1. Linear Equations and Vectors
Chapter 1
Linear Equations and Vectors

2. Matrices and Systems of Linear Equations
Figure 1.1

3. Figure 1.2

4. Figure 1.3

5. Figure 1.4

6. The Vector Space Rn
Figure 1.5 The location of each point in the plane can be described using a rectangular coordinate system. The point A is the point (5,3).

7. Example 1
Figure 1.6

8. Figure 1.7 where (2,4,3) can be interpreted in two ways: as the location of a point in three-space relative to an xyz coordinate system, or as a position vector.

9. Example 3
Figure 1.8

10. Example 3 (cont’d)
Figure 1.9

11. Example 4
Figure 1.10 where (6,4) is a vector in the same direction as (3,2), and 2 times it in length.

12. Example 4 (cont’d)
Figure 1.11

13. Figure 1.12 The commutative property of vector addition.

14. Example 6
Figure 1.13

15. Example 7
Figure 1.14

16. Basis and Dimension
Example 1
Figure 1.15

17. Example 2
Figure 1.16

18. Dot Product, Norm, Angle, and Distance
Figure 1.17

19. Figure 1.18

20. Example 3
Figure 1.19

21. Figure 1.20

22. Theorem 1.6
Figure 1.21

23. Curve Fitting
Figure 1.22

24. Example 1
Figure 1.23

25. Electrical Networks
Example 2
Figure 1.24

26. Example 3
Figure 1.25

27. Traffic Flow
Figure 1.26

28. Exercise Set 1.6
Figure 1.27

29. Figure 1.28

30. Figure 1.29

31. Figure 1.30

32. Figure 1.31

33. Review Exercises
Figure 1.32

34. Figure 1.33