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Formats

Overview
Table of contents

Author

Edition

3rd ISBN

9781442548367
Published Date

16/12/2010
Pages

353
An engaging introductory text to linear algebra for new students entering university and returning mature-age students. It aims to make critical algebraic concepts easy to understand.

- Introduction
**1 Geometric Vectors**- 1.1 Addition of geometric vectors
- 1.2 Multiplication by a scalar
- 1.3 Subtraction of vectors
- 1.4 List of useful properties
- 1.5 The geometry of parallelograms
**2 Position Vectors and Components**- 2.1 Magnitude, unit vectors and hat notation
- 2.2 Parallel vectors
- 2.3 Position vectors and components
- 2.4 Length of a vector
- 2.5 Linear independence for two vectors
**3 Dot Products and Projections**- 3.1 Geometric definition of dot product
- 3.2 Algebraic definition of dot product
- 3.3 Angle between two vectors
- 3.4 Projections and orthogonal components
- 3.5 Another application to geometry in the plane
**4 Cross Products**- 4.1 Definition of cross product
- 4.2 List of useful properties
- 4.3 Method of expanding brackets
- 4.4 Geometric interpretation
- 4.5 Continuity and the right-hand orientation
**5 Lines in Space**- 5.1 Parametric vector and scalar equations of a line
- 5.2 Cartesian equations of a line
- 5.3 Finding a line using two points
- 5.4 Distance from a point to a line
**6 Planes in Space**- 6.1 Vector equation of a plane
- 6.2 Cartesian equation of a plane
- 6.3 Finding a plane using three points
- 6.4 Distance from a point to a plane
**7 Systems of Linear Equations**- 7.1 Consistent and inconsistent systems
- 7.2 Parametric solutions
- 7.3 Augmented matrix of a system
- 7.4 Gaussian elimination
- 7.5 Reduced row echelon form
**8 Matrix Operations**- 8.1 Addition, subtraction and scalar multiplication
- 8.2 Matrix multiplication
- 8.3 Connections with systems of equations
**9 Matrix Inverses**- 9.1 Identity matrices and inverses
- 9.2 Inverses of two-by-two matrices
- 9.3 Powers of a matrix
- 9.4 Using row reduction to find the inverse
- 9.5 Using inverses to solve systems of equations
- 9.6 Elementary matrices
**10 Determinants**- 10.1 Determinant of a 3 × 3 matrix
- 10.2 Cross products revisited
- 10.3 Properties of determinants
- 10.4 Orientation of a triangle
**11 Eigenvalues and Eigenvectors**- 11.1 Existence of eigenvalues
- 11.2 Finding eigenvalues
- 11.3 Reflections and rotations in the plane
**12 Diagonalising a Matrix**- 12.1 An example which cannot be diagonalised
- 12.2 An example of a Markov process
- 12.3 The Jordan form of a matrix
- Hints and Solutions
- Appendix 1 The Theorem of Pythagoras
- Appendix 2 Mathematical Implication
- Appendix 3 Complex Numbers

3/2/2021 7:18:39 PM