This course provides a survey of the concepts related to linear algebra. Students examine the geometry of vectors, matrices, and linear equations, including Gauss-Jordan elimination. Students explore the concepts of linear independence, rank, and linear transformations. Vector spaces, bases, and change of bases are discussed, including orthogonality and the Gram–Schmidt process. In addition, students investigate determinants, eigenvalues, and eigenvectors.
This undergraduate course is 5 weeks.
This course has a prerequisite. Please see details in the Prerequisite section below.
Attendance and participation are mandatory in all university courses, and specific requirements may differ by course. If attendance requirements are not met, a student may be removed from the course. Please review the Course Attendance Policy, Tuition Refund Policy and all University Policies in the Catalog for more information.
Topics and Objectives
Linear Equations and Matrix Algebra
- Solve systems of linear equations with m equations and n unknowns.
- Solve linear equations using Gauss-Jordan elimination.
- Perform matrix operations.
- Determine the invertibility of a matrix.
Determinants and Euclidean Vector Spaces
- Calculate determinants.
- Calculate the dot, or inner, product of two vectors.
- Decompose a vector space into its subspace and orthogonal complement.
- Simplify vectors into linear combinations using vector algebra.
- Determine the kernel and range of the matrix representation of a subspace of Rn.
- Determine a spanning set for independent vectors.
- Transform vectors in two- and three-dimensional spaces using matrices.
- Use linear transformations to transform a vector from Rn to Rm.
Eigenvalues, Eigenvectors, and the Gram-Schmidt Process
- Evaluate eigenvalues and eigenvectors using the characteristic polynomial.
- Perform QR-Decomposition.
Linear Transformation and Applications
- Determine the kernel and range of the matrix representation of a subspace of R,n.
- Apply concepts of linear algebra to examples such as chemistry, electric circuits, and economics (Leontief’s closed model).
A prerequisite is required for this course. The purpose of a prerequisite is to ensure students have the knowledge and/or skills needed to be successful in the course. Students are required to provide proof of prerequisite during the enrollment/registration process. To meet to a course prerequisite requirement, a student must have successfully completed the prerequisite course at University of Phoenix, provide proof via transcript of completing a comparable course (at least 75% match) or higher level course with at least a grade of C at another institution or have a University of Phoenix approved Student Appeal on file with the University.
This course requires the prerequisite below. Click on the prerequisite course to review the course topics and objectives.
- MTH/290 – Calculus II OR
- equivalent or higher college mathematics course
During the checkout process you will be prompted to provide proof of the requirement(s). If you completed the prerequisite at another institution be prepared to upload an official/unofficial transcript. If you have questions about meeting the prerequisite requirements for this course please contact an enrollment representative at 888-484-1815.
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While widely available, not all programs are available in all locations or in both online and on-campus formats. More information about eligibility requirements, policies, and procedures can be found in the catalog.
Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.