MAT-2450 Linear Algebra

Credits: 4
In this course, students examine the fundamental principles of linear algebra in depth. They learn multiple methods for solving systems of linear equations, including Gaussian and Gauss-Jordan elimination, matrix inverses, and LU-factorization. Students perform matrix operations, evaluate determinants and their properties, and construct matrix factorizations. They explore the structure of vector spaces and subspaces, determining bases, dimensions, and ranks. Students also analyze linear transformations by finding their kernels, ranges, and matrix representations. They study eigenvalues, eigenvectors, diagonalization, and orthogonality to deepen their understanding of linear systems and transformations. Finally, students investigate inner product spaces, learning to create orthonormal bases and apply inner product properties to solve least squares problems.

Prerequisite(s): MAT-2410 with a grade of C or higher

Course Outcomes

Solve systems of linear equations using Gaussian elimination, Gauss-Jordan elimination, inverse matrices, and LU-factorization.
Perform operations with matrices including finding the inverse and elementary matrix factorization.
Analyze properties and values of determinants.
Determine bases and dimensions of vector spaces and subspaces.
Determine ranks of vector spaces, subspaces, matrices, and systems of linear equations.
Create orthonormal bases in inner product space.
Apply properties of inner product space to least squares problems.
Find the kernel and range and matrix for a linear transformation.
Find eigenvalues and eigenvectors of a linear transformation and explore diagonalization and orthogonality.