### Matrix and Linear Algebra – MATH 410

CG • Section 8WK • 07/01/2018 to 12/31/2199 • Modified 07/27/2021

### Course Description

Develop an understanding of vector spaces, systems of linear equations, matrix algebra and linear transformations.

For information regarding prerequisites for this course, please refer to the Academic Course Catalog.

### Rationale

This course is an introduction to finite dimensional linear algebra. After successful completion of this course the student should be able to calculate and explain all the major theorems and results of standard undergraduate linear algebra.

The topics covered include matrices, linear transformations, change of basis, eigenvalues, canonical forms, quadratic forms and applications. This should prepare both teachers and students for further study or instruction in linear algebra.

### Measurable Learning Outcomes

Upon successful completion of this course, the student will be able to:

1. Calculate row reductions and explain how the Gauss-Jordan algorithm is used to solve linear systems,
2. Calculate and explain basic matrix algebra including multiplication and determinants,
3. Calculate and explain linear independence of subsets in a vector spaces,
4. Calculate and explain spanning sets in linear algebra,
5. Explain when a transformation is linear and how to find its matrix with respect to a basis,
6. Calculate and explain coordinate systems and change for vectors and linear transformations,
7. Calculate and explain lengths and angles in a vector space given a norm or inner product,
8. Calculate and explain orthogonal projections and the application to least squares,
9. Compute eigenvalues and eigenvectors and appropriate canonical forms,
10. Communicate with the language of linear algebra and apply theorems of linear algebra to solve real world applications.

### Course Assignment

Course Requirement Checklist

After reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in Module/Week 1.

Homework Assignments (15)

The student will complete assignments within WebAssign. The student will be allowed 6 attempts to answer each question. A score of 70% must be obtained to go on to the next assignment, quiz, or test for that week.

WebAssign Quizzes (4)

Each quiz will cover the Reading & Study material for the assigned modules/weeks. Each quiz will be open notes/open book and be completed in WebAssign. The student will have 2 attempts at each quiz.

WebAssign Tests (3)

The student will complete tests during Modules/Weeks 2, 4, and 6. Each test will be 2 hours, open notes/open book, and will cover 2 modules/weeks of material. The tests will be taken in WebAssign. Written work for the tests must be submitted in Blackboard immediately after completing the test in WebAssign and before the due date/time. Tests submitted without accompanying written work will not be accepted. There is only one attempt for tests.

Final Exam

The cumulative Final Exam will be completed using WebAssign software. The exam will be 2 hours and 30 minutes, open notes/open book, and must be completed in a single sitting. Written work for the final exam must be submitted in Blackboard immediately after completing the test in WebAssign. There is only one attempt for the final exam.