Notes |
Topics |

8/30/16 |
Row Reduction and
Echelon Forms, Pivot Positions, Uniqueness of Reduced
Echelon Form |

9/1/16 |
Existence and Uniqueness
of Solutions, Vectors in n-dimensional space, Linear
Combinations |

9/6/16 |
Linear Combinations
(continued), The Span of a Set of Vectors, The Matrix
Equation Ax=b |

9/8/16 |
Existence of Solutions
of Ax=b, Solution Sets of Linear
Systems, Homogeneous and Nonhomogeneous Systems |

9/13/16 |
Solution Sets in
Parametric Vector Form, Linear Independence |

9/15/16 |
Span and Linear
Independence, Linear Transformations, Dilation and
Contraction Operators, Rotation Operators |

9/20/16 |
Linear Transformations
(continued), One-to-one and Onto Mappings |

9/22/16 |
One-to-one and Onto
Mappings (continued), Matrix Operations |

9/27/16 |
Review for Exam 1 |

9/29/16 |
Powers of a Matrix,
Shear Transformations, The Inverse of a Matrix |

10/4/16 |
Elementary Matrices, The
Invertible Matrix Theorem, Invertible Linear
Transformations |

10/6/16 |
Invertible Linear
Transformations (continued), Subspaces of
n-dimensional real vector space |

10/11/16 |
Recap of Linear
Transformations, Subspaces of n-dimensional real
vector space (continued) |

10/13/16 |
The Column Space and
Null Space of a Matrix, Basis for a Subspace |

10/18/16 |
Basis for the Column
Space of a Matrix, Basis for the Null Space of a
Matrix, Dimension and Rank |

10/20/16 |
The Rank Theorem, The
Basis Theorem, The Invertible Matrix Theorem (more
results) |

10/25/16 |
Determinants |

10/27/16 |
Properties of
Determinants |

11/1/16 |
Review for Exam 2 |

11/8/16 |
Eigenvectors and
Eigenvalues |

11/10/16 |
The Characteristic
Equation |

11/15/16 |
The Invertible Matrix
Theorem (more results), Similarity of Matrices |

11/17/16 |
Inner Product, Length,
and Orthogonality, Orthogonal Subspaces |

11/29/16 |
Orthogonal Sets,
Orthogonal Basis, Orthogonal Projections |

12/1/16 |
Orthogonal Projections
(continued), The Gram-Schmidt Process |

12/8/16 |
Review for the Final
Exam |