Abstract

This subject builds on matrix algebra covered in previous studies and includes the topics vector spaces, subspaces, linear transformations, eigenvalues and eigenvectors, inner products and orthonormal bases. Applications of linear algebra are also considered.

Syllabus

Review of vectors in R2 and R3, matrices, determinants, solution of systems of linear equations.Vector spaces, subspaces, bases and dimension.Inner products and orthonormal bases.Linear transformations, matrix representation of a linear transformation.Eigenvalues and eigenvectors.Selected applications of linear algebra.

Learning outcomes

Upon successful completion of this subject, students should:
1.
be able to explain mathematical concepts of linear algebra such as: vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors;
2.
be able to apply the processes of linear algebra to solve particular problems including: solving systems of linear equations, inverting a matrix, finding eigenvalues and eigenvectors;
3.
be able to illustrate the use of linear algebra in relation to a number of real world applications.

Enrolment restrictions

Available to undergraduate students only.
Not available to students who have completed MTH419 Linear Algebra or equivalent.