**Math 520:
Linear Algebra (Spring 2018)**

**Section S03
**

Instructor:
Shamil Asgarli |
Lecture
Time: MWF 12:00 - 12:50 pm |

Email:
shamil_asgarli@brown.edu |
Lecture
Location: Barus & Holley 161 |

My
office: Kassar House, Room 020 |
Office
hours: Wednesdays 3-5 pm |

Click here for the syllabus.

Exam Information:

Midterm 1

Click here to read about the (optional) Final Project.

Quizzes.

Quiz 1 |
Solution | Quiz 6 | Solution |

Quiz 2 | Solution | Quiz 7 | Solution |

Quiz 3 | Solution | Quiz 8 | Solution |

Quiz 4 | Solution | Quiz 9 | Solution |

Quiz 5 |
Solution | Quiz 10 | Solution |

Notes on some topics.
Sometimes I will type notes to expand upon particular concepts from class.
They can be found below:

Note 1. Dimension of a Subspace.

Note 2. Discovering the 3 x 3
Determinant.

Note 3. Determinant of the Transpose.

Class Notes. The notes below are kindly provided by Kanika Gupta, one of the students in the class. The notes will be posted once a week (usually on the weekend).

Notes | Date | Topic | Notes | Date | Topic |

Lecture 1 | Jan 24 | System of linear equations |
Lecture 21 | Mar 14 |
Properties of Determinants |

Lecture 2 | Jan 26 | System of linear equations |
Lecture 22 |
Mar 16 |
Cramer's Rule |

Lecture 3 | Jan 29 | Row reduction / echelon form |
Lecture 23 |
Mar 19 |
Introduction to Vector Spaces |

Lecture 4 | Jan 31 | Vector equations |
Lecture 24 |
Mar 21 |
Subspaces of Vector Spaces |

Lecture 5 | Feb 2 | Matrix equations |
Lecture 25 |
Mar 23 |
Kernel & Range; Linear Independence |

Lecture 6 | Feb 5 | Solution sets of Linear Systems |
Lecture 26 |
Apr 2 |
Linear Independence, and Spanning |

Lecture 7 | Feb 7 | Applications to Chemistry & Econ. |
Lecture 27 |
Apr 4 |
Isomorphism of vector spaces |

Lecture 8 | Feb 9 | Linear independence |
Lecture 28 |
Apr 6 |
Coordinates relative to a basis; Dimension |

Lecture 9 | Feb 12 | Linear independence + Transformations |
Lecture 29 |
Apr 9 |
Basis Theorem + Change of Basis |

Lecture 10 | Feb 14 | Linear transformations (continued) | Lecture 30 | Apr 11 |
Review session for Midterm 2 |

Lecture 11 | Feb 16 | Matrix of a linear transformation |
Lecture 31 |
Apr 13 |
Change of Basis (cont.) + Row Space |

Lecture 12 | Feb 21 | Surjective and injective transformations |
Lecture 32 |
Apr 16 |
Rank-Nullity for abstract vector spaces |

Lecture 13 | Feb 23 | Matrix operations |
Lecture 33 |
Apr 18 |
Eigenvectors and Eigenvalues |

Lecture 14 | Feb 26 | Invertible Matrices |
Lecture 34 |
Apr 20 |
Char. Polynomial; linear independence result |

Lecture 15 | Feb 28 | Invertible Matrices (continued) |
Lecture 35 |
Apr 23 |
Similarity; Diagonalization |

Lecture 16 | Mar 2 | Invertible Matrix Theorem |
Lecture 36 |
Apr 25 |
Diagonalization; Matrix of a transformation |

Lecture 17 | Mar 5 | Subspaces of R^n |
Lecture 37 |
Apr 27 |
Matrix of a linear transformation (cont.) |

Lecture 18 | Mar 7 | Column space and null space |
Lecture 38 |
Apr 30 |
Inner Products |

Lecture 19 | Mar 9 | Dimension of a subspace, and rank |
Lecture 39 |
May 2 |
Orthogonal Complements |

Lecture 20 | Mar 12 | Introduction to Determinants |
Lecture 40 |
May 4 |
Orthogonal Lists and Orthogonal Projection |