------Plan
Finish 3.2
3.3
3.4
3.2
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.
3.3
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.