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.