Mathematics 227 |
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Study Guide (ISBN 0-201-64847-4)

Instructor: Alan Stein <stein@math.uconn.edu>

Section | Topic | Exercises |
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1.1 | Systems of Linear Equations | 5, 6, 9, 10, 19-22, 29, 30 |

1.2 | Row Reduction and Echelon Forms | 1, 2, 5, 6, 13, 14, 21-24 |

1.3 | Vector Equations | 7-12, 21, 22, 31, 32 |

1.4 | Matrix Equations | 3, 4, 7, 8, 19, 20, 23, 24, 29, 30 |

1.5 | Solution Sets of Linear Systems | 1, 2, 7, 8, 13, 14, 21, 22, 25, 26 |

1.6 | Linear Independence | 2, 10, 14, 18, 27, 28 |

1.7 | Linear Transformations | 2, 6, 12, 14, 22 - 24 |

1.8 | Matrix of a Linear Transformation | 4, 12, 14, 22 - 24 |

2.1 | Matrix Operations | 2, 6, 10, 15, 16, 24 |

2.2 | Inverse of a Matrix | 4, 6, 9, 10, 12, 14, 18, 32, 34 |

2.3 | Invertible Matrices | 2, 4, 6, 8, 10, 13, 14 |

2.4 | Partitioned Matrices | 1-7, 8, 10 |

2.5 | Matrix Factorizations | 1, 5, 7, 9, 13 |

3.1 | Determinants | 4, 8, 10, 14, 38 |

3.2 | Properties of Determinants | 12, 14, 16, 18, 20, 22, 26, 27, 28 |

3.3 | Cramer's Rule | 1, 3, 5, 7, 11, 13, 19, 21, 23, 27, 29, 30, 31 |

4.1 | Vector Spaces and Subspaces | 1-11 odd, 16, 18, 22, 28 |

4.2 | Null Spaces, Column Spaces and Linear Transformations | 4, 6, 9-17 odd, 22, 24, 34 |

4.3 | Linearly Independent Sets; Bases | 1-15 odd, 21, 22, 24, 30 |

4.4 | Coordinate Systems | 3-9 odd, 14-16, 20, 28 |

4.5 | Dimension of a Vector Space | 5-13 odd, 22, 29, 30 |

4.6 | Rank | 1-21 odd |

4.7 | Change of Basis | 1-5, 7, 19 |

5.1 | Eigenvectors and Eigenvalues | 9-15 odd, 26, 32 |

5.2 | Characteristic Equation | 2, 6, 10, 14, 16, 18 |

5.3 | Diagonalization | 1-13 odd, 20, 24, 26 |

5.4 | Eigenvectors and Linear Transformations | 1-15 odd |

6.1 | Inner Product, Length and Orthogonality | 1-9 odd, 11, 17, 23 |

6.2 | Orthogonal Sets | 1, 3, 5, 9, 13, 17, 19 |

6.3 | Orthogonal Projections | 1, 3, 5, 7 |

Final Examination | Friday, December 14, 2:00 p.m.-4:00 p.m. |