1. MAT 2401 Linear Algebra 1.2 Part II Gauss-Jordan Elimination http://myhome.spu.edu/lauw

2. HW Written Homework

3. Time Part I may be a bit longer. Part II will be shorter.

4. Preview System with No solutions. System with Infinite Number of solutions.

5. How many solutions? Q: Given a system of 3 equations in 3 unknowns, how many solutions are possible? Inconsistent System Consistent System

6. Example 4 Use Gauss-Jordan Elimination to solve the system. Conclusion: 123

7. Example 5 Use Gauss-Jordan Elimination to solve the system.

8. Example 5 123

9. Geometric Interpretation We are looking for the intersection points of 3 planes (linear equations) It turns out that they are the same intersection points of (another) 2 planes  A straight line

10. Remarks The solution set is the collection of the points on the intersection line of the planes: x-3z=-1 and y-z=0.

11. Expectations Some descriptions are necessary to help your audience to follow your solutions Here, I suggested “The system becomes”. You can use similar wordings if you want.

12. Expectations Since the intersection is a line, it is customary to represent it as a parametric equations (Calculus III)

13. Expectations Instead of “t is any real number”, we use the set notation i.e. t is an element of the real numbers.

14. System of Linear Equations (LE)

15. Homogeneous System of LE

16. Q: Is the system consistent?A:

17. Trivial and Non-Trivial Solutions Trivial Solutions Non-Trivial Solutions At least one of the x i is non-zero. (You need this for today’s HW)

18. Visual Summary