1. MAT 2401 Linear Algebra 4.4 II Spanning Sets and Linear Independence http://myhome.spu.edu/lauw

2. HW WebAssign 4.4 Part II Written Homework

3. Review Linear Combination Spanning Set

4. Review: Example 0 (c)

5. Preview Linear Independent

6. Linear Independence

7. No one vector is a linear combination of the other vectors.

8. Example 6 Let S={(1,0,0), (0,0,2), (1,0,1)} Determine whether the set S is linearly independent or linearly dependent.

9. Example 7 Let S={(1,1,4), (1,0,3), (1,-1,0)} Determine whether the set S is linearly independent or linearly dependent.

10. Test

11. Written HW In this section, two related but different concepts are introduced: the spanning sets and linear independence.

12. Written HW Q1 : If S is a spanning set, does it imply that S is linearly independent?

13. Written HW Q1 : If S is a spanning set, does it imply that S is linearly independent? A1: No. Construct an counter example in R 2 Find S such that S spans R 2 and S is linearly dependent

14. Written HW Q2 : If S is linearly independent, does it imply that S is a spanning set?

15. Written HW Q2 : If S is linearly independent, does it imply that S is a spanning set? A2: No. Construct an counter example in R 3 Find S such that S is linearly independent and S does not span R 3