Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 3.

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Presentation transcript:

Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 3

Chapter 3 Euclidean Vector Spaces 3.1 Vectors in 2-Space, 3-Space, and n-Space 3.2 Norm, Dot Product, and Distance in R n 3.3 Orthogonality 3.4 The Geometry of Linear Systems 3.5 Cross Product

Section 3.1 Vectors Addition of vectors by the parallelogram or triangle rules

: Subtraction: Scalar Multiplication:

Properties of Vectors

Section 3.2 Norm, Dot Product, and Distance in R n Norm: Unit Vectors:

The Dot Product

Properties of the Dot Product

Cauchy-Schwarz Inequality

Dot Products and Matrices

Section 3.3 Orthogonality

Orthogonal Projections

Point-line and point-plane Distance formulas

Section 3.4 The Geometry of Linear Systems

Section 3.5 Cross Product

Cross Products and Dot Products

Properties of Cross Product

Geometry of the Cross Product

Geometry of Determinants