Solving (A|b)x=0 vs Ax=b.