Jan 17/Jan 19
Review Chapter 2
- Review span and linear independence. Relate linear systems and matrices.
- Do the unifying theorem.
- Introduce the standard basis. Use it to understand matrix multiplication.
- Demonstrate that the difference of two solutions is a solution to the homogeneous system.
- Give definition of a linear transformation.
- Give both examples and nonexamples.
- Matrix multiplication is linear. All linear transformations come from this.
- Introduce range, relate to span and existence of solution.
- Introduce 1-1 and onto.
- Talk about span and linear independence again.
- Give the unifying theorem again.
- Show R2 to R2 visualizations.