Linear Algebra –

mth360

(3 credits)

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-level course is 5 weeks. To enroll, speak with an Enrollment Advisor.

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 matricial calculations.
- Determine the invertibility of a matrix.
Vectors and Linear Transformations
- Simplify vectors into linear combinations using vector algebra.
- Solve applications of linear systems.
- 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 R^m.
Vector Spaces
- Determine the kernel and range of the matrix representation of a subspace of Rⁿ.
- Determine the basis and dimension of a subspace of Rⁿ.
- Extrapolate abstract vector spaces from specific vector spaces.
Determinants, Orthogonality, Eigenvalues, and Eigenvectors
- Calculate determinants.
- Calculate the dot, or inner, product of two vectors.
- Decompose a vector space into its subspace and orthogonal complement.
- Evaluate eigenvalues and eigenvectors using the characteristic polynomial.
Algebra Review
- Examine applications of linear algebra using Leontief’s closed model.
- Review linear algebra topics.

The University of Phoenix reserves the right to modify courses.
While widely available, not all programs are available in all locations or in both online and on-campus formats. Please check with a University Enrollment Advisor.
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.

Linear Algebra –

mth360

Linear Equations and Matrix Algebra

Vectors and Linear Transformations

Vector Spaces

Determinants, Orthogonality, Eigenvalues, and Eigenvectors

Algebra Review

We're here to help

Learn more today