## Lectures

Monday, Wednesday and Fridays 9:00AM-9:50AM CB 349.## Literature

*Linear Algebra and its applications.*David C. Lay. Fourth edition.

## Course Contents

The solution of simultaneous linear equations. Matrix algebra. Determinants. Vector spaces. Eigenvalues and Eigenvectors. Inner product spaces and least squares approximation. Most of chapters 1 to 6 from Lay's book.## Examination and Grading

### Tests (50%)

There will be 2 tests. These will be announced at least one week in advance.### Final (30%)

There will be a comprehensive final to be worth 30% on Wednesday 12/17/2014 8:00-10:00 A.M..### Homework and Quizzes (20%)

There will be**both online homework and written homework**to be handed in every week.

The online homework will be assigned and completed in Webwork (http://courses1.webwork.maa.org/webwork2/uky-ma322/). Your username is your LinkBlue ID (use only capital letters), and your password is your student ID number (8 digits).

The written homework will be posted after every class in http://dleon.combinatoria.co/pages/courses/homeworkma322001-201402.html.

The homework posted during each week will be due at the beginning of the class of Friday of the following week. Your written homework should:

**Be clean and organized**. Homework that cannot be understood to be graded will be awarded 0 points.**Be your own work**. A reasonable amount of collaboration is expected but the written solutions should be your own and use your own words.**Show all your work**. There will be no credit for correct answers if you do not show the steps you took to arrive to a solution. Partial credit will be awarded for your work even in the case you arrive to an incorrect answer.

There may also be some additional homework problems without any due date but that you should complete in order to train the concepts given in class. Some of these problems could appear in the quizzes, tests and the final. These problems will be assigned after some of the classes and also posted in the web page of the course.

There will be

**(unannounced) quizzes on some Wednesdays.**

Homework and quizzes are equally weighted for the remaining 20% of the grade.

### Grading Scale

Percentage | Grade |
---|---|

>=90% | A |

>=80% | B |

>=70% | C |

>=60% | D |

<60% | E |

## Syllabus

This is an approximate schedule of the course containing the syllabus:Date | Topic |
---|---|

Wed 8/27 | Introduction. 1.1 Systems of Linear Equations |

Fri 8/29 | 1.2 Row Reduction and Echelon Forms |

Wed 9/3 | 1.3 Vector Equations |

Fri 9/5 | 1.4 The Matrix Equation Ax = b |

Mon 9/8 | 1.5 Solution Sets of Linear Systems |

Wed 9/10 | 1.7 Linear Independence |

Fri 9/12 | 1.8 Introduction to Linear Transformations |

Mon 9/15 | 1.9 The Matrix of a Linear Transformation |

Wed 9/17 | 2.1 Matrix Operations |

Fri 9/19 | 2.2 The Inverse of a Matrix |

Mon 9/22 | 2.3 Characterizations of Invertible Matrices |

Wed 9/24 | 2.5 Matrix Factorizations |

Fri 9/26 | 3.1 Introduction to Determinants |

Mon 9/29 | Review Test 1 |

Wed 10/1 | TEST 1 |

Fri 10/3 | 3.2 Properties of Determinants |

Mon 10/6 | 3.3 Cramer’s Rule, Volume, and Linear Transformations |

Wed 10/8 | 4.1 Vector Spaces and Subspaces |

Fri 10/10 | 4.1 Vector Spaces and Subspaces |

Mon 10/13 | 4.2 Null Spaces, Column Spaces, and Linear Transformations |

Wed 10/15 | 4.2 Null Spaces, Column Spaces, and Linear Transformations |

Fri 10/17 | 4.3 Linearly Independent Sets; Bases |

Mon 10/20 | 4.4 Coordinate Systems |

Wed 10/22 | 4.5 The Dimension of a Vector Space |

Fri 10/24 | 4.6 Rank |

Mon 10/27 | 4.7 Change of Basis |

Wed 10/29 | 4.9 Applications to Markov Chains |

Fri 10/31 | 5.1 Eigenvectors and Eigenvalues |

Mon 11/3 | 5.2 The Characteristic Equation |

Wed 11/5 | 5.3 Diagonalization |

Fri 11/7 | 5.4 Eigenvectors and Linear Transformations |

Mon 11/10 | Review Test 2 |

Wed 11/12 | TEST 2 |

Fri 11/14 | 5.5 Complex Eigenvalues |

Mon 11/17 | 10.2 The Steady-State Vector and Google's PageRank |

Wed 11/19 | More applications of Eigenvalues and Eigenvectors |

Fri 11/21 | 6.1 Inner Product, Length, and Orthogonality |

Mon 11/24 | 6.1 Inner Product, Length, and Orthogonality |

Mon 12/1 | 6.2 Orthogonal Sets |

Wed 12/3 | 6.3 Orthogonal Projections |

Fri 12/5 | 6.4 The Gram—Schmidt Process |

Mon 12/8 | 6.5 Least-Squares Problems |

Wed 12/10 | 6.8 Applications of Inner Product Spaces |

Fri 12/12 | Review Final |

Wed 12/17 | FINAL EXAM 8:00-10:00 A.M. |