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First Course in Linear Algebra with DVD, A, Pearson Original Edition

First Course in Linear Algebra with DVD, A, Pearson Original Edition


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About the Book

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.

The text comes with a DVD. This innovative learning tool contains over 30 presentations or ‘nuggets' which demonstrate critical algebraic concepts in a visual and engaging way. Through examples students are able to place Linear Algebra in the context of their own lives and can see and practice how to solve the related problems. The nuggets are integrated throughout the text so that as students work through the material they can then view the DVD to ensure they understand the concepts discussed.



Table of Contents:
  • 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


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Product Details
  • ISBN-13: 9781442548367
  • Publisher: Pearson Education Australia
  • Publisher Imprint: Pearson Custom Publishing
  • Height: 246 mm
  • No of Pages: 367
  • Weight: 716 gr
  • ISBN-10: 1442548363
  • Publisher Date: 16 Dec 2010
  • Binding: SF
  • Language: English
  • Spine Width: 21 mm
  • Width: 191 mm

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First Course in Linear Algebra with DVD, A, Pearson Original Edition
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