1. MAT 2401 Linear Algebra 4.5 Basis and Dimension http://myhome.spu.edu/lauw

2. HW Written Homework

3. Exam 2 Please study for the exam. Review Lab Solutions. Review written HW solutions. The details in the Keys are the minimum expectations. Resolve any questions you may have.

4. Preview

5. Questions What is the “size” of a vector space? Is R 2 “smaller” than R 3 ? Why? Is R 2 “smaller” than P 2 ? Why?

6. Answers To answer these questions, we need to look into a few things… Linear Combination Spanning Set Linear Independence Basis (4.5) Dimension (4.5)

7. Prototype R n

8. What is so special about S ?

12. Prototype R n

13. Spanning Set

14. Basis

15. Example 1

17. Remarks

21. Example 2

23. Example 3 is the standard basis for M 2,2.

24. Fact #1

26. Fact #2

27. Dimension of a Vector Space

28. Example 6

29. Solon? What’s up?