Linear Equations and Vectors Chapter 1 Linear Equations and Vectors

Matrices and Systems of Linear Equations Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

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).

Example 1 Figure 1.6

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.

Example 3 Figure 1.8

Example 3 (cont’d) Figure 1.9

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

Example 4 (cont’d) Figure 1.11

Figure 1.12 The commutative property of vector addition.

Example 6 Figure 1.13

Example 7 Figure 1.14

Basis and Dimension Example 1 Figure 1.15

Example 2 Figure 1.16

Dot Product, Norm, Angle, and Distance Figure 1.17

Figure 1.18

Example 3 Figure 1.19

Figure 1.20

Theorem 1.6 Figure 1.21

Curve Fitting Figure 1.22

Example 1 Figure 1.23

Electrical Networks Example 2 Figure 1.24

Example 3 Figure 1.25

Traffic Flow Figure 1.26

Exercise Set 1.6 Figure 1.27

Figure 1.28

Figure 1.29

Figure 1.30

Figure 1.31

Review Exercises Figure 1.32

Figure 1.33