## A First Course in Linear Algebra: With Concurrent ExamplesThis is a short, readable introduction to basic linear algebra, as usually encountered in a first course. The development of the subject is integrated with a large number of worked examples that illustrate the ideas and methods. The format of the book, with text and relevant examples on facing pages means that the reader can follow the text uninterrupted. The student should be able to work through the book and learn from it sequentially. Stress is placed on applications of the methods rather than on developing a logical system of theorems. Numerous exercises are provided. |

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### Contents

Solutions to simultaneous equations 1 | 15 |

Matrices and algebraic vectors | 23 |

Special matrices | 33 |

Matrix inverses | 45 |

Linear independence and rank | 55 |

Determinants | 65 |

Solutions to simultaneous equations 2 | 77 |

Vectors in geometry | 87 |

Straight lines and planes | 105 |

Cross product | 123 |

Answers to exercises | 134 |

Sample test papers | 140 |

146 | |

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3-vectors a p x q matrix angle array augmented matrix Calculate Chapter coefficient cofactor column vector coordinate axes coplanar cross product denote diagonal matrix direction dot product elementary matrices elementary row operations entries equal equation Ax equations are inconsistent Evaluate the product Exercises finding the inverse form a linearly geometrical given in Example given vectors Hence identity matrix illustrates infinitely many solutions invertible matrix last row line of intersection list of vectors main diagonal matrix is invertible non-zero rows non-zero vectors normal vector obtain orthogonal orthogonal matrix parallelepiped parallelogram position vector procedure process applied process leads proof pxq matrix rank ratio Rule second equation second row set of equations set of simultaneous Show simultaneous equations singular solve square matrix standard GE process straight line third equation three dimensions three planes three unknowns three vectors Triangle Law unique solution unit vector