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"Degrees & Programs"


Linear Algebra


Total credits


Course length

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Course level: Graduate

The purpose of this course is to provide an introduction to linear algebra, a branch of mathematics dealing with matrices and vector spaces. This course describes the use of linear algebra as a compilation of diverse, but interrelated ideas that provide a way of analyzing and solving problems in many applied fields. Linear algebra has three sides: computational techniques, concepts, and applications. One of the goals of this course is to help you master all facets of the subject and see the interplay among them. The material presented in this course involves theorems, proofs, formulas, and computations of various kinds.


This graduate level course requires proof of completion of a Bachelor's degree. Be prepared to provide documentation during the checkout process.

What you'll learn

Course skills and outcomes

Systems and Linear Equations

  • Solve systems of linear equations.
  • Create spans using vector matrices.
  • Apply linear systems to real-world scenarios.

Linear Transformations, Models, and Matrices

  • Transform linear matrices.
  • Demonstrate matrix operations.
  • Create inverse of matrices.

Matrix Algebra

  • Examine applications of linear algebra in economics using Leontief’s closed model.
  • Apply LU (Lower Upper) factorization to matrices.
  • Describe vector spaces and subspaces.
  • Determine dimension and rank for matrices.

Determinants, Eigenvalues & Eigenvectors, and General Vector Spaces

  • Identify properties of determinants.
  • Apply Cramer’s Rule to solve a linear system.
  • Describe linear transformations using kernel and range.
  • Identify eigenvalues and eigenvectors.

Vectors, Dot Products, and Markov Chains

  • Model linear equations using coordinate vectors.
  • Perform change of basis on a matrix.
  • Apply Markov chains to real-world problems.
  • Calculate orthogonal vectors using dot product.

Review Topics and Objectives from All Weeks

  • Apply the concepts presented in this course.


Why take courses at University of Phoenix

Accreditation that matters

We’ve been accredited by the Higher Learning Commission ( for more than 40 years.

Real-world instructors

Learn from instructors who bring an average of 25 years of working experience to the classroom.

Affordable and potentially reimbursable

Our tuition and fees are competitive and fixed. Also, check to see if your employer will cover you for this course.

Next Steps

Start a conversation about your future with an enrollment representative today.

Start a conversation about your future with an enrollment representative today.

Call (844) 937-8679

Transfer Credits

Credit Transfer

Credit Transfer

Need to transfer credits to another college or university?

Before you enroll in a course, check with your school of choice to make sure they will accept our transfer credits and to understand any requirements or limitations. Then you can complete your course, and request your official transcript be sent to your school. That’s it!

How to request your transcripts