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.
topic title goes here
Determinants, Orthogonality, Eigenvalues, and Eigenvectors
- Decompose a vector space into its subspace and orthogonal complement.
- Evaluate eigenvalues and eigenvectors using the characteristic polynomial.
- Calculate determinants.
- Calculate the dot, or inner, product of two vectors.
- Examine applications of linear algebra using Leontief’s closed model.
- Review linear algebra topics.
Vectors and Linear Transformations
- Transform vectors in two- and three-dimensional spaces using matrices.
- Use linear transformations to transform a vector from Rn to Rm .
- Simplify vectors into linear combinations using vector algebra.
- Solve applications of linear systems.
- Determine a spanning set for independent vectors.
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.
- 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.
Please ask about these special rates:
Teacher Rate: For some courses, special tuition rates are available for current, certified P-12 teachers and administrators. Please speak with an Enrollment Representative today for more details.
Military Rate: For some courses, special tuition rates are available for active duty military members and their spouses. Please speak with an Enrollment Representative today for more details.
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 Representative.
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.