## Purchase Solved MATH 510-Applied Linear Algebra

### Course Description

This course focuses on developing an understanding of vector spaces and their transformations as revealed by the theory of linear algebra and matrices through both examples and proofs.

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

### Rationale

This course is an introduction to finite-dimensional linear algebra at the graduate level. After the 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:

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

### Course Assignment

After reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in the Course Overview.

**Student Introduction Video Assignment**

The purpose of this video is to introduce the student and prepare the student for future video presentations.

**Video Demonstration Assignments (4)**

The student will create 4 video demonstrations based on the provided prompts. Videos must be precise, well-practiced, and a maximum of 8 minutes.

**Homework (6)**

Homework problems are essential to this course and students will be assigned homework problems to complete throughout the course. One homework problem out of the assigned problems will be submitted for grading in Modules 1-3 and 5-7.

**Homework Portfolios (2)**

Homework will be assigned weekly. Homework assignments in Modules 1–4 will be scanned into a single document and submitted as Homework Portfolio Midterm before the Midterm Exam. Homework assignments in Modules 5–8 will be scanned into a single document and submitted as Homework Portfolio Final before the Final Exam. Many exam problems will come from the assigned homework.

**Quizzes (6)**

Each quiz will be timed, handwritten, and open-book/open-notes/open-video and will cover the Learn material from the videos in the assigned modules. The time limit for each quiz is 30 minutes. The quizzes are some combination of T/F, multiple choice, and/or fill-in-the-blank questions.

**Exams (2)**

Each exam will be timed, handwritten, and open-book/open-notes/open-video and will cover the Learn material for the assigned modules. The time limit for the Midterm Exam is 90 minutes (1 hour, 30 minutes) while the time limit for the Final Exam is 120 minutes (2 hours). On all written work, the student is expected to write correct mathematics to avoid point deductions.

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