 First Course In Linear Algebra, A (3e) : 9781442548367

# First Course In Linear Algebra, A (3e)

Easdown, David

Edition

3
ISBN

9781442548367
ISBN 10

1442548363
Published

16/12/2010

Pearson Custom Books
Pages

353
Format

Available on demand Book + Disk
\$99.99

#### Related digital items

\$60.00

##### Description
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