# Linear Algebra

Course Number: |
ENGRG 5030 |

Course Name: |
Linear Algebra (Online) |

Course Description: |
This course is an online introductory course in linear algebra. This foundation course is designed to prepare a student for study in the Master of Science in Engineering program. Matrices, systems of equations, determinants, eigenvalues, eigenvectors, vector spaces, linear transformations, and diagnolization. This course is not appropriate for students seeking a MS or MA degree in mathematics. |

Prerequisites: |
MATH 2740 with a grade of "C" or better |

Level: |
Graduate |

Credits: |
3 |

Format: |
Online |

Program: |
Master of Science in Engineering |

NOTE: The information below is representative of the course and is subject to change. The specific details of the course will be available in the Desire2Learn course instance for the course in which a student registers.

## Additional Information

**Learning Outcomes**

Upon completion of this course, you should be able to

- Develop an understanding of the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.
- Develop your ability to handle some abstract mathematics.

In regard to the second objective, this course may be unlike any mathematics course you have had before. This course will require you not only to solve problems (as you have done in previous math classes) but also to know definitions and theorems and to be able to justify mathematical conclusions with proof. The required answer may be not a number but rather an explanation. In this sense, you may be taking your first real math class.

**Unit Descriptions**

**Unit 1**

Section 1.1: Systems of Linear Equations

Section 1.2: Row Reduction and Echelon Forms

Section 1.3: Vector Equations

Section 1.4: The Matrix Equation

Section 1.5: Solutions Sets of Linear Systems

Section 1.6: Applications of Linear Systems

Section 1.8: Introduction to Linear Transformations

Section 1.9: The Matrix of a Linear Transformation

Section 2.1: Matrix Operations

Section 2.2: The Inverse of a Matrix

Section 2.3: Characterizations of Invertible Matrices

Section 2.7: Applications to Computer Graphics

Section 3.1: Introduction to Determinants**Unit 2**

Section 4.1: Vector Spaces and Subspaces

Section 4.2: Null Space, Column Spaces and Linear Transformations

Section 4.3: Linearly Independent Sets; Bases

Section 4.4: Coordinate Systems

Section 4.5: Dimension of a Vector Space

Section 4.6: Rank

Section 4.9: Markov Chains

Section 5.1: Eigenvectors and Eigenvalues

Section 5.2: The Characteristic Equation

Section 5.3: Diagonalization**Unit 3**

Section 5.4: Eigenvectors and Linear Transformations

Section 5.5: Complex Eigenvalues

Section 6.1: Inner Product, Length, and Orthogonality

Section 6.2: Orthogonal Sets

Section 6.1: Inner Product, Length, and Orthogonality

Section 6.2: Orthogonal Sets

Section 6.3: Orthogonal Projections

Section 6.4: The Gram-Schmidt Process

Section 6.5: Least-Squares Problems

Section 7.1: Diagonalization and Symmetric Matrices

Section 7.2: Quadratic Forms

Section 7.3: Constrained Optimization

**Reading Assignments**

The course is broken into three units. For each unit covered in this class, you will first read the unit materials carefully.**Self-Study Assignments**

After you've read the unit materials, you are asked to look at and work the practice problems at the end of each assigned section in the text. The full solutions to these practice problems can be found immediately after the exercises.

You are then asked to work a number of exercises at the end of each section of the text. After completing these exercises, you should have a good working knowledge of the terms listed in Important Topics/Ideas.

These are the kind of problems that you will be asked and required to work on the exams and the quizzes. Remember, practice makes perfect!**Quizzes and Exams**

There is a total of eight short quizzes (one quiz after [about] every third section of material covered). Each quiz is worth 15 points.

A 120-point exam follows each of the three units. The final exam is worth 200 points and is comprehensive.

A | 90% - 100% |

B | 80% - 89% |

C | 70% - 79% |

D | 60% - 69% |

F | 0% - 59% |