# Linear Algebra with Applications

Time | Section | Suggested Problems |

1 | 1.1 Matrices and systems of linear equations | 5,6, 7, 10, 11, 12, 13 |

1 | 1.2 Gauss- Jordan elimination | 2,3,6, 7, 10, 13 |

1 | 2.1 Operations on matrices | 5, 10, 13, 14, 15, 16, 19,20 |

0.5 | 2.2 Properties of matrix operations | 1,5, 7, 8, 9, 10, 19,20,23,24,28 |

0.5 | 2.3 Symmetric matrices | 1,2,5, 10, 11, 12, 13 |

1 | 2.4 Inverse of a matrix | 2,4, 7, 9, 11, 14, 15, 18, 19,22,24,25,26 |

1 | 3.1 Introduction to determinants | 4,7,8,10,11,13,14,15 |

1 | 3.2 Properties of determinant | 2,3,5, 7, 9, 11, 15, 16, 19 |

0.5 | 3.3 Numerical evaluation of determinants | 4,6, 11, 12, 14 |

1 | 3.4 Determinants, matrix inverses, and systems of linear equations |
4,7,10,14,15,17,19,20,21,22,26 |

0.5 | 4.1 The vector space R^{n} |
3,4, 7, 10, 12 |

1 | 4.2 Dot product , norm, angle, and distance | 2,4,6,10,13,14,16,19,20,22,30,32 |

1 | 4.4 Subspaces of R^{n} |
2,4,5,8,10,11,12 |

1 | 4.5 Linear combinations of vectors | 3,5, 7,8,9, 11, 18 |

1 | 4.6 Linear dependence and independence | 2,4,5,7,8,9 |

1 | 4.7 Basis and dimension | 3,4,5,6, 7, 8, 11, 13, 14, 15, 16 |

1 | 4.8 Rank of a matrix | 2,5,6, 7,8,9, 11, 12, 14, 15 |

1.5 | 4.9 Orthonormal vectors and projections in R^{n} |
2,3,4,6, 7, 8, 9, 10, 14, 16, 17, 18 |

0.5 | 6.4 Solutions of homogeneous and and non-homogeneous systems | 1,3,5,6, 10, 11 + supplementary problems from handout |

TOTAL: 17 periods of lectures + 3 periods for tests and review; 1 period=75-minute lecture.

* Omit projection onto a subspace.

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